{"schema":1,"note":"Search index of https://qrsntu.org: every page listed in https://qrsntu.org/llms.txt and its sections as plain text, plus the Math Notes courses, publications and events, each with its URL (relative to the site). The NeurIPS 2026 guide has its own index at https://qrsntu.org/service/neurips26/data/site-index.json.","entries":[{"id":"/about/","page":"About","section":"","url":"/about/","kind":"page","text":"About QRS@NTU, which develops and conducts student-led research, and its place in the wider QRS network."},{"id":"/about/#Our Vision","page":"About","section":"Our Vision","url":"/about/","kind":"section","text":"QRS@NTU develops and conducts student-led research in quantitative finance, machine learning, and related technical areas."},{"id":"/about/#QRS and QRS@NTU","page":"About","section":"QRS and QRS@NTU","url":"/about/","kind":"section","text":"QRS is the Society's cross-institutional network. Research is conducted under the broader QRS identity to enable collaboration across universities and institutions. QRS@NTU is its originating campus community at Nanyang Technological University, where student-led research is developed and conducted alongside NTU-based events and local activities."},{"id":"/about/#Core Focus Areas","page":"About","section":"Core Focus Areas","url":"/about/","kind":"section","text":"Quantitative Research Original research and projects spanning quantitative finance, machine learning, and related technical areas. See Projects and Publications. Researcher Development Entry-stage research training through the QRS Research Academy, with a path to QRS Researcher roles. Academic & Industry Activity Talks, workshops, and competitions, listed on the Events page. Open Academic Resources Publish notes, problem sets, and past-year papers for NTU modules on Math Notes. Workshop & Research Community Support Web, publicity, outreach, and organisational support for academic workshops …"},{"id":"/about/#sponsors","page":"About","section":"Sponsors & Partners","url":"/about/#sponsors","kind":"section","text":"The largest interview preparation platform for trading and quant finance worldwide. Purpose-built for every stage of the trading and quant interview, with mental maths drills, probability and reasoning tests, market-making games, cognitive games and coding problems. Many trading firms also use Tradermath to screen their own applicants. tradermath.org"},{"id":"/agents/","page":"Using This Site with AI Assistants","section":"","url":"/agents/","kind":"page","text":"How to use qrsntu.org with AI assistants such as Claude, ChatGPT, Gemini and Codex: a ready prompt, llms.txt, Markdown copies of every page, the site search index and the data files."},{"id":"/agents/#ask","page":"Using This Site with AI Assistants","section":"Ask your assistant","url":"/agents/#ask","kind":"section","text":"Copy this prompt into any assistant that can read web pages, then add your question. It tells the assistant to read this site instead of answering from memory, and to give a link for each fact. Answer my questions about the Quantitative Research Society (QRS) from its website, https://qrsntu.org, not from memory. Read https://qrsntu.org/llms.txt first: it lists every page. To find the right pages, search https://qrsntu.org/data/site-index.json (every page and section as plain text, with its URL). For the full text of a page, add index.md to its address (https://qrsntu.org/about/ becomes …"},{"id":"/agents/#files","page":"Using This Site with AI Assistants","section":"What assistants can read","url":"/agents/#files","kind":"section","text":"Everything below is a plain file on the site. No account, API key or JavaScript is needed. llms.txt: an index of every page, by section, with a one-line description of each. index.md beside every page: the page as Markdown, without the layout. Lists that pages draw with JavaScript, such as people, projects and publications, are written out in full. data/site-index.json: every page and section as plain text with its URL, plus the Math Notes courses, publications and events. The site's search box reads this file. llms-full.txt: all pages in one file. Pages longer than about 8 KB are shortened …"},{"id":"/agents/#assistants","page":"Using This Site with AI Assistants","section":"By assistant","url":"/agents/#assistants","kind":"section","text":"Claude, ChatGPT and Gemini apps: turn on web search or browsing if your plan has it, then paste the prompt above. Assistants without web access cannot read the site and will answer from memory. Claude Code, Codex and other coding agents: ask the agent to fetch https://qrsntu.org/llms.txt, or to download data/site-index.json and search it locally. Your own code: fetch the files above directly. They change only when the site is rebuilt; the sitemap gives the date each page's content last changed."},{"id":"/agents/#neurips26","page":"Using This Site with AI Assistants","section":"NeurIPS 2026 guide: API and MCP","url":"/agents/#neurips26","kind":"section","text":"Our NeurIPS 2026 attendee guide has more for assistants than the rest of the site: a REST API and MCP servers that search the schedule, check clashes and save an itinerary at a permanent link. Setup for Claude, ChatGPT and Gemini is on its AI assistants page, and its own index is service/neurips26/llms.txt. The rest of qrsntu.org has no API or MCP server. It is small enough that the files above answer the same questions."},{"id":"/agents/#limits","page":"Using This Site with AI Assistants","section":"What these files hold","url":"/agents/#limits","kind":"section","text":"They hold only what the public pages show. Research Academy applications and assessments are not on this site and are not in these files; see Privacy. Assistants can make mistakes: the web page is the reference, and corrections are welcome at contact@qrsntu.org. Last updated 12 November 2026."},{"id":"/cdl/","page":"Danlin Chen","section":"","url":"/cdl/","kind":"person","text":"BS, Western University"},{"id":"/cdl/#Projects","page":"Danlin Chen","section":"Projects","url":"/cdl/","kind":"section","text":"AI Native Workflow: Research on hierarchical, verification-gated and recoverable workflows for scaling long-horizon AI-assisted research and agent execution. Status: active. People: Yuhe Sui, Jianing Zhang, Shufang Chen, Danlin Chen, Wang Zimeng, Xiaotong Li."},{"id":"/contact/","page":"Contact","section":"","url":"/contact/","kind":"page","text":"Contact the Quantitative Research Society (QRS) for enquiries and collaboration."},{"id":"/contact/#Get in Touch","page":"Contact","section":"Get in Touch","url":"/contact/","kind":"section","text":"For general inquiries, partnership opportunities, or questions about our activities, please reach out to us. We look forward to hearing from you. contact@qrsntu.org We aim to respond to all inquiries within 2-3 business days."},{"id":"/events/","page":"Events","section":"","url":"/events/","kind":"page","text":"Find QRS and QRS@NTU talks, workshops, competitions, and community events."},{"id":"/events/#Events","page":"Events","section":"Events","url":"/events/","kind":"section","text":"Global Market Making Games 2026 — Singapore Qualifier. 2026-10-16, 19:30 to 21:00 (Asia/Singapore). Singapore (venue to be announced). An individual global market-making competition open to university students across Singapore. QRS role: Singapore partner. Organisers: Amsterdam Investment Club. Partners: Trading Interview, Flow Traders (Super Day partner). IMC Tech Race @ NTU. 2026-09-02, 11:00 to 13:00 (Asia/Singapore). Nanyang Technological University. An on-campus coding race by IMC featuring 20 rapid computer-science problems, a live leaderboard, networking with IMC technologists, and …"},{"id":"/gmmg/","page":"Global Market Making Games 2026 Singapore","section":"","url":"/gmmg/","kind":"page","text":"Compete individually in the Global Market Making Games 2026 Singapore qualifier on 16 October. Open to all university students in Singapore."},{"id":"/gmmg/#register","page":"Global Market Making Games 2026 Singapore","section":"Register","url":"/gmmg/#register","kind":"section","text":"Free, individual entry. No team required. Round 1 · Registration open Singapore Qualifier Everyone competes individually in one Singapore sitting. Your result decides who moves on to the Singapore Final. Date Friday 16 October 2026 Time 19:30–21:00 SGT Venue Singapore · Venue to be announced Entry Free · Individual Please complete both signups to register. Singapore Signup Official Games Signup Eligibility Who can join? Open to university students across Singapore. Students from NTU, NUS, SMU, SUTD, SIT, SUSS and other universities in Singapore are welcome to register. You do not need to be …"},{"id":"/gmmg/#how-it-works","page":"Global Market Making Games 2026 Singapore","section":"From Singapore to the World Final","url":"/gmmg/#how-it-works","kind":"section","text":"Part of the official four-round format: society qualifier, campus final, final qualifier and world final. 01 · Qualifier Singapore Qualifier Everyone competes individually. Results count towards the ranking and decide who reaches the Singapore Final. Date Fri 16 Oct 2026 Time 19:30–21:00 SGT 02 · Campus final Singapore Final Leading qualifiers return for the Singapore Final, which decides the Singapore champion. Date Fri 13 Nov 2026 Time 16:00–19:00 SGT 03 · World final day World Final Society champions meet online. A final qualifier fills the ten seats at the final table, followed by the …"},{"id":"/gmmg/#games","page":"Global Market Making Games 2026 Singapore","section":"What Will You Play?","url":"/gmmg/#games","kind":"section","text":"The Games test the kinds of quantitative reasoning used in market-making and trading interviews: pricing, probability, estimation, mental arithmetic, risk-taking and decision-making under pressure. Make Me a Market Market of Cards Probability Betting Fermi Questions Challenge ETF Trading Challenge Explore all games on the official website"},{"id":"/gmmg/#faq","page":"Global Market Making Games 2026 Singapore","section":"FAQ","url":"/gmmg/#faq","kind":"section","text":"Who can participate? The Singapore competition is open to university students across Singapore. You do not need to be an NTU student or an existing QRS member. Is this a team competition? No. Participants compete individually. You do not need to form a team. Do I need prior trading experience? The official Games materials do not list a prior-experience requirement. The Games focus on pricing, probability, estimation and mental arithmetic, and the official website shows each game in detail. How much does it cost? Entry is free. What will I play? The competition uses the Market Making Games …"},{"id":"/gmmg/#organisers","page":"Global Market Making Games 2026 Singapore","section":"Organisers","url":"/gmmg/#organisers","kind":"section","text":"Hosted by Powered by Super Day partner Singapore partner Quantitative Research Society @ NTU View all events"},{"id":"/","page":"Quantitative Research Society (QRS)","section":"","url":"/","kind":"page","text":"QRS connects students and researchers across institutions to advance research in quantitative finance, machine learning, and related technical fields."},{"id":"/#home-news","page":"Quantitative Research Society (QRS)","section":"Latest News","url":"/#home-news","kind":"section","text":"Research, releases and events from QRS. 11 Nov 2026 · Research FRTBTrace: new project page FRTBTrace, our work on exact trade-level attribution of FRTB-IMA capital, now has its own project page: why one attribution vector cannot answer every question about capital, how one reverse pass through the full formula gives a ledger on (date, trade) positions, and the evidence from a pre-registered synthetic benchmark. Two FRTBTrace workshop papers were accepted at ICAIF 2026. 11 Nov 2026 · Research MathResearchOS: new project page and usage guide A command-line system that turns a mathematical …"},{"id":"/#current-work","page":"Quantitative Research Society (QRS)","section":"Current Work","url":"/#current-work","kind":"section","text":"A selection of active QRS research, projects, and competitions. View all projects"},{"id":"/#home-sponsors-h","page":"Quantitative Research Society (QRS)","section":"Supported by","url":"/#home-sponsors-h","kind":"section","text":"About our sponsors"},{"id":"/jn/","page":"Jianing Zhang","section":"","url":"/jn/","kind":"person","text":"Researcher, Quantitative Research Society"},{"id":"/jn/#About","page":"Jianing Zhang","section":"About","url":"/jn/","kind":"section","text":"Jianing is pursuing a master's in Computational Data Science at Carnegie Mellon University. Previous experience at Alphabet and iFLYTEK includes fraud detection and multilingual AI pipelines. Jianing's interests span applied AI, machine learning engineering, data science, and data engineering, with an emphasis on scalable, trustworthy systems for healthcare and other practical applications. Projects · Publications"},{"id":"/jn/#Projects","page":"Jianing Zhang","section":"Projects","url":"/jn/","kind":"section","text":"AI Native Workflow: Research on hierarchical, verification-gated and recoverable workflows for scaling long-horizon AI-assisted research and agent execution. Status: active. People: Yuhe Sui, Jianing Zhang, Shufang Chen, Danlin Chen, Wang Zimeng, Xiaotong Li. GeoAttention: Research on attention geometry, representation-relative identifiability, and geometry-adaptive prediction. Status: active. People: Yuhe Sui, Jianing Zhang, Xiaotong Li. RiskHedge: Research on spectral-risk decisions, diverse scenarios, and selective robustness evaluation. Status: active. People: Yuhe Sui, Yingzhi Tang …"},{"id":"/jn/#Publications","page":"Jianing Zhang","section":"Publications","url":"/jn/","kind":"section","text":"Geometric Attention Fine-Tuning Is Representation-Relative: Autonomous ML Research with AI-Native Workflow (2026). Yuhe Sui, Jianing Zhang, Shufang Chen, Xiaotong Li, Wang Zimeng. AutoMLR Workshop, NeurIPS 2026. Accepted. OpenReview The Approximation Rank of Softmax Attention: Sharp Geometric Laws and Robust Interaction Dimension (2026). Yuhe Sui, Jianing Zhang. NeurReps Workshop, NeurIPS 2026 (extended abstract). Accepted. OpenReview arXiv"},{"id":"/join_us/","page":"Join QRS","section":"","url":"/join_us/","kind":"page","text":"Apply to the QRS Research Academy (2026 Fall #4) or get involved with the QRS@NTU community."},{"id":"/join_us/#QRS@NTU Community","page":"Join QRS","section":"QRS@NTU Community","url":"/join_us/","kind":"section","text":"Help run NTU-based events, local activities, and the operations and infrastructure of QRS@NTU. Upcoming Events"},{"id":"/join_us/#Quant Foundations — TBC","page":"Join QRS","section":"Quant Foundations — TBC","url":"/join_us/","kind":"section","text":"An introductory programme at QRS@NTU is under development. Details will be announced once confirmed. Status"},{"id":"/join_us/#QRS Research Academy","page":"Join QRS","section":"QRS Research Academy","url":"/join_us/","kind":"section","text":"A selective research programme, from guided research towards leading your own project. 2026 Fall #4 is recruiting for the December 2026 – January 2027 research cycle. Apply to QRS Research Academy Programme detail and outcomes Current Projects To get involved, reach out to us directly: contact@qrsntu.org"},{"id":"/join_us/prerequisites/","page":"Application Prerequisite Guidelines","section":"","url":"/join_us/prerequisites/","kind":"page","text":"Prerequisite guidelines for applying to QRS@NTU: mathematics, probability and statistics, and programming foundations."},{"id":"/join_us/prerequisites/#Mathematics Foundations (Linear Algebra & Analysis) — mandatory","page":"Application Prerequisite Guidelines","section":"Mathematics Foundations (Linear Algebra & Analysis) — mandatory","url":"/join_us/prerequisites/","kind":"section","text":"A solid background in linear algebra and introductory analysis is essential for functional analysis, PDEs, and optimization. Advanced Linear Algebra: Foundations to Frontiers (edX, US\\$99) Mathematics for Engineers Specialization (Coursera, free for NTU students) ✅ NTU equivalents include MH1201 Linear Algebra II and MH3100 Real Analysis I."},{"id":"/join_us/prerequisites/#Probability & Statistics — mandatory","page":"Application Prerequisite Guidelines","section":"Probability & Statistics — mandatory","url":"/join_us/prerequisites/","kind":"section","text":"Applicants must have prior exposure to probability and statistics, which underpin stochastic processes, econometrics, and data-driven modeling. Advanced Statistics for Data Science Specialization (Coursera Plus) Econometrics (Coursera, free for NTU students) Data Analysis with R Specialization (Coursera, free for NTU students) ✅ NTU equivalents include MH2500 Probability and HE2003 Econometrics I."},{"id":"/join_us/prerequisites/#Programming & Algorithms — mandatory","page":"Application Prerequisite Guidelines","section":"Programming & Algorithms — mandatory","url":"/join_us/prerequisites/","kind":"section","text":"Strong programming skills are required for research projects, simulations, and optimization. Applicants should be proficient in Python or R; C++ is optional but recommended for computational finance. Algorithms Specialization (Coursera, free for NTU students) Practice on coding platforms: LeetCode HackerRank ✅ NTU equivalents include MH4701 Mathematical Programming."},{"id":"/join_us/prerequisites/#Recommended Preparation — optional but can accelerate placement","page":"Application Prerequisite Guidelines","section":"Recommended Preparation — optional but can accelerate placement","url":"/join_us/prerequisites/","kind":"section","text":"Applicants completing any of these courses may be allowed to skip Semester 1 and start in Semester 2 or 3. Numerical Methods: Numerical Analysis (Coursera, free for NTU students) Optimization: Convex Optimization (Stanford Online, free) Machine Learning: Machine Learning Specialization (Coursera Plus) Finance & Economics: Financial Markets (Coursera, free for NTU students) Principles of Economics: Macroeconomics (Coursera, free for NTU students) Finance Applications: Akuna Capital Options 101 (free) ✅ NTU equivalents include MH3700 Numerical Analysis I, MH3701 Basic Optimization, MH4514 …"},{"id":"/join_us/prerequisites/#Advanced Preparation — guaranteed accelerated placement / research readiness","page":"Application Prerequisite Guidelines","section":"Advanced Preparation — guaranteed accelerated placement / research readiness","url":"/join_us/prerequisites/","kind":"section","text":"Completion of any of the following programs demonstrates advanced mastery, allowing applicants to enter Semester 2, Semester 3, or participate in research projects immediately. MFE Preparation Master of Financial Engineering Berkeley Haas (US$1,995 per course) Math Foundations for Financial Engineers: 30-hour course covering essential math frameworks for financial modeling. Statistics for Financial Engineers: 30-hour course covering probability, statistics, and modeling techniques. (VEE Approved) Pre-MFE Program Baruch College (US$1,650 per course) Advanced Calculus with Financial Engineering …"},{"id":"/learn/post-training/guide/","page":"Post-Training: The Full Guide","section":"","url":"/learn/post-training/guide/","kind":"page","text":"The full guide to LLM post-training: history from ULMFiT to GPT-3, SFT, Bradley-Terry reward models, policy gradients, GAE, PPO, InstructGPT, DPO, RLVR, GRPO and DeepSeek-R1, with derivations and interactive figures."},{"id":"/learn/post-training/guide/#history-h","page":"Post-Training: The Full Guide","section":"One model per task","url":"/learn/post-training/guide/#history-h","kind":"section","text":"Until the late 2010s, natural language processing mostly built one model per problem. A sentiment classifier, a question-answering system and a translation model each had their own architecture, their own labelled dataset and their own training run. If you had trained a good model and then needed to solve a different problem, you trained another model. What was shared was the bottom layer. Word embeddings such as word2vec (Mikolov et al., 2013) and GloVe (Pennington et al., 2014) learned one vector per word from unlabelled text, and task models used those vectors as input features. This was …"},{"id":"/learn/post-training/guide/#pretrain-adapt-h","page":"Post-Training: The Full Guide","section":"Pre-train, then adapt","url":"/learn/post-training/guide/#pretrain-adapt-h","kind":"section","text":"Figure 1. From word vectors to reasoning models. Colour marks the paradigm each milestone belongs to. The quiet start: semi-supervised sequence learning (2015) Dai and Le (2015) pre-trained an LSTM as a language model, or as a sequence autoencoder, and used its weights to initialise a supervised text classifier. The pre-trained networks trained more stably and generalised better on several classification benchmarks. The idea that a language model need not be the final product, but can be a pre-training stage for supervised learning, was already on the table. It did not take over immediately. …"},{"id":"/learn/post-training/guide/#scale-h","page":"Post-Training: The Full Guide","section":"Scale and prompting","url":"/learn/post-training/guide/#scale-h","kind":"section","text":"If one model can be adapted to so many tasks, and pre-training alone already produces some zero-shot ability, do we need to fine-tune for every task at all? GPT-2: language models as unsupervised multitask learners (2019) The GPT-2 paper’s title states its thesis (Radford et al., 2019). Web text is full of implicit task demonstrations: an interview transcript pairs “Q:” with a question and “A:” with its answer; an article followed by “TL;DR:” is followed by a summary. A model that predicts such text well may have to learn what follows “Q: … A:”. So train a large enough model on enough text …"},{"id":"/learn/post-training/guide/#sft-h","page":"Post-Training: The Full Guide","section":"What SFT optimises","url":"/learn/post-training/guide/#sft-h","kind":"section","text":"Supervised fine-tuning (SFT), also called instruction tuning, continues training a pre-trained model on a dataset of prompt–response pairs, so that it learns to follow instructions and answer in the intended way. It usually comes straight after pre-training and is the bridge from general language ability to useful behaviour. The training signal is the same as in pre-training: predict the next token. What changes is the data. Suppose we have $N$ pairs of a prompt $x$ and a reference response $y = (y_1 ,…,y_T )$: $$𝒟 = {(x_i ,y_i )}_{i = 1}^N ,P_θ (y∣x) = ∏_{t = 1}^T P_θ (y_t ∣x,y_{ < t} ).$$ …"},{"id":"/learn/post-training/guide/#sft-data-h","page":"Post-Training: The Full Guide","section":"Data, templates and loss masks","url":"/learn/post-training/guide/#sft-data-h","kind":"section","text":"Where SFT data comes from Human demonstrations. Annotators write a prompt, or take one from real users, and write the response a model ideally should give. InstructGPT fine-tuned GPT-3 on such labeller-written demonstrations (Ouyang et al., 2022). This is the purest form of SFT data, and the most expensive. Reformatted datasets. Existing supervised datasets can be rewritten as instructions. A sentiment example with sentence $s$ becomes “Is the sentiment of the following review positive or negative? $s$” with the answer “positive”. FLAN built its training mixture this way, with several …"},{"id":"/learn/post-training/guide/#sft-why-h","page":"Post-Training: The Full Guide","section":"Why a little data goes far","url":"/learn/post-training/guide/#sft-why-h","kind":"section","text":"A striking empirical fact is how little SFT data is needed to change a model’s behaviour substantially, and that the change generalises. LIMA fine-tuned a 65-billion-parameter LLaMA model on just 1,000 carefully curated prompt–response pairs, with no reinforcement learning, and obtained strong instruction following that generalised to tasks absent from the training data (Zhou et al., 2023). FLAN instruction-tuned a 137-billion-parameter model on more than 60 NLP datasets phrased as instructions. Zero-shot performance on unseen task types improved substantially, and FLAN surpassed zero-shot …"},{"id":"/learn/post-training/guide/#sft-limits-h","page":"Post-Training: The Full Guide","section":"Strengths and limits","url":"/learn/post-training/guide/#sft-limits-h","kind":"section","text":"SFT’s strengths are easy to list. It is simple and stable: supervised learning with a cross-entropy loss. Its signal is direct: people show the model what they want. It is data-efficient, changing behaviour with far less data than pre-training. It is controllable: style, format and domain can be shaped through demonstrations. And instruction tuning brings some generalisation to unseen tasks. Its limits are what motivate the rest of post-training. It shows a good answer, but not which answer is better. SFT says “imitate this response”. Many prompts have no single correct reply: two answers can …"},{"id":"/learn/post-training/guide/#preference-h","page":"Post-Training: The Full Guide","section":"From demonstrations to comparisons","url":"/learn/post-training/guide/#preference-h","kind":"section","text":"Once a model has learned to answer, the next goal is for it to answer better. Often there is no unique reference answer to write down, but saying which of two answers is better is easy. That is the essential difference between demonstration data and preference data: one provides a reference answer to imitate, the other a preference relation between answers. Demonstration (SFT) A prompt and one ideal response, written by a person. Signal: “produce this”. Comparison (preference) A prompt and two or more responses, usually sampled from the model, ranked by a person. Signal: “this one is better …"},{"id":"/learn/post-training/guide/#reward-model-h","page":"Post-Training: The Full Guide","section":"The Bradley–Terry reward model","url":"/learn/post-training/guide/#reward-model-h","kind":"section","text":"So we want a function $r(x,y)$ that scores a single response, learned from pairwise orderings. Since “better” has no fixed definition and human judgements are noisy, a probabilistic model of preferences is the natural starting point. Suppose responses $y_1$ and $y_2$ have scores $r_1$ and $r_2$. A softmax over the two scores gives the probability that $y_1$ wins: $$P(y_1 ≻y_2 ∣x) = \\frac{e^{r_1 } }{e^{r_1 } + e^{r_2 } } = \\frac{1}{1 + e^{ − (r_1 − r_2 )} } = σ(r_1 − r_2 ),$$ where $σ$ is the logistic sigmoid. This is the Bradley–Terry model of paired comparisons (Bradley and Terry, 1952): a …"},{"id":"/learn/post-training/guide/#rl-setup-h","page":"Post-Training: The Full Guide","section":"Agents, MDPs and returns","url":"/learn/post-training/guide/#rl-setup-h","kind":"section","text":"A reward model can say how good an answer is, but it does not make the model produce better answers. For that the model must adjust its generation strategy, its output distribution, in response to the scores. That is reinforcement learning (RL). This part builds the RL needed for RLHF from first principles; Sutton and Barto (2018) is the standard reference for all of it. Agent and environment An agent interacts repeatedly with an environment. At time $t$ it observes the state $S_t = s_t$, chooses an action $A_t = a_t$ according to its policy $π$, and the environment returns a reward $R_{t + …"},{"id":"/learn/post-training/guide/#policy-gradient-h","page":"Post-Training: The Full Guide","section":"Policy gradients","url":"/learn/post-training/guide/#policy-gradient-h","kind":"section","text":"How exactly should the policy change in response to rewards? The intuition: make high-return trajectories more likely and low-return ones less likely. Write $R(τ) = G_0$ for a trajectory’s return. We want to do gradient ascent, $θ ← θ + α∇_θ J(θ)$. $$∇_θ J(θ) = ∇θ 𝔼{τ~π_θ } [R(τ)] = ∇_θ ∑_τ P_θ (τ)R(τ) = ∑_τ ∇_θ P_θ (τ)R(τ).$$ The difficulty is that $θ$ appears in the distribution we are averaging over, so the gradient is not obviously an expectation we can estimate by sampling. The log-derivative trick fixes that: $$∇_θ log P_θ (τ) = \\frac{∇_θ P_θ (τ)}{P_θ (τ)}⟹∇_θ P_θ (τ) = P_θ (τ)∇_θ log …"},{"id":"/learn/post-training/guide/#values-h","page":"Post-Training: The Full Guide","section":"Values and Bellman equations","url":"/learn/post-training/guide/#values-h","kind":"section","text":"The state-value function is the expected return from state $s$ when following $π$, and the action-value function (Q-function) is the expected return after taking action $a$ in state $s$ and following $π$ afterwards: $$V^π (s) = 𝔼_π [G_t ∣S_t = s],Q^π (s,a) = 𝔼_π [G_t ∣S_t = s,A_t = a].$$ They are related directly. In state $s$ the next action is drawn from $π$, so averaging over it gives $$V^π (s) = ∑_a π(a∣s)Q^π (s,a).$$ In the running example, with the SFT policy and the reward model, $V(x)$ for the prompt is the SFT-weighted average reward, 0.60; it reappears in §16. Bellman expectation …"},{"id":"/learn/post-training/guide/#td-h","page":"Post-Training: The Full Guide","section":"Monte Carlo and TD learning","url":"/learn/post-training/guide/#td-h","kind":"section","text":"Monte Carlo The most direct idea returns to the definition $V^π (s) = 𝔼_π [G_t ∣S_t = s]$ and estimates the expectation by sampling: run the policy from $s$ many times, record the returns and average them. Incrementally, after each episode, move the estimate towards the observed return: $$V^π (s) ≈ \\frac{1}{N}∑_{i = 1}^N G_t^{(i)} ,V(S_t ) ← V(S_t ) + α[G_t − V(S_t )].$$ $Q^π (s,a)$ can be estimated the same way from the returns that follow each visit to $(s,a)$, and the policy improved greedily as before, so evaluation and improvement work without a model. But Monte Carlo has to wait until …"},{"id":"/learn/post-training/guide/#advantage-h","page":"Post-Training: The Full Guide","section":"Baselines and advantages","url":"/learn/post-training/guide/#advantage-h","kind":"section","text":"Back to policy gradients. $G_t$ measures an absolute level of return, which mixes three things: how good the state was, how good the action was, and luck. That makes the gradient estimate noisy, and it cannot tell whether a high return was earned by the action or inherited from a good state. The first fix is to replace the sample $G_t$ by its expectation $Q^π (s_t ,a_t )$. Because $∇_θ log π_θ (a_t ∣s_t )$ depends only on $(s_t ,a_t )$ and $𝔼[G_t ∣s_t ,a_t ] = Q^π (s_t ,a_t )$, the tower property leaves the gradient unchanged while removing the sampling noise in the future: $$∇θ J(θ) = 𝔼{π_θ …"},{"id":"/learn/post-training/guide/#gae-h","page":"Post-Training: The Full Guide","section":"Actor–critic and GAE","url":"/learn/post-training/guide/#gae-h","kind":"section","text":"If we do not know the advantage, we can learn it. The policy $π_θ$ is the actor: it acts. A learned value function is the critic: it evaluates, and its evaluation guides the actor’s updates. This is the actor–critic family; with the advantage as the weight it is often called advantage actor–critic, or A2C, the synchronous variant of A3C (Mnih et al., 2016). Learning both $Q$ and $V$ to subtract them would be cumbersome. The TD error avoids it. If $V$ is the true value function of the policy, the expected TD error is the advantage: $$𝔼[δ_t ∣s_t ,a_t ] = 𝔼[r_{t + 1} + γV^π (s_{t + 1} )∣s_t ,a_t …"},{"id":"/learn/post-training/guide/#trpo-ppo-h","page":"Post-Training: The Full Guide","section":"From TRPO to PPO","url":"/learn/post-training/guide/#trpo-ppo-h","kind":"section","text":"A vanilla policy-gradient step has two practical problems. First, the gradient is only valid at the current policy: the data were sampled from $π_θ$, so once $θ$ moves the samples no longer describe the new policy, and each batch can safely be used for only one small step. Second, the step size is hard to choose: a small change in parameters can be a large change in behaviour, and one bad step can collapse a policy that then generates only bad data from which it cannot recover. A surrogate objective with importance weights The performance difference lemma (Kakade and Langford, 2002) says …"},{"id":"/learn/post-training/guide/#instructgpt-h","page":"Post-Training: The Full Guide","section":"The InstructGPT pipeline","url":"/learn/post-training/guide/#instructgpt-h","kind":"section","text":"Preference-based RL for language models predates InstructGPT: it had been applied to stylistic continuation and summarisation (Ziegler et al., 2019; Stiennon et al., 2020), building on deep RL from human preferences (Christiano et al., 2017). InstructGPT (Ouyang et al., 2022) assembled the pieces into the pipeline that became the template for chat assistants; Anthropic trained helpful and harmless assistants with a similar pipeline in the same year (Bai et al., 2022a). RLHF as in InstructGPT Supervised fine-tuning. Collect labeller-written demonstrations for prompts, many of them submitted by …"},{"id":"/learn/post-training/guide/#rlhf-limits-h","page":"Post-Training: The Full Guide","section":"The limits of RLHF","url":"/learn/post-training/guide/#rlhf-limits-h","kind":"section","text":"RLHF works, but each stage carries its own failure modes; Casper et al. (2023) survey them in detail. The feedback. Labellers disagree, make mistakes, and have their own preferences and blind spots. A single scalar reward cannot represent a population with genuinely different preferences. Good feedback on hard tasks needs expertise and is slow and costly. The reward model. It is an imperfect proxy trained on limited data. Optimised hard, the policy finds its errors: over-optimisation lowers true quality even as the proxy score rises (Gao et al., 2023). Learned shortcuts. Some flaws are …"},{"id":"/learn/post-training/guide/#dpo-h","page":"Post-Training: The Full Guide","section":"Direct preference optimisation","url":"/learn/post-training/guide/#dpo-h","kind":"section","text":"The KL-regularised objective of §16 has a remarkable property: for a fixed reward, its optimal policy can be written in closed form. Direct preference optimisation (DPO) (Rafailov et al., 2023) uses that to skip both the reward model and the RL loop. The optimal policy, in closed form Fix a prompt $x$ and consider any distribution $π$ over responses. Collect the reward and the KL term into one logarithm: $$𝔼_{y~π} [r(x,y)] − βKL(π‖π_{ref} )& = − β𝔼_{y~π} [ log \\frac{π(y∣x)}{π_{ref} (y∣x) exp (r(x,y)/β)}]& = − β𝔼_{y~π} [ log \\frac{π(y∣x)}{π^⋆ (y∣x)}] + β log Z(x) = − βKL(π‖π^⋆ ) + β log …"},{"id":"/learn/post-training/guide/#grpo-h","page":"Post-Training: The Full Guide","section":"Verifiable rewards and GRPO","url":"/learn/post-training/guide/#grpo-h","kind":"section","text":"Learned reward models are the weak point of RLHF: they are approximate, they can be hacked, and they need preference data. For some tasks they are unnecessary. A mathematics problem with a known answer, code with unit tests, or an instruction with a checkable constraint can be scored by a program. Training against such checks is called reinforcement learning with verifiable rewards (RLVR), a name introduced with the Tülu 3 models (Lambert et al., 2024). A rule-based reward is hard to hack in the way a neural reward model is, although a checker that only inspects the final answer says nothing …"},{"id":"/learn/post-training/guide/#r1-h","page":"Post-Training: The Full Guide","section":"DeepSeek-R1 and reasoning","url":"/learn/post-training/guide/#r1-h","kind":"section","text":"In 2024 OpenAI reported that o1’s performance improves both with more reinforcement learning and with more time spent thinking at test time (OpenAI, 2024), without describing the method in detail. DeepSeek-R1 (DeepSeek-AI, 2025) described an openly documented route to similar behaviour, built on GRPO and verifiable rewards. DeepSeek-R1-Zero: RL only GRPO applied directly to the pre-trained base model, with no SFT. The rewards are rule-based: accuracy (is the final answer correct, or does the code pass the tests?) and format (is the reasoning placed between thinking tags?). A neural reward …"},{"id":"/learn/post-training/guide/#compare-h","page":"Post-Training: The Full Guide","section":"Methods side by side","url":"/learn/post-training/guide/#compare-h","kind":"section","text":"The four families of methods in this guide differ less in their mathematics, which they share, than in what they need and where their learning signal comes from. Model copies are counted at full size; a critic is often smaller or shares the policy’s network, and RLVR describes the reward source, which can be paired with PPO, GRPO or other optimisers. Method Data needed Models in memory Sampling Learning signal Main failure modes SFT Prompt–response demonstrations 1: the policy Offline: a fixed dataset, teacher forcing Log-likelihood of the demonstration Copies the data’s flaws; exposure bias …"},{"id":"/learn/post-training/guide/#practice-h","page":"Post-Training: The Full Guide","section":"Running it: settings, cost, failures","url":"/learn/post-training/guide/#practice-h","kind":"section","text":"Settings the papers report Hyperparameters depend on the model, the data and the code base, so the values below are reference points from the papers that report them, not recommendations. Setting What it controls Reported value Source PPO clip $ϵ$ How far one batch may move each action’s probability 0.2, the best of the settings compared Schulman et al. (2017) GAE $λ$, discount $γ$ Bias–variance of the advantage; horizon $λ = 0.95$, $γ = 0.99$ in its benchmark experiments Schulman et al. (2017) RLHF KL weight $β$ Distance from the SFT model 0.02; pre-training mix coefficient 27.8 for PPO-ptx …"},{"id":"/learn/post-training/guide/#evaluation-h","page":"Post-Training: The Full Guide","section":"How post-trained models are measured","url":"/learn/post-training/guide/#evaluation-h","kind":"section","text":"Post-training changes behaviour, so its evaluations measure behaviour: which answer people prefer, and whether answers are correct. Preferences: people and model judges Human win rates. Show raters the outputs of two models for the same prompt and count how often each is preferred. InstructGPT’s headline result was such a comparison (Ouyang et al., 2022). Arena rankings. Chatbot Arena collects pairwise votes from users who chat with two anonymous models and fits a Bradley–Terry model to the votes to rank the models (Chiang et al., 2024): the same model as our reward model in §9, used to score …"},{"id":"/learn/post-training/guide/#open-h","page":"Post-Training: The Full Guide","section":"Open questions","url":"/learn/post-training/guide/#open-h","kind":"section","text":"We started with a question from GPT-1: does post-training teach new abilities, or elicit abilities the model already has? The evidence so far leans towards elicitation for SFT (§6), and the same debate has reopened for RL (§24). Does RL create reasoning or sharpen it? The pass@$k$ results above suggest sharpening on the problems studied. Whether longer, broader or differently designed RL changes this is open. Rewards beyond verification. Verifiable rewards cover mathematics, code and checkable constraints. Most of what people want, such as good writing, sound advice or honest uncertainty, is …"},{"id":"/learn/post-training/guide/#summary-h","page":"Post-Training: The Full Guide","section":"In brief","url":"/learn/post-training/guide/#summary-h","kind":"section","text":"The methods Pre-training supplies what the model knows; post-training changes which of its possible outputs it gives. Supervised fine-tuning imitates demonstrations. A reward model learns from human comparisons, and PPO optimises against it while a KL penalty holds the model near its starting point. DPO folds the reward model into one loss on preference pairs, and GRPO replaces the learned critic with a group of samples scored by a checker. What they share The reinforcement learning methods are variations on one policy-gradient estimate, differing in how the weight on each log-probability is …"},{"id":"/learn/post-training/guide/#references-h","page":"Post-Training: The Full Guide","section":"References","url":"/learn/post-training/guide/#references-h","kind":"section","text":"Armen Aghajanyan, et al. (2021). Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning. ACL 2021. Mohammad Gheshlaghi Azar, et al. (2024). A General Theoretical Paradigm to Understand Learning from Human Preferences. AISTATS 2024. Yuntao Bai, et al. (2022). Constitutional AI: Harmlessness from AI Feedback. arXiv:2212.08073. Yuntao Bai, et al. (2022). Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback. arXiv:2204.05862. Ralph Allan Bradley, Milton E. Terry (1952). Rank Analysis of Incomplete Block Designs: I. The Method of …"},{"id":"/learn/post-training/","page":"Post-Training, Explained","section":"","url":"/learn/post-training/","kind":"page","text":"An illustrated explainer on LLM post-training: how supervised fine-tuning, reward models, RLHF with PPO, DPO and GRPO turn a pre-trained language model into an assistant."},{"id":"/learn/post-training/#pipeline-h","page":"Post-Training, Explained","section":"The pipeline at a glance","url":"/learn/post-training/#pipeline-h","kind":"section","text":"The classic recipe runs left to right. The last column shows the two main departures from it. Starting point Pre-training Predict the next token on a very large amount of text. Knowledge and skills, but no notion of answering. History → Imitate Supervised fine-tuning Train on prompt–response demonstrations with the same next-token loss, counted on the response only. SFT → Compare Reward model Fit a scalar score to human comparisons with the Bradley–Terry model: the preferred reply should score higher. Reward model → Optimise RL with PPO Sample replies, score them, and push the policy towards …"},{"id":"/learn/post-training/#learn-h","page":"Post-Training, Explained","section":"What you will learn","url":"/learn/post-training/#learn-h","kind":"section","text":"From task models to pre-train and adapt ULMFiT, GPT-1, BERT, GPT-2, T5 and GPT-3, and the question they leave open. Supervised fine-tuning The objective, derived; chat templates and loss masks; why a little data goes a long way. Learning from preferences Why comparisons, the Bradley–Terry reward model, and reward hacking. Reinforcement learning, from scratch MDPs, returns, policy gradients, value functions, Bellman equations, TD and GAE. RLHF in practice Trust regions, PPO’s clipped objective, the InstructGPT pipeline and its limits. Beyond PPO DPO, verifiable rewards, GRPO and DeepSeek-R1. …"},{"id":"/learn/post-training/zh/","page":"后训练：完整指南","section":"","url":"/learn/post-training/zh/","kind":"page","text":"LLM 后训练完整指南（中文版）：从 ULMFiT 到 GPT-3 的历史，SFT、Bradley–Terry 奖励模型、策略梯度、GAE、PPO、InstructGPT、DPO、RLVR、GRPO 与 DeepSeek-R1，含推导与交互图。"},{"id":"/learn/post-training/zh/#history-h","page":"后训练：完整指南","section":"一个任务一个模型","url":"/learn/post-training/zh/#history-h","kind":"section","text":"直到 2010 年代后期，自然语言处理基本上是一个问题一个模型。情感分类器、问答系统和翻译模型各有各的架构、标注数据和训练流程；一个模型训练好之后，若要解决另一个问题，就再训练一个模型。 能共享的只有最底层。word2vec (Mikolov et al., 2013) 和 GloVe (Pennington et al., 2014) 这样的词向量从无标注文本中为每个词学习一个向量，任务模型把这些向量当作输入特征。这已经是迁移学习，但比较浅：每个词无论上下文如何都只有一个向量，所以 “river bank” 和 “bank account” 里的 bank 看起来一样，而词向量之上的一切仍然需要为每个任务从头学起。 2015 到 2020 年间，情况变了。领域逐渐收敛到另一套做法：在海量无标注文本上训练一个大型语言模型，保留下来，再适配到各个任务。这种“广泛训练一次、低成本适配多次”的做法，就是今天预训练与后训练分工的雏形。"},{"id":"/learn/post-training/zh/#pretrain-adapt-h","page":"后训练：完整指南","section":"先预训练，再适配","url":"/learn/post-training/zh/#pretrain-adapt-h","kind":"section","text":"图 1. 从词向量到推理模型。颜色表示每个节点所属的范式。 悄然开场：半监督序列学习（2015） Dai and Le (2015) 先把 LSTM 预训练成语言模型或序列自编码器，再用它的权重初始化有监督的文本分类器。经过预训练的网络在训练时更稳定，在多个分类基准上也有更好的泛化表现。“语言模型不必是最终产品，而可以作为有监督学习的*预训练阶段*”这一想法，在当时已经出现。 但这一想法并未立刻流行起来。LSTM 沿着序列逐步处理，训练难以并行，规模一大成本就很高。在缺乏充分证据表明预训练整个网络确实值得之前，人们没有足够理由放弃熟悉的“预训练词向量 + 任务专用模型”模式。 上下文相关的表示：ELMo（2018） ELMo (Peters et al., 2018) 针对的是“一个词只有一个向量”的局限。它训练了一个双向 LSTM 语言模型：一个方向预测下一个词，另一个方向预测前一个词，因此每个词的内部表示都依赖上下文。不同层捕捉的信息不同，因此 ELMo 的最终表示是各层的*任务特定加权组合*，权重为每个任务单独学习。 ELMo 表明，大规模预训练语言模型学到的表示可以迁移到许多任务，并将这一领域从静态表示推向了上下文表示。但它仍然是基于特征的迁移：预训练模型生成特征，再交给一个独立的任务模型使用。 微调整个模型：ULMFiT（2018） ULMFiT (Howard and …"},{"id":"/learn/post-training/zh/#scale-h","page":"后训练：完整指南","section":"规模与提示","url":"/learn/post-training/zh/#scale-h","kind":"section","text":"既然一个模型可以适配这么多任务，而仅凭预训练就已能产生一些零样本能力，我们真的还需要为每个任务做微调吗？ GPT-2：语言模型是无监督的多任务学习者（2019） GPT-2 论文的标题就是它的论点 (Radford et al., 2019)。网络文本中充满了隐含的任务示范：采访记录里“Q:”后面跟着问题，“A:”后面跟着回答；文章后面接“TL;DR:”，再往后就是摘要。一个能很好地预测这类文本的模型，可能不得不学会“Q: … A:”之后应该跟什么。因此，在足够多的文本上训练足够大的模型，任务就可能在没有被标注为任务的情况下被学会。 GPT-2 拥有 15 亿参数，是 GPT-1 的十倍以上，训练数据是 WebText，约 40 GB 文本，来自约 800 万个网页文档。作者训练了多个规模的模型，并在不做任何微调的零样本设置下评测；各任务上的性能随模型规模大致呈对数线性提升。这是后来被系统研究的规模规律 (Kaplan et al., 2020) 的早期信号。 GPT-2 显然仅凭预训练就获得了与任务相关的行为。这也说明为什么预训练不是全部：问它一个问题，基座模型可能会继续续写文档而不是回答，比如接着写更多问题。它有知识，却没有按用户期望去使用知识的习惯。这一差距正是指令微调最重要的动机之一。 T5：一切都是文本到文本（2019） T5 (Raffel et al., 2020) …"},{"id":"/learn/post-training/zh/#sft-h","page":"后训练：完整指南","section":"SFT 优化的是什么","url":"/learn/post-training/zh/#sft-h","kind":"section","text":"监督微调（Supervised Fine-Tuning，SFT），又称指令微调，是在由提示–回复对组成的数据集上继续训练预训练模型，使其学会遵循指令并按预期方式作答。它通常紧接在预训练之后，是从通用语言能力通往有用行为的桥梁。 训练信号与预训练相同：预测下一个 token。变化的是数据。假设我们有 $N$ 对提示 $x$ 和参考回复 $y = (y_1 ,…,y_T )$： $$𝒟 = {(x_i ,y_i )}_{i = 1}^N ,P_θ (y∣x) = ∏_{t = 1}^T P_θ (y_t ∣x,y_{ < t} ).$$ 这一分解正是概率的链式法则：模型逐个生成 token，每个 token 都以提示和此前生成的 token 为条件。最大似然会选择使观测到的回复概率尽可能大的参数。 假设样本对彼此独立，则似然为各样本概率的乘积；取负对数后转化为可最小化的求和： $$θ^⋆ = argmax_θ ∏_{i = 1}^N P_θ (y_i ∣x_i ) = argmin_θ [ − ∑_{i = 1}^N log P_θ (y_i ∣x_i )].$$ 代入分解式后，乘积的对数化为对数之和，每个回复 token 对应一项： $$ℒ_{SFT} (θ) = − ∑{i = 1}^N ∑{t = 1}^{T_i } log P_θ (y_{i,t} ∣x_i ,y_{i, < …"},{"id":"/learn/post-training/zh/#sft-data-h","page":"后训练：完整指南","section":"数据、模板与损失掩码","url":"/learn/post-training/zh/#sft-data-h","kind":"section","text":"SFT 数据的来源 人工示范。标注者会编写一个提示（或取自真实用户），并写出模型在理想情况下应给出的回复。InstructGPT 正是在这类标注者编写的示范上对 GPT-3 进行微调(Ouyang et al., 2022)。这是最纯粹但也最昂贵的 SFT 数据。 改写已有数据集。已有的监督数据集可以改写为指令形式。例如，一个句子$s$的情感分类样本，可以改写为“下面这条评论的情感是积极还是消极？$s$”，答案为“积极”。FLAN 正是以这种方式构建训练数据，为每个数据集配置多个自然语言模板(Wei et al., 2022a)。 合成数据。由模型生成指令和回复，经筛选后加入训练集。Self-Instruct 正是从少量种子任务出发，以这种方式自举生成指令数据(Wang et al., 2023)。 领域数据。当模型需要覆盖某个特定领域时，可使用代码、数学、医学或公司内部文档。 现代 SFT 通常会混合使用上述所有来源的数据。数据覆盖哪些行为、质量如何、各类比例怎样，在很大程度上决定了最终结果。训练前通常需要清洗数据：过滤有害、错误、低质量或不希望模型学习的样本，并平衡数据配比，避免某一类占据主导。 对话模板 对话会被序列化为一个 token 序列，并用特殊 token 标记角色。不同模型家族使用的具体 token 有所不同，示意如下： < system > You are a …"},{"id":"/learn/post-training/zh/#sft-why-h","page":"后训练：完整指南","section":"为什么少量数据就够","url":"/learn/post-training/zh/#sft-why-h","kind":"section","text":"一个非常强的经验事实是：只需很少的 SFT 数据，就能大幅改变模型行为，并且这种改变能够泛化。 LIMA 只用 1,000 条精心挑选的提示—回复对微调了 650 亿参数的 LLaMA 模型，在没有使用强化学习的情况下就获得了很强的指令遵循能力，并且能泛化到训练数据中未出现过的任务 (Zhou et al., 2023)。 FLAN 在 60 多个以指令形式表述的 NLP 数据集上对一个 1370 亿参数的模型做了指令微调。它在*未见过的任务类型*上的零样本表现显著提升，在评测的 25 个数据集中有 20 个超过了零样本的 175B GPT-3 (Wei et al., 2022a)。它的消融实验同样很有启发：任务簇越多越好，自然语言指令本身很重要，而且收益只在模型足够大时出现；在测试的较小模型上，指令微调反而损害了留出任务上的表现。 预训练已经让模型见过海量文本。很难相信一千个样本能教给它足够多的新*知识*，来解释如此大的变化。一个广为接受的观点，也就是 LIMA 作者所说的表层对齐假说（superficial alignment hypothesis），认为模型的知识和能力几乎全部在预训练中习得，对齐主要是教会它在与用户交互时采用哪种格式和风格 (Zhou et al., 2023)。 图 2. SFT 重塑下一个 token 的分布。这是贯穿全文的例子在第一个 token …"},{"id":"/learn/post-training/zh/#sft-limits-h","page":"后训练：完整指南","section":"优点与局限","url":"/learn/post-training/zh/#sft-limits-h","kind":"section","text":"SFT 的优点很容易概括。它简单稳定：就是带有交叉熵损失的监督学习。它的信号直接：人类直接示范期望的输出。它数据效率高，只需比预训练少得多的数据就能改变行为。它可控：风格、格式和领域都能通过示范塑造。指令微调还带来一定的泛化能力，能迁移到未见过的任务。 真正推动后续发展的，是它的局限。 它告诉模型好答案是什么样子，却不告诉模型哪个答案更好。SFT 说的是“模仿这个回复”。但许多提示并没有唯一正确的回复：两个答案可能都可以接受，只是其中一个更准确、更简洁、更有帮助或更安全。在我们的例子中，经过 SFT 后，“Paris.”和完整句子都很可能出现；SFT 数据中没有任何信息说明哪个更受欢迎。而且对人来说，写出理想答案往往比比较两个答案更难。在*提升质量*时，比较可能是更容易提供、也更直接的信号。 它的上限取决于示范。模型只是在模仿训练回复。如果示范平庸、有偏差或前后不一致，模型会把这些缺陷一并学会；而最大似然的“覆盖”性质（§4）意味着它会学会复现整个分布，而不只是最好的部分。 它看不到自己的错误。使用 teacher forcing 时，模型总是以真实前文为条件；推理时却以自己的生成结果为条件。小错误可能不断累积，使模型进入训练数据从未覆盖的状态。这种不匹配被称为暴露偏差（exposure bias）(Ranzato et al., 2016)，而 SFT …"},{"id":"/learn/post-training/zh/#preference-h","page":"后训练：完整指南","section":"从示范到比较","url":"/learn/post-training/zh/#preference-h","kind":"section","text":"模型学会回答之后，下一个目标是让它回答得*更好*。很多时候，写不出唯一的参考答案，判断两个答案哪个更好却很容易。这就是示范数据和偏好数据最本质的区别：前者提供可供模仿的参考答案，后者提供答案之间的*偏好关系*。 示范（SFT） 一个提示和一个由人写出的理想回复。 信号：“生成这个”。 比较（偏好） 一个提示和两个或更多回复，通常由模型采样得到，由人排序。 信号：“这个比那个好”。 偏好数据的来源可以非常多样。人可以针对某个属性写出对比样本，比如希望回答详细时，写一个简略回复和一个详细回复。更常见的是由*模型*生成候选、由人来评判。在 SFT 中这样做很危险，因为在一个尚弱的模型输出上训练，可能会强化它的缺陷；但对比较数据来说，这很自然。“模型生成、人来评价”的这种分工，正是 RLHF 所利用的 (Christiano et al., 2017; Stiennon et al., 2020)。它还有一个好处：反馈针对的是模型*自己*的输出，而这恰恰是我们关心的输出。 比较不是免费的午餐。有些比较本身就很难，人与人之间会有分歧；单条“A 比 B 好”所携带的信息，比一整段高质量示范要少。它真正的优势在于：对许多开放式生成任务来说，比较是一种更容易扩展的监督接口。 现在的数据形如下式，其中 $y^w$ 是被偏好（“胜出”）的回复，$y^l$ 是被拒绝（“落败”）的回复： …"},{"id":"/learn/post-training/zh/#reward-model-h","page":"后训练：完整指南","section":"Bradley–Terry 奖励模型","url":"/learn/post-training/zh/#reward-model-h","kind":"section","text":"因此，我们想从成对排序中学到一个能为单个回复打分的函数 $r(x,y)$。由于“更好”本身没有固定定义，人的判断又带有噪声，偏好的*概率*模型便成为自然的出发点。设回复 $y_1$ 和 $y_2$ 的分数分别为 $r_1$ 和 $r_2$，对两个分数做 softmax，就得到 $y_1$ 胜出的概率： $$P(y_1 ≻y_2 ∣x) = \\frac{e^{r_1 } }{e^{r_1 } + e^{r_2 } } = \\frac{1}{1 + e^{ − (r_1 − r_2 )} } = σ(r_1 − r_2 ),$$ 其中 $σ$ 是 logistic sigmoid 函数。这就是成对比较中的 Bradley–Terry 模型 (Bradley and Terry, 1952)：一个只依赖分数差的 logistic 模型。按标准最大似然方法，我们最大化观测偏好的概率，等价于最小化负对数似然： $$ℒ_{RM} (ϕ) = − ∑_{i = 1}^N log σ(r_ϕ (x_i ,y_i^w ) − r_ϕ (x_i ,y_i^l )).$$ 图 3. 偏好概率是奖励差的 sigmoid。只有差值 $Δ = r(A) − r(B)$ 起作用。图中沿用我们的例子：A 是 $y_4$（奖励 1.6），B 是 $y_3$（奖励 0.5），因此奖励模型预测标注者以 75% …"},{"id":"/learn/post-training/zh/#rl-setup-h","page":"后训练：完整指南","section":"智能体、MDP 与回报","url":"/learn/post-training/zh/#rl-setup-h","kind":"section","text":"奖励模型能判断一个答案有多好，却不能让模型生成更好的答案。为此，模型必须根据分数调整自己的*生成策略*，也就是输出分布。这就是强化学习（RL）。本节从第一性原理出发，构建 RLHF 所需的强化学习；Sutton and Barto (2018) 是本节内容的标准参考书。 智能体与环境 智能体（agent）不断与环境（environment）交互。在时刻 $t$，它观察到状态 $S_t = s_t$，按照自己的策略（policy）$π$ 选择动作 $A_t = a_t$，环境返回奖励 $R_{t + 1} = r_{t + 1}$ 和新状态 $S_{t + 1} = s_{t + 1}$： $$S_t → ^π A_t → ^{\\text{environment}} (R_{t + 1} ,S_{t + 1} ).$$ 我们通常假设环境具有马尔可夫性： $$P(S_{t + 1} ∣S_t ,A_t ,S_{t − 1} ,A_{t − 1} ,…,S_0 ,A_0 ) = P(S_{t + 1} ∣S_t ,A_t ).$$ 一个常见的误解是“未来与过去无关”。正确的理解是：当前状态已经包含了历史中所有会影响未来的信息，所以更早的状态不再提供额外信息。对语言模型来说，状态很自然地就是 $$s_t = (x,y_{ < t} ),a_t = y_t ,s_{t + 1} = …"},{"id":"/learn/post-training/zh/#policy-gradient-h","page":"后训练：完整指南","section":"策略梯度","url":"/learn/post-training/zh/#policy-gradient-h","kind":"section","text":"策略究竟应该如何根据奖励来调整？直觉是：让高回报的轨迹更可能出现，让低回报的轨迹更不可能出现。把一条轨迹的回报记为 $R(τ) = G_0$。我们想进行梯度上升 $θ ← θ + α∇_θ J(θ)$。 $$∇_θ J(θ) = ∇θ 𝔼{τ~π_θ } [R(τ)] = ∇_θ ∑_τ P_θ (τ)R(τ) = ∑_τ ∇_θ P_θ (τ)R(τ).$$ 难点在于 $θ$ 出现在我们取平均所用的分布里，所以这个梯度看起来不像一个可以通过采样估计的期望。对数导数技巧（log-derivative trick）解决了这个问题： $$∇_θ log P_θ (τ) = \\frac{∇_θ P_θ (τ)}{P_θ (τ)}⟹∇_θ P_θ (τ) = P_θ (τ)∇_θ log P_θ (τ),$$ $$∇_θ J(θ) = ∑_τ P_θ (τ)∇_θ log P_θ (τ)R(τ) = 𝔼_{τ~π_θ } [R(τ)∇_θ log P_θ (τ)].$$ 再展开轨迹的对数概率。初始状态项和转移项来自环境，与 $θ$ 无关，因此梯度为零；这也意味着我们永远不需要环境模型： $$log P_θ (τ) = log ρ_0 (s_0 ) + ∑_t ( log π_θ (a_t ∣s_t ) + log P(s_{t + 1} ∣s_t ,a_t ))⟹∇_θ log P_θ …"},{"id":"/learn/post-training/zh/#values-h","page":"后训练：完整指南","section":"价值函数与 Bellman 方程","url":"/learn/post-training/zh/#values-h","kind":"section","text":"状态价值函数是从状态 $s$ 出发、按照 $π$ 行动得到的期望回报；动作价值函数（Q 函数）是在状态 $s$ 采取动作 $a$、之后按照 $π$ 行动得到的期望回报： $$V^π (s) = 𝔼_π [G_t ∣S_t = s],Q^π (s,a) = 𝔼_π [G_t ∣S_t = s,A_t = a].$$ 两者直接相关：在状态 $s$ 下，下一个动作从 $π$ 中采样，对其取平均即得 $$V^π (s) = ∑_a π(a∣s)Q^π (s,a).$$ 在我们的例子中，对于 SFT 策略和奖励模型，提示的价值 $V(x)$ 就是按 SFT 概率加权的平均奖励 0.60；它会在 §16 再次出现。 Bellman 期望方程 利用 $G_t = R_{t + 1} + γG_{t + 1}$ 以及马尔可夫性，一步之后的价值等于即时奖励加上到达状态的折扣价值。记 $p(s^′ ,r∣s,a)$ 为转移到 $s^′$ 并获得奖励 $r$ 的概率： $$Q^π (s,a) = ∑_{s^′ ,r} p(s^′ ,r∣s,a)[r + γV^π (s^′ )],V^π (s) = ∑a π(a∣s)∑{s^′ ,r} p(s^′ ,r∣s,a)[r + γV^π (s^′ )].$$ 将第一个关系代入自身，就得到只含 $Q$ 的同一递推： $$Q^π (s,a) = ∑{s^′ …"},{"id":"/learn/post-training/zh/#td-h","page":"后训练：完整指南","section":"蒙特卡洛与 TD 学习","url":"/learn/post-training/zh/#td-h","kind":"section","text":"蒙特卡洛 最直接的想法是回到定义 $V^π (s) = 𝔼_π [G_t ∣S_t = s]$，通过采样来估计这个期望：从 $s$ 出发多次运行策略，记录回报并取平均。增量形式是每个回合结束后把估计朝观测到的回报移动一点： $$V^π (s) ≈ \\frac{1}{N}∑_{i = 1}^N G_t^{(i)} ,V(S_t ) ← V(S_t ) + α[G_t − V(S_t )].$$ $Q^π (s,a)$ 也可以用每次访问 $(s,a)$ 之后的回报来估计，再像之前那样贪心地改进策略，因此评估和改进都不需要模型。但蒙特卡洛必须等回合结束才能更新，而且一整条轨迹的随机性使 $G_t$ 的方差很大，回合越长越明显。 时序差分学习 Bellman 方程告诉我们不必等待： $$V^π (s) = 𝔼_π [R_{t + 1} + γV^π (S_{t + 1} )∣S_t = s].$$ 走一步之后我们观察到 $r$ 和 $s^′$，而 $r + γV(s^′ )$ 已经是对 $V(s)$ 的一个新估计。时序差分（TD）学习 (Sutton, 1988) 把旧估计朝它移动： $$V(S_t ) ← V(S_t ) + α[R_{t + 1} + γV(S_{t + 1} ) − V(S_t )],δ_t = R_{t + 1} + γV(S_{t + 1} ) − V(S_t …"},{"id":"/learn/post-training/zh/#advantage-h","page":"后训练：完整指南","section":"Baseline 与 advantage","url":"/learn/post-training/zh/#advantage-h","kind":"section","text":"回到策略梯度。$G_t$ 衡量的是回报的*绝对*水平，它混杂了三类因素：状态有多好、动作有多好，以及运气。这让梯度估计噪声很大，而且难以区分高回报究竟来自动作本身，还是继承自好的状态。 第一步是把样本 $G_t$ 替换为它的期望 $Q^π (s_t ,a_t )$。由于 $∇_θ log π_θ (a_t ∣s_t )$ 只依赖 $(s_t ,a_t )$，且 $𝔼[G_t ∣s_t ,a_t ] = Q^π (s_t ,a_t )$，根据全期望公式，梯度保持不变，而未来采样带来的噪声被去掉了： $$∇θ J(θ) = 𝔼{π_θ } [∑_t Q^{π_θ } (s_t ,a_t )∇_θ log π_θ (a_t ∣s_t )].$$ 这正是策略梯度定理 (Sutton et al., 2000) 的形式，在策略由一般函数逼近器表示时同样成立。但它仍然没有把状态和动作分开。于是，减去一个衡量状态好坏的 baseline $b(s_t )$，用*相对*回报来加权： $$∇θ J(θ) = 𝔼{π_θ } [∑_t (Q^{π_θ } (s_t ,a_t ) − b(s_t ))∇_θ log π_θ (a_t ∣s_t )].$$ 为了保持梯度不变，baseline 这一项的期望必须为零。只要 baseline 只依赖状态而不依赖动作，任何 baseline 都满足： …"},{"id":"/learn/post-training/zh/#gae-h","page":"后训练：完整指南","section":"Actor–critic 与 GAE","url":"/learn/post-training/zh/#gae-h","kind":"section","text":"如果不知道 advantage，就去学习它。策略 $π_θ$ 是 actor，负责行动；学到的价值函数是 critic，负责评价，并用评价指导 actor 更新。这就是 actor–critic 方法族；用 advantage 作为权重时，常称为 advantage actor–critic，即 A2C，它是 A3C (Mnih et al., 2016) 的同步版本。 同时学习 $Q$ 和 $V$ 再相减会带来额外负担。TD 误差绕开了这个问题：如果 $V$ 是策略的真实价值函数，那么 TD 误差的期望*就是* advantage： $$𝔼[δ_t ∣s_t ,a_t ] = 𝔼[r_{t + 1} + γV^π (s_{t + 1} )∣s_t ,a_t ] − V^π (s_t ) = Q^π (s_t ,a_t ) − V^π (s_t ) = A^π (s_t ,a_t ).$$ 因此只需学习一个 critic $V_w ≈ V^π$：用 $V_w$ 算出的 $δ_t$ 就是一步 advantage 估计。critic 本身则像 TD 学习一样，通过向目标回归来训练。 但一步估计太短视了：它只使用一个真实奖励，就把整个未来交给 $V(s_{t + 1} )$；一旦 critic 不够准，它的误差就会直接污染 …"},{"id":"/learn/post-training/zh/#trpo-ppo-h","page":"后训练：完整指南","section":"从 TRPO 到 PPO","url":"/learn/post-training/zh/#trpo-ppo-h","kind":"section","text":"普通的策略梯度更新存在两个实际问题。第一，梯度只在当前策略处有效：数据是从 $π_θ$ 采样的，一旦 $θ$ 改变，这些样本就不再描述新策略，因此每批数据只能安全地用于一小步更新。第二，步长很难选择：参数的微小变化可能导致行为的巨大改变，一次糟糕的更新就可能让策略崩溃，之后它只会继续生成糟糕的数据，难以恢复。 带重要性权重的替代目标 性能差异引理 (Kakade and Langford, 2002) 精确地说明了新策略 $π^′$ 比 $π$ 好多少：等于沿 $π^′$ 的轨迹累积的 advantage $π$， $$J(π^′ ) − J(π) = 𝔼_{τ~π^′ } [∑_t γ^t A^π (s_t ,a_t )].$$ 但在更新之前，我们并不知道 $π^′$ 会访问哪些状态。 如果新策略与旧策略足够接近，就可以沿用旧策略访问到的状态，并用重要性比率修正动作分布。这就得到了替代目标（surrogate objective） $$L_{θ_{old} } (θ) = 𝔼_{s,a~π_{θ_{old} } } [\\frac{π_θ (a∣s)}{π_{θ_{old} } (a∣s)}A^{π_{θ_{old} } } (s,a)],$$ 它可以用旧样本估计，并且在 $θ = θ_{old}$ 处的梯度等于策略梯度。不过，它只在 $θ_{old}$ 附近可信。 …"},{"id":"/learn/post-training/zh/#instructgpt-h","page":"后训练：完整指南","section":"InstructGPT 流程","url":"/learn/post-training/zh/#instructgpt-h","kind":"section","text":"基于偏好的语言模型强化学习早于 InstructGPT：此前已用于风格续写和摘要(Ziegler et al., 2019; Stiennon et al., 2020)，并建立在基于人类偏好的深度强化学习(Christiano et al., 2017)之上。InstructGPT · (Ouyang et al., 2022) 把这些组件组装成了后来成为对话助手模板的流程；同年，Anthropic 也采用类似流程训练了有用且无害的助手(Bai et al., 2022a)。 InstructGPT 中的 RLHF 监督微调。针对提示（其中许多由 API 用户提交）收集标注者编写的示例，并在这些示例上微调 GPT-3（§4–5）。 奖励模型。对每个提示，从模型中采样多个输出，由标注者排序，再用 Bradley–Terry 损失在每个排序的所有成对比较上训练奖励模型（§9）。 强化学习。用 PPO 针对奖励模型优化 SFT 模型，并加入对 SFT 模型的逐 token KL 惩罚（§16）。第 2 步和第 3 步可以迭代：在当前策略上收集新的比较数据。 最终目标还多了一项。RLHF 在若干公开 NLP 基准上造成退化，即所谓“对齐税”（alignment tax）；于是作者混入了预训练目标，并将该变体称为 PPO-ptx（他们把这个系数写作$γ$，与折扣因子无关）： …"},{"id":"/learn/post-training/zh/#rlhf-limits-h","page":"后训练：完整指南","section":"RLHF 的局限","url":"/learn/post-training/zh/#rlhf-limits-h","kind":"section","text":"RLHF 有效，但每个阶段都有各自的失败模式；Casper et al. (2023) 对此做了详细综述。 反馈本身。标注者之间会有分歧、会犯错，也有各自的偏好和盲区。单一标量奖励无法代表偏好真正不同的人群。在困难任务上提供好的反馈需要专业知识，既慢又贵。 奖励模型。它是在有限数据上训练的不完美代理。当被强烈优化时，策略会找到它的错误：过度优化会在代理分数上升的同时降低真实质量 (Gao et al., 2023)。 学到的捷径。有些缺陷是系统性的。更长的回答往往更受青睐，RLHF 中测得的奖励提升，很大一部分可以归因于回答变长 (Singhal et al., 2023)。用人类反馈训练的助手倾向于谄媚（sycophancy），说用户似乎想听的话；而人类偏好判断有时会偏爱有说服力的谄媚回答，而不是正确回答 (Sharma et al., 2024)。我们例子中奉承式的 $y_6$ 就是这两者的漫画版。 成本与稳定性。内存里有四个模型，训练循环中包含在线生成，并且对 $β$、$ϵ$ 和学习率等超参数敏感。 此后出现了两个方向。一个是在书面原则指导下用 AI 反馈代替人类标注者，例如 Constitutional AI (Bai et al., 2022b)，以扩展监督规模。另一个是简化优化本身，这正是下一部分的内容。 第 5 部分一句话总结 PPO …"},{"id":"/learn/post-training/zh/#dpo-h","page":"后训练：完整指南","section":"直接偏好优化","url":"/learn/post-training/zh/#dpo-h","kind":"section","text":"§16 中带 KL 正则的目标有一个重要的性质：对于固定的奖励，其最优策略可以写成闭式解。直接偏好优化（DPO）(Rafailov et al., 2023) 利用这一点，同时跳过了奖励模型和 RL 循环。 闭式的最优策略 固定一个提示 $x$，考虑回复上的任意分布 $π$。将奖励项和 KL 项合并到一个对数里： $$𝔼_{y~π} [r(x,y)] − βKL(π‖π_{ref} )& = − β𝔼_{y~π} [ log \\frac{π(y∣x)}{π_{ref} (y∣x) exp (r(x,y)/β)}]& = − β𝔼_{y~π} [ log \\frac{π(y∣x)}{π^⋆ (y∣x)}] + β log Z(x) = − βKL(π‖π^⋆ ) + β log Z(x),$$ 其中归一化分布的定义见下式。$Z(x)$ 与 $π$ 无关，而 KL 散度非负，且仅当两个分布相同时为零。因此目标恰好在 $π = π^⋆$ 处达到最大： $$π^⋆ (y∣x) = \\frac{1}{Z(x)}π_{ref} (y∣x) exp (\\frac{r(x,y)}{β}),Z(x) = ∑y π{ref} (y∣x) exp (\\frac{r(x,y)}{β}).$$ 最优策略就是用指数化的奖励对参考模型重新加权。$β$ 相当于温度：$β$ 较大时贴近 $π_{ref}$，$β$ …"},{"id":"/learn/post-training/zh/#grpo-h","page":"后训练：完整指南","section":"可验证奖励与 GRPO","url":"/learn/post-training/zh/#grpo-h","kind":"section","text":"学习得到的奖励模型是 RLHF 的薄弱环节：它是一个近似模型，容易被投机利用，而且需要偏好数据。对某些任务来说，它完全没有必要。答案已知的数学题、带单元测试的代码、带可检查约束的指令，都可以由程序打分。针对这类检查进行训练称为基于可验证奖励的强化学习（RLVR），这一名称随 Tülu 3 模型提出 (Lambert et al., 2024)。基于规则的奖励不太会像神经奖励模型那样被投机利用；不过，只检查最终答案的检查器，并不能说明推理过程是否可靠。 人们早已知道推理受益于中间步骤：提示模型写出思维链能提升大模型的多步推理 (Wei et al., 2022b)；STaR 则通过在自己生成的、得出正确答案的推理过程上微调来自举推理能力 (Zelikman et al., 2022)。直接奖励步骤本身（过程监督）在训练数学奖励模型时优于只奖励最终答案 (Lightman et al., 2023)，但步骤级标注成本很高。来自验证器的结果奖励成本低，也容易扩展。 GRPO：用一组样本替代 critic 组相对策略优化（GRPO）由 DeepSeekMath 提出 (Shao et al., 2024)。它保留了 PPO 的裁剪目标，但去掉了价值网络。对于每个提示 $q$，它从旧策略中采样一*组* $G$ 个输出 $o_1 ,…,o_G$，给它们打分，并用这组样本本身作为 …"},{"id":"/learn/post-training/zh/#r1-h","page":"后训练：完整指南","section":"DeepSeek-R1 与推理","url":"/learn/post-training/zh/#r1-h","kind":"section","text":"2024 年，OpenAI 报告 o1 的表现既随着更多强化学习而提升，也随着测试时更长的思考而提升 (OpenAI, 2024)，但没有详细描述方法。DeepSeek-R1 (DeepSeek-AI, 2025) 公开给出了一条实现类似行为的路线，它建立在 GRPO 和可验证奖励之上。 DeepSeek-R1-Zero：只用 RL 直接在预训练基座模型上应用 GRPO，不做 SFT。奖励基于规则：准确性（最终答案是否正确、代码是否通过测试）和*格式*（推理是否放在思考标签之间）。出于对 reward hacking 的担忧，刻意没有使用神经奖励模型。 训练过程中，回复自发变得越来越长，并涌现出重新检查、重新评估先前步骤等行为，其中包括被广泛引用的“顿悟时刻”（aha moment）。但输出难以阅读，还会混用语言。 DeepSeek-R1：多阶段流程 冷启动：在少量较长且可读的思维链样本上做 SFT。 像 R1-Zero 那样进行面向推理的 RL，并额外加入语言一致性奖励。 从该模型进行拒绝采样，并加入通用数据，再做一轮 SFT。 最后一个 RL 阶段覆盖各类提示，兼顾推理、有用性和无害性。 还有两个发现对全局也很重要。论文通过在 R1 的输出上做普通 SFT，将其推理能力蒸馏到更小的开源模型中，并发现蒸馏比直接在小模型上做大规模 RL …"},{"id":"/learn/post-training/zh/#compare-h","page":"后训练：完整指南","section":"方法并排对比","url":"/learn/post-training/zh/#compare-h","kind":"section","text":"本文中的四类方法，与其说差别在数学（它们共享同一套数学），不如说在于需要什么，以及学习信号从哪里来。模型副本按完整大小计数；critic 往往更小或与策略共享网络；RLVR 描述的是奖励来源，可以与 PPO、GRPO 或其他优化器搭配。 方法 所需数据 内存中的模型 采样方式 学习信号 主要失败模式 SFT 提示–回复示范 1 个：策略 离线：固定数据集，teacher forcing 示范的对数似然 照搬数据中的缺陷；暴露偏差；新知识学得慢，并与更多幻觉相关 奖励模型 + PPO 排序比较（用于训练奖励模型）和提示 4 个：策略、参考模型、奖励模型、critic On-policy：每轮迭代都要生成 学到的奖励减去 KL 惩罚，再转化为 GAE advantage Reward hacking、长度偏差与谄媚；KL 失控；成本高、对调参敏感 DPO 偏好对 $(x,y^w ,y^l )$ 2 个：策略和参考模型 （参考模型的对数概率可预先计算） 离线：训练中不生成 每个偏好对的隐式奖励差 受限于所收集的样本对；缺少对自身输出的反馈；在近乎确定的偏好上可能过拟合 GRPO 配合 RLVR 带有可检查答案的提示，或一个奖励模型 2 个：策略和参考模型 （如用奖励模型则再加一个） On-policy：每个提示 $G$ 个样本 相对于组均值的奖励，无 critic …"},{"id":"/learn/post-training/zh/#practice-h","page":"后训练：完整指南","section":"实际运行：设置、成本、故障","url":"/learn/post-training/zh/#practice-h","kind":"section","text":"论文报告的设置 超参数的取值取决于模型、数据和代码实现，因此下表中的数值只是相应论文报告的参考点，而非推荐值。 设置 作用 报告的取值 来源 PPO 裁剪 $ϵ$ 每批数据最多能将每个动作的概率改变多少 0.2（在所比较的设置中效果最好） Schulman et al. (2017) GAE $λ$、折扣 $γ$ advantage 估计的偏差–方差权衡；有效视野 在其基准实验中 $λ = 0.95$、$γ = 0.99$ Schulman et al. (2017) RLHF 的 KL 权重 $β$ 策略与 SFT 模型之间的距离 0.02；PPO-ptx 的预训练混合系数为 27.8 Ouyang et al. (2022) 自适应 KL 不固定 $β$，而是让 KL 保持在目标值附近 在训练中动态调整 $β$，使 KL 接近目标值 Ziegler et al. (2019) DPO 的 $β$ 隐式 KL 约束的强度 默认 0.1；TL;DR 摘要任务为 0.5 Rafailov et al. (2023) GRPO 组大小 $G$、KL 权重 $β$ 每个提示用于构造 baseline 的样本数；策略与参考模型之间的距离 $G = 64$，$β = 0.04$ Shao et al. (2024) 解耦的裁剪范围 让低概率 token 的概率上升空间大于下降空间 …"},{"id":"/learn/post-training/zh/#evaluation-h","page":"后训练：完整指南","section":"后训练模型如何评测","url":"/learn/post-training/zh/#evaluation-h","kind":"section","text":"后训练改变的是行为，因此对它评测时衡量的也应是行为：人们更偏好哪个回答，以及回答是否正确。 偏好：人与模型评判者 人类胜率。将两个模型对同一提示的输出交给评审者，统计各自被偏好的频率。InstructGPT 最主要的结果正是这样一种比较 (Ouyang et al., 2022)。 竞技场排名。Chatbot Arena 收集用户与两个匿名模型对话后的成对投票，并对投票拟合 Bradley–Terry 模型来给模型排名 (Chiang et al., 2024)：这正是 §9 中奖励模型用到的那个模型，只不过这里是在给模型打分，而不是给回复打分。 模型评判者。一个强大的语言模型可以充当评判者。Zheng et al. (2023) 发现，强评判者与人类偏好一致的频率，与人类之间彼此一致的频率相当，同时还记录了位置偏差、冗长偏差和自我偏好偏差。由于评判者倾向于偏爱更长的回答，长度控制版本会对长度做校正 (Dubois et al., 2024)。 可验证的基准 当答案可以核验时，基准就不再需要评判者：GSM8K 中的小学数学应用题 (Cobbe et al., 2021)、MATH 中的竞赛数学 (Hendrycks et al., 2021)，以及 HumanEval 中带单元测试的编程题 (Chen et al., 2021)。它们正是 RLVR …"},{"id":"/learn/post-training/zh/#open-h","page":"后训练：完整指南","section":"开放问题","url":"/learn/post-training/zh/#open-h","kind":"section","text":"我们从 GPT-1 留下的问题出发：后训练是在教会模型新能力，还是在激发模型已有的能力？到目前为止，SFT 方面的证据偏向“激发”（§6），而同样的争论在 RL 上又重新展开（§24）。 RL 是在创造推理，还是在锐化推理？上文的 pass@$k$ 结果表明，在所研究的问题上，它起到的是锐化作用。更长、更广或设计不同的 RL 是否会改变这一点，仍是开放问题。 超越可验证奖励。可验证奖励覆盖数学、代码以及可检查的约束。人们想要的大部分东西，例如好的写作、可靠的建议或诚实的不确定性，都无法被机械地检查；这又把我们带回学习到的奖励及其失败模式。 优化什么。GRPO 及其后继方法与 DPO 家族之间的差别在于归一化、裁剪和损失聚合方式，看似细枝末节，却会改变行为。哪些选择重要、为何重要，仍在研究之中。 谁的偏好？单一奖励模型是在彼此存在分歧的人群上取平均。如何表示多元偏好，以及如何在人类难以评判的任务上监督模型，仍然悬而未决。 后训练至今的轨迹是：模仿好的答案，学会哪些答案更好，再让模型针对无法被糊弄的信号从自身的尝试中改进。每一步对人类标注者的要求都更少，对模型的要求都更多。 自测 经过 RLVR 之后，一个模型的 pass@1 上升了，但 pass@256 没有变化。这说明什么？ 这说明 RL …"},{"id":"/learn/post-training/zh/#summary-h","page":"后训练：完整指南","section":"要点","url":"/learn/post-training/zh/#summary-h","kind":"section","text":"方法 预训练决定模型知道什么；后训练改变的是模型在所有可能输出中实际给出哪一个。监督微调模仿示范答案。奖励模型从人类的比较中学习，PPO 针对它进行优化，同时用 KL 惩罚让模型不偏离起点。DPO 把奖励模型并入偏好对上的单一损失，GRPO 则用一组由检查器打分的样本取代学习得到的 critic。 共同之处 这些强化学习方法都是同一个策略梯度估计的变体，区别在于每个 log 概率前的权重如何构造。从一种方法到下一种，信号的来源依次从人类示范，到人类比较，再到程序可以检查的奖励。 开放问题 RL 是赋予模型新的推理能力，还是让已有的推理更可靠；如何为无法检查的品质设计奖励；目标函数中的哪些细节真正重要；单一奖励模型应当代表谁的偏好。详见开放问题。"},{"id":"/learn/post-training/zh/#references-h","page":"后训练：完整指南","section":"参考文献","url":"/learn/post-training/zh/#references-h","kind":"section","text":"Armen Aghajanyan, et al. (2021). Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning. ACL 2021. Mohammad Gheshlaghi Azar, et al. (2024). A General Theoretical Paradigm to Understand Learning from Human Preferences. AISTATS 2024. Yuntao Bai, et al. (2022). Constitutional AI: Harmlessness from AI Feedback. arXiv:2212.08073. Yuntao Bai, et al. (2022). Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback. arXiv:2204.05862. Ralph Allan Bradley, Milton E. Terry (1952). Rank Analysis of Incomplete Block Designs: I. The Method of …"},{"id":"/math_notes/br2207/","page":"BR2207 Quantitative Analysis: NTU Past-Year Papers","section":"","url":"/math_notes/br2207/","kind":"page","text":"Past-year papers for NTU BR2207 Quantitative Analysis: final exams 2022-23 to 2024-25. 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Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/br2210/#finals","page":"BR2210 Financial Markets and Products: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/br2210/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2024-25 Semester 2 Question paper — 2023-24 Semester 2 Question paper — 2022-23 Semester 2 Question paper —"},{"id":"/math_notes/br2211/","page":"BR2211 Financial and Risk Analytics I: NTU Past-Year Papers","section":"","url":"/math_notes/br2211/","kind":"page","text":"Past-year papers for NTU BR2211 Financial and Risk Analytics I: final exams 2022-23 to 2024-25. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/br2211/#finals","page":"BR2211 Financial and Risk Analytics I: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/br2211/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2024-25 Semester 2 Question paper — 2023-24 Semester 2 Question paper — 2022-23 Semester 2 Question paper —"},{"id":"/math_notes/br3208/","page":"BR3208 Operational Risk Management: NTU Past-Year Papers","section":"","url":"/math_notes/br3208/","kind":"page","text":"Past-year papers for NTU BR3208 Operational Risk Management: final exams 2022-23 to 2023-24. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/br3208/#finals","page":"BR3208 Operational Risk Management: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/br3208/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2023-24 Semester 1 Question paper — 2022-23 Semester 1 Question paper —"},{"id":"/math_notes/br3213/","page":"BR3213 Valuation and Risk Models: NTU Past-Year Papers","section":"","url":"/math_notes/br3213/","kind":"page","text":"Past-year papers for NTU BR3213 Valuation and Risk Models: final exams 2022-23 to 2024-25. 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Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh3500/#finals","page":"MH3500 Statistics: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/mh3500/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2024-25 Semester 2 Question paper — 2023-24 Semester 2 Question paper — 2022-23 Semester 2 Question paper —"},{"id":"/math_notes/mh3510/","page":"MH3510 Regression Analysis: NTU Past-Year Papers","section":"","url":"/math_notes/mh3510/","kind":"page","text":"Past-year papers for NTU MH3510 Regression Analysis: final exams 2022-23 to 2024-25. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh3510/#finals","page":"MH3510 Regression Analysis: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/mh3510/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2024-25 Semester 1 Question paper — 2022-23 Semester 1 Question paper —"},{"id":"/math_notes/mh3700/","page":"MH3700 Numerical Analysis I: NTU Past-Year Papers","section":"","url":"/math_notes/mh3700/","kind":"page","text":"Past-year papers for NTU MH3700 Numerical Analysis I: final exams 2022-23 to 2024-25. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh3700/#finals","page":"MH3700 Numerical Analysis I: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/mh3700/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2024-25 Semester 2 Question paper — 2023-24 Semester 2 Question paper — 2022-23 Semester 2 Question paper —"},{"id":"/math_notes/mh3701/","page":"MH3701 Basic Optimization: NTU Past-Year Papers","section":"","url":"/math_notes/mh3701/","kind":"page","text":"Past-year papers for NTU MH3701 Basic Optimization: final exams 2022-23 to 2024-25. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh3701/#finals","page":"MH3701 Basic Optimization: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/mh3701/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2024-25 Semester 2 Question paper — 2023-24 Semester 2 Question paper — 2022-23 Semester 2 Question paper —"},{"id":"/math_notes/mh4100/","page":"MH4100 Real Analysis II: NTU Past-Year Papers","section":"","url":"/math_notes/mh4100/","kind":"page","text":"Past-year papers for NTU MH4100 Real Analysis II: final exams 2022-23 to 2024-25. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh4100/#finals","page":"MH4100 Real Analysis II: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/mh4100/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2024-25 Semester 2 Question paper — 2023-24 Semester 2 Question paper — 2022-23 Semester 2 Question paper —"},{"id":"/math_notes/mh4110/","page":"MH4110 Partial Differential Equations: NTU Past-Year Papers","section":"","url":"/math_notes/mh4110/","kind":"page","text":"Past-year papers for NTU MH4110 Partial Differential Equations: final exams 2022-23 to 2024-25. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh4110/#finals","page":"MH4110 Partial Differential Equations: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/mh4110/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2024-25 Semester 2 Question paper — 2023-24 Semester 2 Question paper — 2022-23 Semester 2 Question paper —"},{"id":"/math_notes/mh4200/","page":"MH4200 Abstract Algebra II: NTU Past-Year Papers","section":"","url":"/math_notes/mh4200/","kind":"page","text":"Past-year papers for NTU MH4200 Abstract Algebra II: final exams 2022-23 to 2024-25. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh4200/#finals","page":"MH4200 Abstract Algebra II: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/mh4200/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2024-25 Semester 2 Question paper — 2023-24 Semester 2 Question paper — 2022-23 Semester 1 Question paper —"},{"id":"/math_notes/mh4300/","page":"MH4300 Combinatorics: NTU Past-Year Papers","section":"","url":"/math_notes/mh4300/","kind":"page","text":"Past-year papers for NTU MH4300 Combinatorics: final exams 2022-23 to 2024-25. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh4300/#finals","page":"MH4300 Combinatorics: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/mh4300/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2024-25 Semester 1 Question paper — 2023-24 Semester 1 Question paper — 2022-23 Semester 1 Question paper —"},{"id":"/math_notes/mh4301/","page":"MH4301 Set Theory and Logic: NTU Past-Year Papers","section":"","url":"/math_notes/mh4301/","kind":"page","text":"Past-year papers for NTU MH4301 Set Theory and Logic: final exams 2024-25. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh4301/#finals","page":"MH4301 Set Theory and Logic: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/mh4301/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2024-25 Semester 1 Question paper —"},{"id":"/math_notes/mh4311/","page":"MH4311 Cryptography: NTU Past-Year Papers","section":"","url":"/math_notes/mh4311/","kind":"page","text":"Past-year papers for NTU MH4311 Cryptography: final exams 2022-23 to 2024-25. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh4311/#finals","page":"MH4311 Cryptography: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/mh4311/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2024-25 Semester 1 Question paper — 2023-24 Semester 1 Question paper — 2022-23 Semester 1 Question paper —"},{"id":"/math_notes/mh4320/","page":"MH4320 Computational Economics: NTU Past-Year Papers","section":"","url":"/math_notes/mh4320/","kind":"page","text":"Past-year papers for NTU MH4320 Computational Economics: final exams 2023-24 to 2024-25. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh4320/#finals","page":"MH4320 Computational Economics: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/mh4320/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2024-25 Semester 1 Question paper — 2023-24 Semester 1 Question paper —"},{"id":"/math_notes/mh4500/","page":"MH4500 Time Series Analysis: NTU Past-Year Papers","section":"","url":"/math_notes/mh4500/","kind":"page","text":"Past-year papers for NTU MH4500 Time Series Analysis: final exams 2022-23. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh4500/#finals","page":"MH4500 Time Series Analysis: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/mh4500/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2022-23 Semester 2 Question paper —"},{"id":"/math_notes/mh4501/","page":"MH4501 Multivariate Analysis: NTU Past-Year Papers","section":"","url":"/math_notes/mh4501/","kind":"page","text":"Past-year papers for NTU MH4501 Multivariate Analysis: final exams 2022-23 to 2024-25. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh4501/#finals","page":"MH4501 Multivariate Analysis: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/mh4501/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2024-25 Semester 2 Question paper — 2023-24 Semester 2 Question paper — 2022-23 Semester 2 Question paper —"},{"id":"/math_notes/mh4511/","page":"MH4511 Sampling & Survey: NTU Past-Year Papers","section":"","url":"/math_notes/mh4511/","kind":"page","text":"Past-year papers for NTU MH4511 Sampling & Survey: final exams 2022-23 to 2024-25. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh4511/#finals","page":"MH4511 Sampling & Survey: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/mh4511/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2024-25 Semester 1 Question paper — 2023-24 Semester 1 Question paper — 2022-23 Semester 1 Question paper —"},{"id":"/math_notes/mh4512/","page":"MH4512 Clinical Trials: NTU Past-Year Papers","section":"","url":"/math_notes/mh4512/","kind":"page","text":"Past-year papers for NTU MH4512 Clinical Trials: final exams 2022-23 to 2024-25. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh4512/#finals","page":"MH4512 Clinical Trials: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/mh4512/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2024-25 Semester 2 Question paper — 2023-24 Semester 2 Question paper — 2022-23 Semester 2 Question paper —"},{"id":"/math_notes/mh4514/","page":"MH4514 Financial Mathematics: NTU Past-Year Papers","section":"","url":"/math_notes/mh4514/","kind":"page","text":"Past-year papers for NTU MH4514 Financial Mathematics: final exams 2022-23 to 2024-25 and revision notes. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh4514/#finals","page":"MH4514 Financial Mathematics: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/mh4514/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2024-25 Semester 2 Question paper — 2023-24 Semester 2 Question paper — 2022-23 Semester 2 Question paper —"},{"id":"/math_notes/mh4514/#notes","page":"MH4514 Financial Mathematics: NTU Past-Year Papers","section":"Revision notes and cheat sheets","url":"/math_notes/mh4514/#notes","kind":"section","text":"Revision notes"},{"id":"/math_notes/mh4517/","page":"MH4517 Data Applications in Natural Sciences: NTU Past-Year Papers","section":"","url":"/math_notes/mh4517/","kind":"page","text":"Past-year papers for NTU MH4517 Data Applications in Natural Sciences: final exams 2022-23. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh4517/#finals","page":"MH4517 Data Applications in Natural Sciences: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/mh4517/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2022-23 Semester 2 Question paper —"},{"id":"/math_notes/mh4518/","page":"MH4518 Simulation Techniques in Finance: NTU Past-Year Papers","section":"","url":"/math_notes/mh4518/","kind":"page","text":"Past-year papers for NTU MH4518 Simulation Techniques in Finance: final exams 2022-23 to 2024-25. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh4518/#finals","page":"MH4518 Simulation Techniques in Finance: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/mh4518/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2024-25 Semester 1 Question paper — 2023-24 Semester 1 Question paper — 2022-23 Semester 1 Question paper —"},{"id":"/math_notes/mh4521/","page":"MH4521 Reinforcement Learning: NTU Past-Year Papers","section":"","url":"/math_notes/mh4521/","kind":"page","text":"Past-year papers for NTU MH4521 Reinforcement Learning: final exams 2024-25. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh4521/#finals","page":"MH4521 Reinforcement Learning: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/mh4521/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2024-25 Semester 1 Question paper —"},{"id":"/math_notes/mh4522/","page":"MH4522 Spatial Data Science: NTU Past-Year Papers","section":"","url":"/math_notes/mh4522/","kind":"page","text":"Past-year papers for NTU MH4522 Spatial Data Science: final exams 2024-25. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh4522/#finals","page":"MH4522 Spatial Data Science: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/mh4522/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2024-25 Semester 2 Question paper —"},{"id":"/math_notes/mh4600/","page":"MH4600 Algebraic Topology: NTU Past-Year Papers","section":"","url":"/math_notes/mh4600/","kind":"page","text":"Past-year papers for NTU MH4600 Algebraic Topology: final exams 2022-23 to 2024-25. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh4600/#finals","page":"MH4600 Algebraic Topology: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/mh4600/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2024-25 Semester 2 Question paper — 2022-23 Semester 2 Question paper —"},{"id":"/math_notes/mh4601/","page":"MH4601 Differential Geometry: NTU Past-Year Papers","section":"","url":"/math_notes/mh4601/","kind":"page","text":"Past-year papers for NTU MH4601 Differential Geometry: final exams 2023-24. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh4601/#finals","page":"MH4601 Differential Geometry: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/mh4601/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2023-24 Semester 2 Question paper —"},{"id":"/math_notes/mh4700/","page":"MH4700 Numerical Analysis II: NTU Past-Year Papers","section":"","url":"/math_notes/mh4700/","kind":"page","text":"Past-year papers for NTU MH4700 Numerical Analysis II: final exams 2022-23 to 2024-25. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh4700/#finals","page":"MH4700 Numerical Analysis II: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/mh4700/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2024-25 Semester 1 Question paper — 2023-24 Semester 1 Question paper — 2022-23 Semester 1 Question paper —"},{"id":"/math_notes/mh4701/","page":"MH4701 Mathematical Programming: NTU Past-Year Papers","section":"","url":"/math_notes/mh4701/","kind":"page","text":"Past-year papers for NTU MH4701 Mathematical Programming: final exams 2022-23 to 2024-25. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh4701/#finals","page":"MH4701 Mathematical Programming: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/mh4701/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2024-25 Semester 1 Question paper — 2023-24 Semester 1 Question paper — 2022-23 Semester 1 Question paper —"},{"id":"/math_notes/mh4930/","page":"MH4930 Special Topics in Mathematics: NTU Past-Year Papers","section":"","url":"/math_notes/mh4930/","kind":"page","text":"Past-year papers for NTU MH4930 Special Topics in Mathematics: final exams 2022-23. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh4930/#finals","page":"MH4930 Special Topics in Mathematics: NTU Past-Year Papers","section":"Final examinations","url":"/math_notes/mh4930/#finals","kind":"section","text":"Academic year Semester Question paper Solutions 2022-23 Semester 1 Question paper —"},{"id":"/math_notes/mh5100/","page":"MH5100 Advanced Investigations in Calculus I: NTU Notes and Solutions","section":"","url":"/math_notes/mh5100/","kind":"page","text":"Notes and solutions for NTU MH5100 Advanced Investigations in Calculus I: revision notes and 9 problem sheets, with 8 solutions. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh5100/#notes","page":"MH5100 Advanced Investigations in Calculus I: NTU Notes and Solutions","section":"Revision notes and cheat sheets","url":"/math_notes/mh5100/#notes","kind":"section","text":"Revision notes"},{"id":"/math_notes/mh5100/#problem-sheets","page":"MH5100 Advanced Investigations in Calculus I: NTU Notes and Solutions","section":"Problem sheets","url":"/math_notes/mh5100/#problem-sheets","kind":"section","text":"Problem sheet Question paper Solutions Week 2 Question paper/MH5100_AdvancedInvestigationsinCalculusI_25-26_Sem1_ProblemSheet_Week%202_QuestionPaper.pdf) Solution/MH5100_AdvancedInvestigationsinCalculusI_25-26_Sem1_ProblemSheet_Week%202_Solution.pdf) Week 3 Question paper/MH5100_AdvancedInvestigationsinCalculusI_25-26_Sem1_ProblemSheet_Week%203_QuestionPaper.pdf) Solution/MH5100_AdvancedInvestigationsinCalculusI_25-26_Sem1_ProblemSheet_Week%203_Solution.pdf) Week 4 Question paper/MH5100_AdvancedInvestigationsinCalculusI_25-26_Sem1_ProblemSheet_Week%204_QuestionPaper.pdf) …"},{"id":"/math_notes/mh5200/","page":"MH5200 Advanced Investigations in Linear Algebra I: NTU Notes and Solutions","section":"","url":"/math_notes/mh5200/","kind":"page","text":"Notes and solutions for NTU MH5200 Advanced Investigations in Linear Algebra I: revision notes and 8 problem sheets, with 8 solutions written by QRS. Free PDF downloads from QRS Math Notes."},{"id":"/math_notes/mh5200/#notes","page":"MH5200 Advanced Investigations in Linear Algebra I: NTU Notes and Solutions","section":"Revision notes and cheat sheets","url":"/math_notes/mh5200/#notes","kind":"section","text":"Revision notes"},{"id":"/math_notes/mh5200/#problem-sheets","page":"MH5200 Advanced Investigations in Linear Algebra I: NTU Notes and Solutions","section":"Problem sheets","url":"/math_notes/mh5200/#problem-sheets","kind":"section","text":"Problem sheet Solutions Problem sheet 1 Solution by QRS Problem sheet 2 Solution by QRS Problem sheet 3 Solution by QRS Problem sheet 4 Solution by QRS Problem sheet 5 Solution by QRS Problem sheet 6 Solution by QRS Problem sheet 7 Solution by QRS Problem sheet 8 Solution by QRS"},{"id":"/news/dec2025-major-update/","page":"QRS@NTU Major Update","section":"","url":"/news/dec2025-major-update/","kind":"page","text":"The December 2025 QRS@NTU update: website fixes to folders, search and ranking, and final examination papers for over 70 SPMS and NBS courses."},{"id":"/news/dec2025-major-update/#✔ Folder Button (Expandable Sections) — Fixed","page":"QRS@NTU Major Update","section":"✔ Folder Button (Expandable Sections) — Fixed","url":"/news/dec2025-major-update/","kind":"section","text":"Previously, some folders failed to expand or load their contents. This has now been resolved, and all nested course directories open correctly without refresh errors."},{"id":"/news/dec2025-major-update/#✔ Search Function — Fully Restored","page":"QRS@NTU Major Update","section":"✔ Search Function — Fully Restored","url":"/news/dec2025-major-update/","kind":"section","text":"Search now properly indexes every file across: Finals archives Revision notes Problem sheets Solutions (typed and handwritten) Users should experience significantly more reliable and accurate search results."},{"id":"/news/dec2025-major-update/#✔ Ranking Logic — Redesigned","page":"QRS@NTU Major Update","section":"✔ Ranking Logic — Redesigned","url":"/news/dec2025-major-update/","kind":"section","text":"Courses are now automatically ranked based on number of files available, allowing students to quickly identify: Modules with comprehensive resources Newly updated courses Courses requiring further expansion This upgrade also ensures consistency as new materials are added. 2. Finals Archive Expansion (AY22/23 – AY24/25) Final examination papers have been added for over 70 SPMS and NBS courses, including multiple academic years for each module. Some of the major courses receiving full finals coverage include: SPMS Mathematics MH1201, MH1301, MH1403 MH2500, MH3100, MH3300, MH3500 MH3700, MH3701 …"},{"id":"/news/dec2025-major-update/#📘 MH1300 — Enhanced Revision Notes","page":"QRS@NTU Major Update","section":"📘 MH1300 — Enhanced Revision Notes","url":"/news/dec2025-major-update/","kind":"section","text":"The MH1300 Foundations of Mathematics notes have been substantially expanded: More step-by-step proofs Additional examples Highlighted standard methods (truth tables, modular arithmetic, induction, Euclid algorithm, etc.) Improved visual structure for clarity Added unofficial Mark Scheme"},{"id":"/news/dec2025-major-update/#📘 MH4514 — New Revision Notes","page":"QRS@NTU Major Update","section":"📘 MH4514 — New Revision Notes","url":"/news/dec2025-major-update/","kind":"section","text":"Complete revision notes for Financial Mathematics (MH4514) have been added: Coverage of all major topics Clean structure with definitions, examples, and key formulas Consistent layout following QRS@NTU’s latest formatting standards"},{"id":"/news/dec2025-major-update/#📘 MH5200 — New Revision Notes","page":"QRS@NTU Major Update","section":"📘 MH5200 — New Revision Notes","url":"/news/dec2025-major-update/","kind":"section","text":"Full revision notes for Advanced Investigations in Linear Algebra I (MH5200) are now available: Expanded explanations Intuitive interpretations of abstract concepts Additional theorems, examples, and diagrams Polished LaTeX with unified formatting"},{"id":"/news/dec2025-major-update/#📘 MH5200 Problem Sheet Solutions Enhanced","page":"QRS@NTU Major Update","section":"📘 MH5200 Problem Sheet Solutions Enhanced","url":"/news/dec2025-major-update/","kind":"section","text":"At least two solution methods for each problem (e.g., algebraic vs geometric, or direct vs spectral approach) Clarified reasoning steps More intermediate derivations Added alternative insights, interpretations, and common pitfalls Updated notation to match advanced linear algebra conventions This makes MH5200’s solution set one of the most comprehensive in QRS@NTU. 4. Marking Schemes Included in New Solutions Where feasible, mark distributions are now included in: Finals solutions Problem sheet solutions Selected revision notes This provides clearer expectations on exam-style writing and …"},{"id":"/news/events-guide-2026-jan/","page":"Quant & FinTech Events Guide","section":"","url":"/news/events-guide-2026-jan/","kind":"page","text":"Quant and fintech events for students in January 2026: campus events, recruiting programmes, conferences and industry expos."},{"id":"/news/events-guide-2026-jan/#🗓️ Quick Reference","page":"Quant & FinTech Events Guide","section":"🗓️ Quick Reference","url":"/news/events-guide-2026-jan/","kind":"section","text":"Date Event Location Registration ROI Jan 28 🏢 Jane Street @ NUS Career Fair 🇸🇬 Singapore (NUS) 📝 Sign up required ⭐⭐ Feb 6 💻 Optiver Tech Talk (Virtual) 🌐 Zoom 🔗 Open ⭐⭐ Feb 11 🧮 Jane Street Estimathon® 🇸🇬 NTU, Singapore 📝 Due Feb 9 EOD 🔥🔥🔥 Feb 27 🎯 Citadel Discover 🇸🇬 Singapore ⏰ Due Feb 1 🔥🔥🔥 Mar 20-21 🎯 Citadel Discover 🇭🇰 Hong Kong ⏰ Due Mar 1 🔥🔥🔥 Mar 29-Apr 1 💰 Jane Street FTTP 🇭🇰 Hong Kong ⏰ Due Feb 15 🔥🔥🔥 Jun 14-15 🏆 5th HK FinTech & AI Conf 🇭🇰 CityU, Hong Kong 📜 Papers due Mar 1 ⭐⭐ Jul 23-24 🌐 WikiEXPO Hong Kong 🇭🇰 Hong Kong 🆓 Open ⭐⭐ Nov 2-6 👑 HK FinTech Week 2026 🇭🇰 Hong Kong 📋 …"},{"id":"/news/events-guide-2026-jan/#📋 SECTION 1: CAMPUS EVENTS","page":"Quant & FinTech Events Guide","section":"📋 SECTION 1: CAMPUS EVENTS","url":"/news/events-guide-2026-jan/","kind":"section","text":"Event 1.1: Jane Street @ NUS Computing Career Fair Organizer: Jane Street + NUS School of Computing Date: Tuesday, January 28, 2026 careerfair.comp.nus.edu Time & Time Zone: 12:00 PM – 5:00 PM SGT Location: Physical COM3 Multi-Purpose Hall & Foyer, National University of Singapore careerfair.comp.nus.edu What It's About: Campus fair booth with Jane Street recruiters. Opportunity to collect company materials, ask questions about roles, and network with representatives. Part of a larger computing career fair with 50+ companies. careerfair.comp.nus.edu Target Audience: All NUS computing …"},{"id":"/news/events-guide-2026-jan/#📋 SECTION 2: RECRUITING PROGRAMS","page":"Quant & FinTech Events Guide","section":"📋 SECTION 2: RECRUITING PROGRAMS","url":"/news/events-guide-2026-jan/","kind":"section","text":"Event 2.1: Jane Street FTTP (First-Year Trading & Technology Program) – Hong Kong Organizer: Jane Street Date: Saturday, March 29 – Tuesday, April 1, 2026 janestreet Time & Time Zone: Multi-day program (exact daily schedule shared with admitted students) Location: Physical Jane Street Hong Kong Office, Chater House, Central janestreet What It's About: Immersive 3-day program for first-year university students covering Jane Street's trading and technology models through classes, mock trading simulations, and firm culture exposure. No prior finance knowledge required. janestreet Target …"},{"id":"/news/events-guide-2026-jan/#📋 SECTION 3: ACADEMIC & RESEARCH CONFERENCES","page":"Quant & FinTech Events Guide","section":"📋 SECTION 3: ACADEMIC & RESEARCH CONFERENCES","url":"/news/events-guide-2026-jan/","kind":"section","text":"Event 3.1: 5th Annual Hong Kong Conference on FinTech and AI in Finance Organizer: City University of Hong Kong (CityU) Date: Saturday, June 14 – Sunday, June 15, 2026 cityuhkfintech Time & Time Zone: Full-day conference (exact schedule TBA) Location: Physical City University of Hong Kong campus What It's About: Premier academic-practitioner forum featuring frontier research in FinTech, AI applications in finance, machine learning in financial econometrics, blockchain/digital assets, and big data in empirical finance. Includes keynote by Dr. Allan Timmermann (UC San Diego), 3 invited …"},{"id":"/news/events-guide-2026-jan/#📋 SECTION 4: INDUSTRY EXPOS & NETWORKING EVENTS","page":"Quant & FinTech Events Guide","section":"📋 SECTION 4: INDUSTRY EXPOS & NETWORKING EVENTS","url":"/news/events-guide-2026-jan/","kind":"section","text":"Event 4.1: WikiEXPO Hong Kong 2026 (Wiki Finance Expo) Organizer: WikiEXPO Date: Wednesday, July 23 – Thursday, July 24, 2026 weex Time & Time Zone: 10:00 AM – 6:00 PM HKT (both days) linkedin Location: Physical Hopewell Hotel, Hong Kong weex What It's About: Asia's largest FinTech and Web3.0 expo attracting 12,000+ professionals, 200+ speakers, and 100+ exhibitors from 120+ countries. Topics include FinTech, AI in finance, cryptocurrency & digital assets, forex & liquidity, Web3 & DeFi, next-gen payments, and ESG in finance. Features keynotes, panels, fireside chats, and networking sessions …"},{"id":"/news/icaif-2026-workshops/","page":"Six works accepted to ICAIF 2026 workshops","section":"","url":"/news/icaif-2026-workshops/","kind":"page","text":"Six works from QRS research programmes were accepted to ICAIF 2026 workshops, including the first first-author workshop papers of three 2026 Fall #2 Research Academy members."},{"id":"/news/","page":"News","section":"","url":"/news/","kind":"page","text":"News from QRS: research, releases, events and guides, with search and filters and an RSS feed."},{"id":"/news/neurips-2026-attendee-guide/","page":"NeurIPS 2026 Attendee Guide for Sydney, Atlanta and Paris","section":"","url":"/news/neurips-2026-attendee-guide/","kind":"page","text":"The Quantitative Research Society, Singapore, has published a free, unofficial guide for NeurIPS 2026 in Sydney, Atlanta and Paris: schedule, city guides, hotels, presenting and data for AI assistants."},{"id":"/news/neurips-2026-attendee-guide/#What the guide covers","page":"NeurIPS 2026 Attendee Guide for Sydney, Atlanta and Paris","section":"What the guide covers","url":"/news/neurips-2026-attendee-guide/","kind":"section","text":"Schedule: every session, paper and event at the three sites, read from the official NeurIPS pages and updated every six hours, and every two hours during the conference. City guides for Sydney, Atlanta and Paris: the key facts at a glance, each day of the conference with its main sessions, times and rooms, getting to the venue, entry rules, food, and what is still to be published. My plan: a personal schedule that shows clashes and can be added to a calendar, so changes to rooms and times reach your phone. Hotels: hotels in each city compared by price, door-to-door commute and breakfast, with …"},{"id":"/news/neurips-2026-workshops/","page":"Five works accepted to NeurIPS 2026 workshops","section":"","url":"/news/neurips-2026-workshops/","kind":"page","text":"Five works from the QRS Research Academy's inaugural cohort were accepted to NeurIPS 2026 workshops."},{"id":"/news/neurips-2026-workshops/#The accepted works","page":"Five works accepted to NeurIPS 2026 workshops","section":"The accepted works","url":"/news/neurips-2026-workshops/","kind":"section","text":"Geometric Attention Fine-Tuning Is Representation-Relative: Autonomous ML Research with AI-Native Workflow AutoMLR Workshop, NeurIPS 2026 · AI Native Workflow PolicyAttention: Robustness and Failure Modes of Softmax Policy Improvement EvoRobust Workshop, NeurIPS 2026 · PolicyAttention PolicyAttention: When Softmax Attention Becomes Policy Improvement PTA Workshop, NeurIPS 2026 · PolicyAttention Diverse Scenarios, Selective Evaluation: Certified Spectral-Risk Decisions under Costly Robustness Tests EvoRobust Workshop, NeurIPS 2026 · RiskHedge The Approximation Rank of Softmax Attention: Sharp …"},{"id":"/people/annie-huaiyu-wang/","page":"Annie Huaiyu Wang","section":"","url":"/people/annie-huaiyu-wang/","kind":"person","text":"QRS Research Academy Member"},{"id":"/people/annie-huaiyu-wang/#About","page":"Annie Huaiyu Wang","section":"About","url":"/people/annie-huaiyu-wang/","kind":"section","text":"Annie is a first-year undergraduate in Mathematics and Applied Mathematics at Tsinghua University, in Qiuzhen College and the Yau Mathematical Sciences Leaders Program. Her interests include quantitative finance, risk and mathematical machine learning. She has previously worked on machine learning for mining signal peptides in plant genomes and on agent tools for meteorological data. Projects · Publications"},{"id":"/people/annie-huaiyu-wang/#Projects","page":"Annie Huaiyu Wang","section":"Projects","url":"/people/annie-huaiyu-wang/","kind":"section","text":"FRTBTrace: Active research on faithful, auditable, trade-level FRTB attribution. Status: active. People: Yuhe Sui, Yingzhi Tang."},{"id":"/people/duy-anh-nguyen/","page":"Duy Anh Nguyen","section":"","url":"/people/duy-anh-nguyen/","kind":"person","text":"BS, Nanyang Technological University"},{"id":"/people/","page":"People","section":"","url":"/people/","kind":"page","text":"Meet QRS@NTU officers and QRS researchers, and explore their profiles, projects, and publications."},{"id":"/people/#Officers","page":"People","section":"Officers","url":"/people/","kind":"section","text":"Yuhe Sui President & Founder, QRS@NTU · Principal Researcher, Quantitative Research Society Wang Zimeng NUS Sub-branch Coordinator Luis Ji QRS@NTU Mi Zeyuan Vice President, QRS@NTU Xinyue Wu QRS@NTU"},{"id":"/people/#researchers-section","page":"People","section":"Researchers","url":"/people/#researchers-section","kind":"section","text":"Jianing Zhang Researcher, Quantitative Research Society Yingzhi Tang Researcher, Quantitative Research Society QRS Research Academy"},{"id":"/people/#branches-section","page":"People","section":"Other School Branches","url":"/people/#branches-section","kind":"section","text":"QRS@NUS QRS@NTU (Taiwan) QRS@CMU — Coming soon QRS@CUHKSZ 量化研究协会@港中深 — Coming soon QRS@FDU 量化研究协会@复旦 — Coming soon QRS@SJTU 量化研究协会@交大 — Coming soon"},{"id":"/people/#People","page":"People","section":"People","url":"/people/","kind":"section","text":"Yuhe Sui: President & Founder, QRS@NTU; Principal Researcher, Quantitative Research Society Jianing Zhang: Researcher, Quantitative Research Society Danlin Chen Shufang Chen: QRS Research Academy Member Xiaotong Li: QRS Research Academy Member Wang Zimeng: NUS Sub-branch Coordinator; QRS Research Academy Member Duy Anh Nguyen Luis Ji. QRS@NTU Mi Zeyuan: Vice President, QRS@NTU Yingzhi Tang: Researcher, Quantitative Research Society Xinyue Wu: QRS Research Academy Member. QRS@NTU Jingshu Liu: QRS Research Academy Member Yizhe Chia: QRS Research Academy Member Annie Huaiyu Wang: QRS Research …"},{"id":"/people/jingshu-liu/","page":"Jingshu Liu","section":"","url":"/people/jingshu-liu/","kind":"person","text":"QRS Research Academy Member"},{"id":"/people/jingshu-liu/#Projects","page":"Jingshu Liu","section":"Projects","url":"/people/jingshu-liu/","kind":"section","text":"SoftRank: Theoretical research on softmax-attention approximation rank, support geometry, and robust interaction dimension. Status: active. People: Yuhe Sui, Jianing Zhang, Yingzhi Tang."},{"id":"/people/luis-ji/","page":"Luis Ji","section":"","url":"/people/luis-ji/","kind":"person","text":"QRS@NTU"},{"id":"/people/luis-ji/#About","page":"Luis Ji","section":"About","url":"/people/luis-ji/","kind":"section","text":"Happy to connect. Projects · Publications"},{"id":"/people/luis-ji/#Projects","page":"Luis Ji","section":"Projects","url":"/people/luis-ji/","kind":"section","text":"CFFA 2026 — China Future Financial Analyst Competition: • Built a Greenwashing Risk Score across 1,676 Chinese green-bond issuances (2016–2025), using issue-spread regressions and portfolio sorts. • Pricing effects are weak unconditionally, but meaningful within credit-risk buckets after controls. Status: active."},{"id":"/people/mi-zeyuan/","page":"Mi Zeyuan","section":"","url":"/people/mi-zeyuan/","kind":"person","text":"Vice President, QRS@NTU"},{"id":"/people/mi-zeyuan/#About","page":"Mi Zeyuan","section":"About","url":"/people/mi-zeyuan/","kind":"section","text":"Mi studies Accountancy and Data Science & Artificial Intelligence at Nanyang Technological University, with an interest in quantitative finance. Through URECA, Mi researches volatility pricing and leverage-decay risk in leveraged ETF options, and has worked on systematic investment strategies with the Nanyang Student Investment Fund. Technical interests include statistical modelling and using mathematical and computational methods to study financial markets. Projects · Publications"},{"id":"/people/mi-zeyuan/#Projects","page":"Mi Zeyuan","section":"Projects","url":"/people/mi-zeyuan/","kind":"section","text":"RiskHedge: Research on spectral-risk decisions, diverse scenarios, and selective robustness evaluation. Status: active. People: Yuhe Sui, Yingzhi Tang, Jianing Zhang, Mi Zeyuan."},{"id":"/people/shufang-chen/","page":"Shufang Chen","section":"","url":"/people/shufang-chen/","kind":"person","text":"QRS Research Academy Member"},{"id":"/people/shufang-chen/#Projects","page":"Shufang Chen","section":"Projects","url":"/people/shufang-chen/","kind":"section","text":"AI Native Workflow: Research on hierarchical, verification-gated and recoverable workflows for scaling long-horizon AI-assisted research and agent execution. Status: active. People: Yuhe Sui, Jianing Zhang, Shufang Chen, Danlin Chen, Wang Zimeng, Xiaotong Li. PolicyAttention: Research on softmax policy improvement, its robustness, and its failure modes. Status: active. People: Yuhe Sui, Shufang Chen, Yingzhi Tang, Xinyue Wu."},{"id":"/people/shufang-chen/#Publications","page":"Shufang Chen","section":"Publications","url":"/people/shufang-chen/","kind":"section","text":"Geometric Attention Fine-Tuning Is Representation-Relative: Autonomous ML Research with AI-Native Workflow (2026). Yuhe Sui, Jianing Zhang, Shufang Chen, Xiaotong Li, Wang Zimeng. AutoMLR Workshop, NeurIPS 2026. Accepted. OpenReview"},{"id":"/people/wang-zimeng/","page":"Wang Zimeng","section":"","url":"/people/wang-zimeng/","kind":"person","text":"NUS Sub-branch Coordinator; QRS Research Academy Member"},{"id":"/people/wang-zimeng/#Projects","page":"Wang Zimeng","section":"Projects","url":"/people/wang-zimeng/","kind":"section","text":"AI Native Workflow: Research on hierarchical, verification-gated and recoverable workflows for scaling long-horizon AI-assisted research and agent execution. Status: active. People: Yuhe Sui, Jianing Zhang, Shufang Chen, Danlin Chen, Wang Zimeng, Xiaotong Li. RiskHedge: Research on spectral-risk decisions, diverse scenarios, and selective robustness evaluation. Status: active. People: Yuhe Sui, Yingzhi Tang, Jianing Zhang, Mi Zeyuan. CFFA 2026 — China Future Financial Analyst Competition: • Built a Greenwashing Risk Score across 1,676 Chinese green-bond issuances (2016–2025), using …"},{"id":"/people/wang-zimeng/#Publications","page":"Wang Zimeng","section":"Publications","url":"/people/wang-zimeng/","kind":"section","text":"Geometric Attention Fine-Tuning Is Representation-Relative: Autonomous ML Research with AI-Native Workflow (2026). Yuhe Sui, Jianing Zhang, Shufang Chen, Xiaotong Li, Wang Zimeng. AutoMLR Workshop, NeurIPS 2026. Accepted. OpenReview"},{"id":"/people/xiaotong-li/","page":"Xiaotong Li","section":"","url":"/people/xiaotong-li/","kind":"person","text":"QRS Research Academy Member"},{"id":"/people/xiaotong-li/#Projects","page":"Xiaotong Li","section":"Projects","url":"/people/xiaotong-li/","kind":"section","text":"AI Native Workflow: Research on hierarchical, verification-gated and recoverable workflows for scaling long-horizon AI-assisted research and agent execution. Status: active. People: Yuhe Sui, Jianing Zhang, Shufang Chen, Danlin Chen, Wang Zimeng, Xiaotong Li. GeoAttention: Research on attention geometry, representation-relative identifiability, and geometry-adaptive prediction. Status: active. People: Yuhe Sui, Jianing Zhang, Xiaotong Li."},{"id":"/people/xiaotong-li/#Publications","page":"Xiaotong Li","section":"Publications","url":"/people/xiaotong-li/","kind":"section","text":"Geometric Attention Fine-Tuning Is Representation-Relative: Autonomous ML Research with AI-Native Workflow (2026). Yuhe Sui, Jianing Zhang, Shufang Chen, Xiaotong Li, Wang Zimeng. AutoMLR Workshop, NeurIPS 2026. Accepted. OpenReview"},{"id":"/people/xinyue-wu/","page":"Xinyue Wu","section":"","url":"/people/xinyue-wu/","kind":"person","text":"QRS Research Academy Member; QRS@NTU"},{"id":"/people/xinyue-wu/#Projects","page":"Xinyue Wu","section":"Projects","url":"/people/xinyue-wu/","kind":"section","text":"PolicyAttention: Research on softmax policy improvement, its robustness, and its failure modes. Status: active. People: Yuhe Sui, Shufang Chen, Yingzhi Tang, Xinyue Wu."},{"id":"/people/xinyue-wu/#Publications","page":"Xinyue Wu","section":"Publications","url":"/people/xinyue-wu/","kind":"section","text":"PolicyAttention: Robustness and Failure Modes of Softmax Policy Improvement (2026). Yuhe Sui, Yingzhi Tang, Xinyue Wu. EvoRobust Workshop, NeurIPS 2026. Accepted. OpenReview"},{"id":"/people/yizhe-chia/","page":"Yizhe Chia","section":"","url":"/people/yizhe-chia/","kind":"person","text":"QRS Research Academy Member"},{"id":"/people/yizhe-chia/#About","page":"Yizhe Chia","section":"About","url":"/people/yizhe-chia/","kind":"section","text":"An early fascination with the Pythagorean theorem inspired Yizhe to study Mathematical Sciences. Yizhe is interested in exploring connections across mathematics and applying mathematical ideas to practical problems. Projects · Publications"},{"id":"/people/yizhe-chia/#Projects","page":"Yizhe Chia","section":"Projects","url":"/people/yizhe-chia/","kind":"section","text":"AI Native Workflow: Research on hierarchical, verification-gated and recoverable workflows for scaling long-horizon AI-assisted research and agent execution. Status: active. People: Yuhe Sui, Jianing Zhang, Shufang Chen, Danlin Chen, Wang Zimeng, Xiaotong Li."},{"id":"/privacy/","page":"Privacy","section":"","url":"/privacy/","kind":"page","text":"How the Quantitative Research Society handles personal data: the website, Research Academy applications and Google account data."},{"id":"/privacy/#This website","page":"Privacy","section":"This website","url":"/privacy/","kind":"section","text":"qrsntu.org sets no tracking cookies and runs no analytics or advertising scripts. Our hosting provider, Cloudflare, processes standard request data such as IP addresses to serve and protect the site."},{"id":"/privacy/#Research Academy applications","page":"Privacy","section":"Research Academy applications","url":"/privacy/","kind":"section","text":"When you apply to the QRS Research Academy we collect what you submit: your name, email addresses, university, programme and year of study, availability, the answers on the application form, your résumé, and, if you are invited, your Online Assessment answers and timings and your Research Assessment submission. The Online Assessment also records interactions with the assessment page, such as leaving the page or pasting text, to help us review attempts fairly. We use this information only to run the selection and to contact you about it. It is seen by the selection committee and is never sold …"},{"id":"/privacy/#Google account data","page":"Privacy","section":"Google account data","url":"/privacy/","kind":"section","text":"Our internal tools sign in with the Society's own Google account, with read-only access, to fetch application form responses and the résumés uploaded with them. Committee members may also sign in with Google to reach the committee site, which uses only their email address to confirm access. We do not access applicants' Google accounts. Our use of information received from Google APIs adheres to the Google API Services User Data Policy, including the Limited Use requirements. This data is used only for the selection described above and is not transferred to others or used for advertising."},{"id":"/privacy/#Your choices","page":"Privacy","section":"Your choices","url":"/privacy/","kind":"section","text":"You may ask to see, correct or delete your data, or withdraw an application, at any time by writing to contact@qrsntu.org. Last updated 12 November 2026."},{"id":"/programmes/","page":"Programmes","section":"","url":"/programmes/","kind":"page","text":"The QRS Research Academy is QRS's research programme for students, with applications for 2026 Fall #4, and a path to QRS Researcher roles."},{"id":"/projects/ai-native-workflow/","page":"AI Native Workflow","section":"","url":"/projects/ai-native-workflow/","kind":"page","text":"Research on hierarchical, verification-gated and recoverable workflows for scaling long-horizon AI-assisted research and agent execution."},{"id":"/projects/ai-native-workflow/#Accepted Research","page":"AI Native Workflow","section":"Accepted Research","url":"/projects/ai-native-workflow/","kind":"section","text":"### Geometric Attention Fine-Tuning Is Representation-Relative: Autonomous ML Research with AI-Native Workflow Yuhe Sui, Jianing Zhang, Shufang Chen, Xiaotong Li, Wang Zimeng AutoMLR Workshop, NeurIPS 2026 · 2026 · Accepted [[OpenReview]](https://openreview.net/forum?id=9PwlVQ3gyj)"},{"id":"/projects/ai-native-workflow/#Related projects","page":"AI Native Workflow","section":"Related projects","url":"/projects/ai-native-workflow/","kind":"section","text":"GeoAFT"},{"id":"/projects/ai-native-workflow/#Publications","page":"AI Native Workflow","section":"Publications","url":"/projects/ai-native-workflow/","kind":"section","text":"Geometric Attention Fine-Tuning Is Representation-Relative: Autonomous ML Research with AI-Native Workflow (2026). Yuhe Sui, Jianing Zhang, Shufang Chen, Xiaotong Li, Wang Zimeng. AutoMLR Workshop, NeurIPS 2026. Accepted. OpenReview"},{"id":"/projects/alphaallocator/details/","page":"AlphaAllocator: How It Works","section":"","url":"/projects/alphaallocator/details/","kind":"page","text":"How AlphaAllocator works: why not one LLM, two small models for relevance and tone, a capped news tilt on a risk-parity base, the leakage-safe backtest, NLPCC 2026 results and ablations, and reproducibility notes."},{"id":"/projects/alphaallocator/details/#why-not-llm-h","page":"AlphaAllocator: How It Works","section":"Why not just ask an LLM?","url":"/projects/alphaallocator/details/#why-not-llm-h","kind":"section","text":"The obvious way to build a trading agent that reads the news is to give the headlines to a large language model and ask it for the answer: the trade itself, a tilt on top of a portfolio, or an event signal to act on. It is quick to build, and one model does everything. That is also the problem. Inside one answer the model has to decide which asset a story is about, whether it is good or bad news, and how much money to move. When the result is wrong, you cannot tell which of the three went wrong; the answer can shift with the wording of the prompt; and nothing in it knows about risk, turnover …"},{"id":"/projects/alphaallocator/details/#questions-h","page":"AlphaAllocator: How It Works","section":"Two questions, two small models","url":"/projects/alphaallocator/details/#questions-h","kind":"section","text":"Which asset? Relevance model A small sentence encoder (4 layers, BGE family) turns each article and a short description of each asset into vectors, and their similarity says how much the article is about that asset. One article can matter to several assets. Good or bad? Tone model A financial sentiment classifier (FinBERT) reads the same article and gives probabilities for positive, neutral and negative. The tone is positive minus negative, between −1 and +1. How much? Risk model, with a cap Not a language question. A risk-parity portfolio sets the weights from prices, and the news score may …"},{"id":"/projects/alphaallocator/details/#why-h","page":"AlphaAllocator: How It Works","section":"Why the news only nudges","url":"/projects/alphaallocator/details/#why-h","kind":"section","text":"Even with good relevance and tone, turning each headline straight into a large position is fragile: small day-to-day changes in the news would make the portfolio churn. So the news score enters as a small, centred adjustment: what one asset gains, others give up, and the total size of the adjustment is capped. Figure 2. Try it. A base portfolio over the Track 1 assets, a news score per asset, and the tilt the agent would apply: centred, scaled by $η = 0.010$, capped so that $‖Δw‖_1 ≤ η$, then clipped and rescaled to 97% invested. Illustrative base and scores, not model output. The cap is a …"},{"id":"/projects/alphaallocator/details/#method-h","page":"AlphaAllocator: How It Works","section":"The system in one picture","url":"/projects/alphaallocator/details/#method-h","kind":"section","text":"Figure 3. The pipeline. The stages carry the names of the paper’s Fig. 1. A price branch builds the quantitative base; a text branch reads the visible news with the two local models and produces one score per asset. The centred score becomes a capped tilt, which is added to the base, normalised and handed to the order planner. Prices decide. In Track 1 a shrinkage risk-parity portfolio gives every asset an equal share of portfolio risk. Text is local and deterministic. Both models load from local files, with no online calls; the encoder was adapted on 2024 data only. Failures are explicit. No …"},{"id":"/projects/alphaallocator/details/#where-h","page":"AlphaAllocator: How It Works","section":"Where it runs","url":"/projects/alphaallocator/details/#where-h","kind":"section","text":"Nothing in the design is tied to one market: the relevance model needs a short description of each asset, the tone model needs text in the market’s language, and the risk model needs prices. NLPCC 2026 Shared Task 4 tested Chinese funds · daily decisions · Chinese news Track 1, our main system: 11 macro and broad-market assets, from the CSI 300 and ChiNext to government bonds and gold. It placed 1st of 10 teams. Track 2, a secondary extension over 16 sector funds, placed 6th of 13. ACM ICAIF 2026 Trading Agent Competition Coming soon US equities · 7 decisions a day · English news The same …"},{"id":"/projects/alphaallocator/details/#backtest-h","page":"AlphaAllocator: How It Works","section":"A leakage-safe backtest","url":"/projects/alphaallocator/details/#backtest-h","kind":"section","text":"A backtest leaks when a decision uses something it could not have known. At NLPCC 2026 the official loader rules this out by construction, and our agent never steps outside it. We fitted and selected everything on 2024, replayed the frozen system on the public 2025 data, and the organizers ranked submissions on a hidden 2026 period. Figure 4. What the agent can see. Top: on decision day t it sees full bars up to t−1, today’s open, and news published before 15:00; today’s close, high, low and change are masked, and orders fill at the close. Bottom: 2024 for fitting and selection (193 trading …"},{"id":"/projects/alphaallocator/details/#results-h","page":"AlphaAllocator: How It Works","section":"Results: Track 1","url":"/projects/alphaallocator/details/#results-h","kind":"section","text":"Track 1 is where the design was meant to work, and where it did: over 11 macro assets it ranked first on the organizers’ hidden evaluation. Official ranking Hidden 2026 period · organizer-run 1st Sharpe 1.1144 Result. 1st of 10 teams. Annualised return 13.52%, maximum drawdown −6.23%. 2025 replay Public 2025 · 243 decisions 24.30% · Sharpe 2.270 Result. Maximum drawdown 5.83%; target turnover 0.77% a day. With and without news Same agent, news score zeroed 2.270 vs 2.198 Result. Sharpe with news against the same agent with news zeroed (23.31% return). Figure 5. Every team’s official result. …"},{"id":"/projects/alphaallocator/details/#ablations-h","page":"AlphaAllocator: How It Works","section":"News on and off","url":"/projects/alphaallocator/details/#ablations-h","kind":"section","text":"The cleanest test is same stack, news zeroed: the identical Track 1 agent run over 2025 with an all-zero news score. The date-offset rows feed each day the complete news set from 5 or 21 dates later, and the reference rows are separately locked no-news systems. Figure 11. Controls in the public-2025 replay. Each panel has its own axis range, printed beneath it. On narrow screens only Sharpe and turnover are drawn; the table in §15 has all four. With the news zeroed, the same Track 1 agent returns 23.31% at Sharpe 2.198, against 24.30% at 2.270 with the news, with almost identical drawdown. …"},{"id":"/projects/alphaallocator/details/#icaif-h","page":"AlphaAllocator: How It Works","section":"ICAIF 2026 Coming soon","url":"/projects/alphaallocator/details/#icaif-h","kind":"section","text":"AlphaAllocator is also being used, adapted to US equities, in the ACM ICAIF 2026 Trading Agent Competition: 30 US-listed stocks, 7 decisions a day, evaluated live. The questions stay the same; the asset descriptions, the text models’ language and the decision clock change. Results and a write-up are coming soon."},{"id":"/projects/alphaallocator/details/#limitations-h","page":"AlphaAllocator: How It Works","section":"Limitations and what didn’t work","url":"/projects/alphaallocator/details/#limitations-h","kind":"section","text":"Scope One task, one market. The NLPCC results come from a shared task and its evaluation protocol, and are historical backtests. The official rank evaluates the complete Track 1 system; it does not show that the separation of questions or news models in general improve portfolios. This is an academic system, not investment advice. The 2025 replay. The repository cannot show when 2025 outcomes were first looked at, so we call it public-2025 replay evidence, not a held-out or preregistered test. It is one year, and we make no statistical power claim. It compounds each day’s target weights from …"},{"id":"/projects/alphaallocator/details/#next-h","page":"AlphaAllocator: How It Works","section":"What we would change","url":"/projects/alphaallocator/details/#next-h","kind":"section","text":"These directions come from the paper’s own limitations; none has been run. ### Cleaner tests of the news Preregistered controls over several periods, and a replay with the official order, cost and rejection rules, so the news effect can be measured rather than described. Any learned query or threshold should be chosen without consulting the evaluation period. ### Better links from news to assets Entity and event linking, so a sector query can separate news about the sector itself from news about its suppliers, customers or the whole market. This is where we would look first for Track 2’s weak …"},{"id":"/projects/alphaallocator/details/#cores-h","page":"AlphaAllocator: How It Works","section":"The two quantitative bases","url":"/projects/alphaallocator/details/#cores-h","kind":"section","text":"Track 1. The agent requests 60 rows: 59 completed bars and the masked current row. Simple returns come from positive prior closes, aligned across assets to the shortest history (at most 58 observations). With sample covariance $S_t$, the fixed shrinkage is $$Σ_t = (1 − α)S_t + αT_t ,(T_t )_{ij} = 1[i = j]diag(S_t )^― ,α = 0.2.$$ Each asset’s share of portfolio variance is $c_i (w) = w_i (Σ_t w)_i /w^⊤ Σ_t w$. Starting from inverse volatility, the weights are updated multiplicatively towards equal shares $b_i = 1/n$, $$w_i ← w_i \\sqrt{\\frac{b_i }{max(c_i ,10^{ − 12} )}},$$ and after every …"},{"id":"/projects/alphaallocator/details/#score-h","page":"AlphaAllocator: How It Works","section":"The news score","url":"/projects/alphaallocator/details/#score-h","kind":"section","text":"Cleaning. Each article is its title, a space and its content, whitespace-collapsed and cut to 1,200 characters. Empty records are skipped; duplicates are found by hashing the title and the first 500 content characters; the official ranking order is restored and at most 20 articles kept. Both tokenizers truncate at 256 tokens, batch size 16. Relevance and recency. An asset query is its identifier followed by fixed Chinese keywords. Articles and queries are mean-pooled over the attention mask and L2-normalised, so dot products are cosines. For article $k$ and asset $j$, with a two-day …"},{"id":"/projects/alphaallocator/details/#orders-h","page":"AlphaAllocator: How It Works","section":"From tilt to orders","url":"/projects/alphaallocator/details/#orders-h","kind":"section","text":"With sensitivity $η$ (0.010 in Track 1, 0.012 in Track 2), the raw tilt is $$d = η(z − z^¯ ),Δw = dmin(1, \\frac{η}{‖d‖_1 })(Δw = d\\text{if}‖d‖_1 = 0).$$ The path from base to holdings has six distinct states, and the cap applies only to the second: Base weights from the quantitative core, already capped at 35%. Raw tilt $Δw$, centred and L1-capped at $η$. Agent target: base plus tilt, negatives clipped, rescaled to 97%. The 35% cap is not reapplied here. Planner target: each coordinate clipped to 35% without redistribution, then blended towards current holdings within a 25% one-way turnover …"},{"id":"/projects/alphaallocator/details/#tables-h","page":"AlphaAllocator: How It Works","section":"Full tables","url":"/projects/alphaallocator/details/#tables-h","kind":"section","text":"Official hidden-2026 B-list results Official, hidden 2026 Rank Sharpe Annualised return Maximum drawdown Track 1 1st 1.1144 13.52% −6.23% Track 2 6th 0.7566 15.32% −7.49% Organizer evaluation; drawdown in their signed-negative convention. Public-2025 gross target-weight replay Public 2025, gross replay Return Sharpe Max drawdown Turnover News-active days Track 1 · submitted text system 24.30% 2.270 5.83% 0.77% 243 Track 1 · same stack, news zeroed 23.31% 2.198 5.83% 1.47% 0 Track 1 · news from 5 dates later 24.30% 2.271 5.83% 0.77% 241 Track 1 · news from 21 dates later 24.30% 2.271 5.83% …"},{"id":"/projects/alphaallocator/details/#repro-h","page":"AlphaAllocator: How It Works","section":"Reproducibility notes","url":"/projects/alphaallocator/details/#repro-h","kind":"section","text":"The submission is a standalone package: the two track agents, a vendored copy of the runtime they need, an official-style local server, the configuration and both model snapshots, loaded with local files only. Commands, expected outputs and audits ship with it. Final configuration SHA-256 b4fc52e37f0fdb4c5704b196ff2f22980473f11f1713525110961b4ccdfb3d43; declares 2024-only selection, no 2025 tuning, no hidden-2026 use, no network. Encoder weights SHA-256 003563924b66722e96f19f5dedb33794c8a63f6d19e333fb83fc1a28c655ca41 FinBERT weights SHA-256 …"},{"id":"/projects/alphaallocator/details/#summary-h","page":"AlphaAllocator: How It Works","section":"In brief","url":"/projects/alphaallocator/details/#summary-h","kind":"section","text":"Design Two small language models read each day’s news. One judges which of the 11 assets a story concerns; the other judges whether its tone is positive or negative. Their combined score shifts a risk-parity portfolio, and the shift is limited to 1.0% of the portfolio in total. Results On the organizers’ hidden 2026 evaluation the Track 1 agent ranked 1st of 10 teams, with a Sharpe ratio of 1.1144, and the Track 2 agent ranked 6th of 13. In the public 2025 replay, the Track 1 Sharpe ratio was 2.270 with the news and 2.198 with it removed. Open questions How much of the gain comes from what …"},{"id":"/projects/alphaallocator/details/#sources-h","page":"AlphaAllocator: How It Works","section":"Sources","url":"/projects/alphaallocator/details/#sources-h","kind":"section","text":"Paper: NTU-QRS AlphaAllocator: Bounded Transformer News Overlays for Chinese Macro-Asset Allocation, NLPCC 2026 Shared Task 4, poster and oral, 5 November 2026. [[OpenReview]](https://openreview.net/forum?id=u09PzTYNHk)"},{"id":"/projects/alphaallocator/details/#Recognition","page":"AlphaAllocator: How It Works","section":"Recognition","url":"/projects/alphaallocator/details/","kind":"section","text":"NLPCC 2026 Shared Task 4 · Track 1 · 1st NLPCC 2026 Shared Task 4 · Track 2 · 6th Official results are the organizers’ release as reported in the paper; the 2025 numbers come from the replay outputs of the NLPCC submission. Asset names paraphrase the keyword lists in the reproducibility manifest. Back to top ↑"},{"id":"/projects/alphaallocator/","page":"AlphaAllocator","section":"","url":"/projects/alphaallocator/","kind":"page","text":"AlphaAllocator: a news-reading allocation agent that asks one small model which asset a story is about and another whether it is good or bad, and lets a risk model allocate. 1st in NLPCC 2026 Track 1; ICAIF 2026 coming soon."},{"id":"/projects/alphaallocator/#glance-h","page":"AlphaAllocator","section":"AlphaAllocator at a glance","url":"/projects/alphaallocator/#glance-h","kind":"section","text":"The idea For news to help a portfolio, an agent has to know two things: which asset an item is about, and whether it is good or bad news. We give each question its own small model and multiply the answers: $$news score_j = relevance_j × tone_j$$ The scores, weighted for recency and certainty and centred across assets, tilt a risk-parity portfolio. The whole tilt is capped at 1.0% of the portfolio, so prices decide and news only nudges. Experiments NLPCC 2026 · Chinese funds tested Track 1 Sharpe Ann. return Max DD 1st 1.1144 13.52% −6.23% 2025 replay Sharpe, with news · 2.270 · same agent …"},{"id":"/projects/alphaallocator/#next-h","page":"AlphaAllocator","section":"Where this is going proposed","url":"/projects/alphaallocator/#next-h","kind":"section","text":"### Cleaner tests of the news Preregistered controls over several periods and markets, with the official order and cost rules. ### Better links from news to assets Entity and event linking, so a query can tell direct, upstream, downstream and market-wide news apart. ### Constraints that are enforced Pass the realised previous weights to every guard and test how often each limit binds, end to end. What we would change, in full →"},{"id":"/projects/alphaallocator/#Papers","page":"AlphaAllocator","section":"Papers","url":"/projects/alphaallocator/","kind":"section","text":"### NTU-QRS AlphaAllocator: Bounded Transformer News Overlays for Chinese Macro-Asset Allocation NLPCC 2026 Shared Task 4 · poster and oral · oral at Evaluation Workshop I, 5 November 2026 [[OpenReview]](https://openreview.net/forum?id=u09PzTYNHk) [[Talk slides, PDF]](https://qrsntu.org/projects/alphaallocator/assets/alphaallocator-nlpcc2026-talk.pdf) ### ACM ICAIF 2026 Trading Agent Competition Write-up coming soon"},{"id":"/projects/alphaallocator/#Recognition","page":"AlphaAllocator","section":"Recognition","url":"/projects/alphaallocator/","kind":"section","text":"NLPCC 2026 Shared Task 4 · Track 1 · 1st NLPCC 2026 Shared Task 4 · Track 2 · 6th Scan to open this page"},{"id":"/projects/alphaallocator/#Publications","page":"AlphaAllocator","section":"Publications","url":"/projects/alphaallocator/","kind":"section","text":"NTU-QRS AlphaAllocator: Bounded Transformer News Overlays for Chinese Macro-Asset Allocation (2026). Yuhe Sui. NLPCC 2026 Shared Task 4 · Poster + Oral. OpenReview"},{"id":"/projects/cffa-2026/","page":"CFFA 2026 — China Future Financial Analyst Competition","section":"","url":"/projects/cffa-2026/","kind":"page","text":"• Built a Greenwashing Risk Score across 1,676 Chinese green-bond issuances (2016–2025), using issue-spread regressions and portfolio sorts. • Pricing effects are weak unconditionally, but meaningful within credit-risk buckets after controls."},{"id":"/projects/cffa-2026/#Recognition","page":"CFFA 2026 — China Future Financial Analyst Competition","section":"Recognition","url":"/projects/cffa-2026/","kind":"section","text":"CFFA 2026 · National Finalist [[GitHub]](https://github.com/yuhesui/CFFA-2026)"},{"id":"/projects/decisionrank/","page":"DecisionRank","section":"","url":"/projects/decisionrank/","kind":"page","text":"An early-stage research programme with derived research in progress."},{"id":"/projects/frtbtrace/details/","page":"FRTBTrace: How It Works","section":"","url":"/projects/frtbtrace/details/","kind":"page","text":"How FRTBTrace works: why one attribution vector is not enough, ties and history, the capital graph, a pre-registered benchmark of 60 synthetic books, the comparison with published allocators, and the limitations."},{"id":"/projects/frtbtrace/details/#why-not-one-h","page":"FRTBTrace: How It Works","section":"Why not one attribution vector?","url":"/projects/frtbtrace/details/#why-not-one-h","kind":"section","text":"Under the internal-models approach of the Fundamental Review of the Trading Book (FRTB-IMA), market-risk capital is set for a bank’s approved trading desks as a whole. The rules do not say how that number should be split across trades, yet risk managers, capital planners and validators ask for exactly that. The obvious answer is to compute one number per trade, usually a gradient (Euler) allocation or one of the published FRTB allocation rules, and to use it wherever a trade-level number is needed. That vector is then asked several different questions. A desk report needs numbers that add up …"},{"id":"/projects/frtbtrace/details/#questions-h","page":"FRTBTrace: How It Works","section":"Five questions","url":"/projects/frtbtrace/details/#questions-h","kind":"section","text":"Marginal Which trades move K locally today? A gradient on today’s book. At a tie it is a set; the engine returns one flagged element of it. Adds up to K: not in general Removal What happens to K if trade i goes? A finite counterfactual, answered by revaluing the book without the trade. Adds up to K: not in general Accounting How should K be split over current trades or desks? A declared remap of the origin ledger onto today’s trades. Adds up to K: yes Origin Which (date, trade) positions generated K? The ledger from the reverse pass, one entry per stored date and trade. Adds up to K: yes …"},{"id":"/projects/frtbtrace/details/#ties-h","page":"FRTBTrace: How It Works","section":"Ties and history","url":"/projects/frtbtrace/details/#ties-h","kind":"section","text":"Two features of the formula pull the questions apart. The first is ties. Take capital $K = max(w_1 ,w_2 )$, which is itself a two-scenario expected shortfall, at $w = (1,1)$. Removing either trade leaves $K = 1$, so both removal effects are zero and their sum is zero, not one. The local marginal is the whole segment between $(1,0)$ and $(0,1)$. An accounting ledger can still add up to K, but only by declaring how the tie is split. Two trades, one tie Illustrative Move trade 2 off the tie and the marginal becomes one gradient; at the tie it is a set, the removal effects stop adding up, and the …"},{"id":"/projects/frtbtrace/details/#method-h","page":"FRTBTrace: How It Works","section":"The method in one picture","url":"/projects/frtbtrace/details/#method-h","kind":"section","text":"FRTBTrace writes the full capital calculation as a graph. Expected shortfall is evaluated on blocks for each risk class, factor set and liquidity horizon, aggregated over horizons, scaled by a floored stress ratio and combined into the internal-models charge; non-modellable and default-risk charges are added; history enters through maxima against moving averages; and the result is compared with standardised-approach capital. Figure 2. The FRTB-IMA capital graph. Shaded nodes can be nondifferentiable. The nodes inside the dashed box are evaluated on each stored date’s book and feed the history …"},{"id":"/projects/frtbtrace/details/#where-h","page":"FRTBTrace: How It Works","section":"Where it runs","url":"/projects/frtbtrace/details/#where-h","kind":"section","text":"Exact engine tested A deterministic finance tool, not an AI model Evaluates capital before and after an action, with every node value and branch state, and returns the typed answer with its reconciliation check. Most nodes detect ties at relative tolerance $10^{ − 12}$; expected-shortfall scenario losses and the stress-ratio floor detect them only at exact equality. The benchmark protocol and result schema give each answer one of 6 outcomes: answered, no answer on this book, not applicable, declines, fails, or not run; the engine itself does not yet emit them, and the command-line prototype …"},{"id":"/projects/frtbtrace/details/#benchmark-h","page":"FRTBTrace: How It Works","section":"A pre-registered benchmark","url":"/projects/frtbtrace/details/#benchmark-h","kind":"section","text":"The benchmark has 60 books fixed before any method was run. There are 42 small tie books of 10–14 trades, 36 of them built to sit on one kink each and 6 smooth controls, and 18 main books of 96 trades: three draws of each of six portfolio types (ordinary, nonlinear, tail-difficult, regulatory near-tie, history-heavy, and held-out, a generator from a different rule family fixed once and never tuned). Each main book has 24 modellable factors, 256 current and 256 stressed scenarios per expected-shortfall block, 60 daily and 12 weekly stored observations, and a default law of 20,500 scenarios on …"},{"id":"/projects/frtbtrace/details/#results-h","page":"FRTBTrace: How It Works","section":"Results: capital on past dates","url":"/projects/frtbtrace/details/#results-h","kind":"section","text":"Past-date capital 14 smooth main books 61% median share of capital on past observation dates; range 21–99%. Ledger adds up All 60 books 5.6 × 10⁻¹⁶ largest relative gap to the engine’s capital on the tie books; 4.3 × 10⁻¹⁶ on the main books. Origin ledger vs finite differences 80,640 (date, trade) positions 80,630 agree within $10^{ − 8}$ at relative step $10^{ − 6}$; median per-book maximum error 1.7 × 10⁻¹⁰. Figure 3. Capital on past observation dates, per main book. The frozen remainder as a share of K. The history-heavy books, with larger past perturbations and a smaller current book, sit …"},{"id":"/projects/frtbtrace/details/#tie-results-h","page":"FRTBTrace: How It Works","section":"Results: ties","url":"/projects/frtbtrace/details/#tie-results-h","kind":"section","text":"For the 36 books built on a kink, the reference is the set of marginals that can actually be realised, constructed without reading the engine’s allocation or its tie convention: the benchmark forces the tied branches through the graph and probes 26 generic nearby books per case. Every nearby gradient lies in the reference set, every vertex of the set is observed, and the engine’s flagged representative lies within normalised distance 1.5 × 10⁻¹⁶ of the set. The representative is therefore a valid marginal point; the engine does not yet list the complete set. Being close is not enough at a …"},{"id":"/projects/frtbtrace/details/#coverage-h","page":"FRTBTrace: How It Works","section":"What other methods answer","url":"/projects/frtbtrace/details/#coverage-h","kind":"section","text":"We implemented six published allocation rules from their source equations, plus a numerical Euler control, and ran them on the same books. Each answers at most 2 of the five questions. Most gaps are structural rather than numerical: single-trade FRTB capitals are often undefined, Li–Xing does not extend through an active stress-ratio floor, and marginal measures cover only part of the graph. Removal and hedge choice are revaluations and the origin ledger is our own construct, so an uncovered column is not a failure of the published method. Figure 4. Which questions each method answers. Books …"},{"id":"/projects/frtbtrace/details/#audit-h","page":"FRTBTrace: How It Works","section":"One book, audited","url":"/projects/frtbtrace/details/#audit-h","kind":"section","text":"One ordinary main book shows why the type of an answer matters. Its capital is 105.39. The origin ledger puts 75.98 (72.1%) on past dates, so today’s-book sensitivities account for 29.41. Removal effects and candidate actions can still be answered by revaluation, but under the benchmark’s convention Shapley values over trades have no answer: 77 of the 96 single-trade capitals they need are unavailable. They are computed under two declared conventions in Shapley values and a larger book. Figure 5. Audit record for one main book. Exact capital after each of 8 candidate actions in one of the …"},{"id":"/projects/frtbtrace/details/#shapley-h","page":"FRTBTrace: How It Works","section":"Results: Shapley values and a larger book","url":"/projects/frtbtrace/details/#shapley-h","kind":"section","text":"Shapley values average a trade’s removal effect over all sub-books, so they need capital on sub-books where the formula is undefined: a risk class with no reduced-set exposure, or amber desks with no capital. The benchmark therefore records them as having no answer. Two declared conventions fill those sub-books. Under convention A an undefined term is dropped, so capital of the stored history alone remains and the values add up to K minus that amount. Under convention B such a sub-book takes its standardised capital, and the values add up to K. Tie books, exact 42 books, every sub-book 18% …"},{"id":"/projects/frtbtrace/details/#repricing-h","page":"FRTBTrace: How It Works","section":"Certified selective repricing specialist","url":"/projects/frtbtrace/details/#repricing-h","kind":"section","text":"On books whose options belong to a convex single-factor class, a certified approximation can reprice only the tail scenarios it cannot bound and still return the exact engine’s answer. Of 12 option books, 6 are in that class (American options at low volatility and at high nonlinearity); the basket and barrier books are declared not applicable. On all 6, the certified output matches the exact engine’s marginal and origin allocations within 2.2 × 10⁻¹⁶, bit for bit on 1. This is a specialist result: it says nothing about speed, and it covers no removal or hedge-choice question."},{"id":"/projects/frtbtrace/details/#limitations-h","page":"FRTBTrace: How It Works","section":"Limitations and what didn’t work","url":"/projects/frtbtrace/details/#limitations-h","kind":"section","text":"Scope Synthetic books. Every book is synthetic: the benchmark books have at most 96 trades on 24 factors, and the one larger book (960 trades) comes from the same generator, so nothing is shown about bank portfolios. The non-modellable and default charges come from declared synthetic models, standardised-approach capital is a homogeneous stand-in with exact Euler allocations rather than the regulatory formula, and the multiplier on the averaged internal-models charge is fixed at 1.5 (no backtesting add-on). Exact, but relative to a choice. The ledger is exact relative to the implemented …"},{"id":"/projects/frtbtrace/details/#next-h","page":"FRTBTrace: How It Works","section":"What comes next","url":"/projects/frtbtrace/details/#next-h","kind":"section","text":"These directions come from the papers’ own priorities for validation; none has been run. ### An independent check of capital A second implementation of K, so that agreement is no longer self-referenced, and the complete set of realisable marginals at ties rather than one representative. ### Real books and desk views Bank-style portfolios with real management remaps and groupings, reviewed error accounting for any approximation, and backtests of expected-shortfall contributions over time. ### Agents in the loop The typed answers, outcome codes and guarantees exposed through a tool protocol …"},{"id":"/projects/frtbtrace/details/#formula-h","page":"FRTBTrace: How It Works","section":"The capital formula","url":"/projects/frtbtrace/details/#formula-h","kind":"section","text":"Expected shortfall at $β = 0.025$ of the loss vector $z = Lw$, with scenario weights $p$ and caps $c_s = p_s /β$, in its primal and dual forms: $$ρ(z) = min_τ {τ + β^{ − 1} ∑_s p_s (z_s − τ){ + } }$$ $$ρ(z) = max{q^⊤ z:0 ≤ q ≤ c, 1^⊤ q = 1}$$ Blocks $e{c,v,j}$ for risk class $c$, factor set $v$ and liquidity horizon $j$ aggregate as $E_{c,v} = (∑_j a_j e_{c,v,j}^2 )^{1/2}$ with $a = (1,1,2,2,6)$. The floored stress ratio and the internal-models charge are $$G_c = S_c max(1,F_c /R_c )$$ $$I = \\frac{1}{2}G_0 + \\frac{1}{2}∑_{c = 1}^5 G_c$$ where $S_c$, $F_c$ and $R_c$ are $E_{c,v}$ on the …"},{"id":"/projects/frtbtrace/details/#theory-h","page":"FRTBTrace: How It Works","section":"Node rules and identities","url":"/projects/frtbtrace/details/#theory-h","kind":"section","text":"Allocations propagate node by node: $A^b = ∑j c{bj} A^j$ over the children of node $b$, with coefficients that depend on node values but not on allocations. The rules are the dual weights $w⊙L^⊤ q$ at each expected shortfall; $∑_j (a_j e_j /E)A^{e_j }$ at the horizons; at the stress ratio $A^S$ when $F < R$, $\\frac{F}{R}A^S + \\frac{S}{R}A^F − \\frac{SF}{R^2 }A^R$ when $F > R$, and a declared tie weight $λ ∈ [0,1]$ between them at a tie; the active scenario row at the default quantile; and the active branch, or a declared tie weight, at every maximum, minimum and positive part. Recursive …"},{"id":"/projects/frtbtrace/details/#tables-h","page":"FRTBTrace: How It Works","section":"Full tables","url":"/projects/frtbtrace/details/#tables-h","kind":"section","text":"Every book, by portfolio type Per portfolio type: benchmark outcome and post-review measurements Portfolio type Tier Books Trades Capital K Past-date share, median Questions answered Shapley A−B gap, median Removal short of K, median Amber term non-zero Marginal set at today’s book Ordinary main 3 96 76.42–127.56 57% M D A H Q 2.2% 71% 2 single point Nonlinear main 3 96 79.59–95.42 56% M D A H Q 2.8% 64% 3 single point Tail-difficult main 3 96 311.01–454.17 75% M D A H Q 3.5% 74% 1 single point Regulatory near-tie main 3 96 66.57–138.16 – D A H Q 2.4% 60% 2 exact set on 1 of 3 History-heavy …"},{"id":"/projects/frtbtrace/details/#repro-h","page":"FRTBTrace: How It Works","section":"Reproducibility notes","url":"/projects/frtbtrace/details/#repro-h","kind":"section","text":"Benchmark results are read from frozen result files by a script that checks each file’s SHA-256 hash. Tie books Core results, tier S: SHA-256 prefix 8747184b Main books Core results, tier M: 717cdf51 Option books Certified selective repricing: 37d6d63e Summary scores 4474986f Finite-difference check Summary 074389be, residual diagnosis 084b9c12; 14 books, 60 dates × 96 trades each Source revision Private repository, commit 61cba9e56a Summary"},{"id":"/projects/frtbtrace/details/#summary-h","page":"FRTBTrace: How It Works","section":"In brief","url":"/projects/frtbtrace/details/#summary-h","kind":"section","text":"Design Requests for a trade-level explanation of capital are sorted into five types before anything is computed. One forward and one reverse pass through the regulatory formula give a ledger indexed by stored date and trade, while what-if and action questions are revalued exactly. Results On 60 synthetic books the ledgers balance to the engine’s capital at the level of rounding error, and each established method covers no more than 2 of the five request types. On the typical smooth main book, 61% of the charge traces back to positions held on earlier dates. Open questions Whether the same …"},{"id":"/projects/frtbtrace/details/#sources-h","page":"FRTBTrace: How It Works","section":"Sources","url":"/projects/frtbtrace/details/#sources-h","kind":"section","text":"Paper: Exact Trade-Level Attribution of FRTB-IMA Capital, arXiv 2609.32238, 26 September 2026. [[arXiv]](https://arxiv.org/abs/2609.32238) Workshop papers, ICAIF 2026 (Milan, 14–15 November 2026), both accepted: Auditable FRTB Capital Explanations: A Tool Contract for Financial AI Agents (Yuhe Sui), Workshop on Responsible AI Operations for Finance; and What Post-hoc Attributions of FRTB-IMA Capital Answer (Yuhe Sui, Yingzhi Tang), Workshop on Interpretability and Alignment in Financial Models. ICAIF 2026 news → The finite-difference check of the origin ledger and the agent prototype appear …"},{"id":"/projects/frtbtrace/","page":"FRTBTrace","section":"","url":"/projects/frtbtrace/","kind":"page","text":"FRTBTrace: exact trade-level attribution of FRTB-IMA market-risk capital. Five typed questions, one reverse pass through the full formula, and a ledger on (date, trade) positions that adds up to capital."},{"id":"/projects/frtbtrace/#glance-h","page":"FRTBTrace","section":"FRTBTrace at a glance","url":"/projects/frtbtrace/#glance-h","kind":"section","text":"The idea Write the whole capital calculation as one graph over (observation date, trade) positions. A forward pass records which branch is active at every floor, maximum and minimum; one reverse pass then carries the allocation back to every position. The resulting ledger adds up to capital: $$∑{s,i} A{s,i}^K = K$$ Sensitivities to today’s book miss exactly the part on past dates. Removal effects and hedge choices are answered by exact revaluation, and ties are flagged rather than hidden. Experiments Synthetic benchmark · 60 books tested Capital on past dates, median 61% Range, 14 smooth main …"},{"id":"/projects/frtbtrace/#next-h","page":"FRTBTrace","section":"Where this is going proposed","url":"/projects/frtbtrace/#next-h","kind":"section","text":"### An independent check of capital A second implementation of the capital calculation, and the complete set of marginals at ties. ### Real books and desk views Bank-style portfolios, real management groupings, and backtests of expected-shortfall contributions over time. ### Agents in the loop Typed answers behind a tool interface, tested end to end with timing and scaling measured. What comes next, in full →"},{"id":"/projects/frtbtrace/#Papers","page":"FRTBTrace","section":"Papers","url":"/projects/frtbtrace/","kind":"section","text":"### Exact Trade-Level Attribution of FRTB-IMA Capital arXiv 2609.32238 · 26 September 2026 [[arXiv]](https://arxiv.org/abs/2609.32238) ### Auditable FRTB Capital Explanations: A Tool Contract for Financial AI Agents Yuhe Sui Workshop on Responsible AI Operations for Finance (RAIOps4Fin), ICAIF 2026 · accepted [[News]](https://qrsntu.org/news/icaif-2026-workshops/) ### What Post-hoc Attributions of FRTB-IMA Capital Answer Yuhe Sui, Yingzhi Tang Workshop on Interpretability and Alignment in Financial Models (IAFM), ICAIF 2026 · accepted [[News]](https://qrsntu.org/news/icaif-2026-workshops/) …"},{"id":"/projects/frtbtrace/results/","page":"FRTBTrace: Full Results","section":"","url":"/projects/frtbtrace/results/","kind":"page","text":"FRTBTrace full results: per-book outcomes for all 60 benchmark books, per-trade and per-date answers for a 960-trade book and the audited book, the multiplier sweep and certified repricing, as CSV files with SHA-256 hashes."},{"id":"/projects/frtbtrace/results/#books-h","page":"FRTBTrace: Full Results","section":"Every benchmark book","url":"/projects/frtbtrace/results/#books-h","kind":"section","text":"18 main books of 96 trades and 42 small tie books. The benchmark columns (point, capital, past-date share, ledger gap, questions answered, hedge libraries) are the frozen benchmark results. The Shapley, removal, amber-term and main-book tie-set columns were computed after the benchmark. Column headings sort each table. Every benchmark book Book Trades Point Capital K Past-date share Ledger gap Answered Hedge libraries Shapley A−B gap Max SE, A / B Removal short of K Removal non-additivity Amber term, largest desk move Marginal set Ordinary · 94101 · tier_m_ordinary_94101 96 smooth 105.39 …"},{"id":"/projects/frtbtrace/results/#book-960-h","page":"FRTBTrace: Full Results","section":"The 960-trade book after the benchmark","url":"/projects/frtbtrace/results/#book-960-h","kind":"section","text":"One synthetic book of 960 trades from the benchmark generator: marginal, removal, accounting and origin answers per trade, Shapley values under both conventions from 112 permutation pairs, and hedge choice in every action library. Per trade Per-trade answers CSV, 960 rows, 227 kB Per desk Per desk Desk Status Trades Accounting Marginal Removal Shapley A (exact) Shapley B (exact) D1 green 160 36.88 25.63 23.04 7.95 93.65 D2 green 160 74.10 24.64 16.57 6.40 92.09 D3 green 160 99.44 34.37 30.64 10.87 96.56 D4 amber 160 105.22 42.41 31.84 10.86 96.56 D5 amber 160 75.93 36.99 23.09 8.33 94.03 D6 …"},{"id":"/projects/frtbtrace/results/#book-audited-h","page":"FRTBTrace: Full Results","section":"The audited book","url":"/projects/frtbtrace/results/#book-audited-h","kind":"section","text":"The ordinary main book with seed 94101 (capital 105.39), answered in the same way after the benchmark, with Shapley values from 4,000 permutation pairs. These are an independent run from the 1,000-pair values in the table of every book and in the per-trade files of section 4. Per trade Per-trade answers CSV, 96 rows, 23 kB Per desk Per desk Desk Status Trades Accounting Marginal Removal Shapley A (exact) Shapley B (exact) D1 green 16 12.90 0.25 0.09 0.19 4.59 D2 green 16 11.41 0.33 0.37 0.38 17.76 D3 green 16 1.61 0.19 0.18 0.22 17.60 D4 amber 16 30.51 0.65 0.40 0.52 17.90 D5 amber 16 4.42 …"},{"id":"/projects/frtbtrace/results/#per-trade-h","page":"FRTBTrace: Full Results","section":"Per-trade files, every book after the benchmark","url":"/projects/frtbtrace/results/#per-trade-h","kind":"section","text":"For each of the 60 books: the accounting share, marginal, removal effect and Shapley values under both conventions per trade; removal effects under both conventions with domain walls; and, where the amber term is non-zero, its entry per trade. Per-date origin ledgers were kept for the two books above only. Show all 60 books Per-trade files Book Per trade Removal, per trade Amber term, per trade Ordinary · 94101 · tier_m_ordinary_94101 answers and Shapley values CSV, 96 rows, 14 kB removal effects CSV, 96 rows, 11 kB – Ordinary · 94202 · tier_m_ordinary_94202 answers and Shapley values CSV, 96 …"},{"id":"/projects/frtbtrace/results/#sweep-h","page":"FRTBTrace: Full Results","section":"Multiplier and history sweep after the benchmark","url":"/projects/frtbtrace/results/#sweep-h","kind":"section","text":"Median past-date share over the main books that are smooth at each grid point (their number in brackets), for five ways of generating past positions and five multipliers. The benchmark uses the benchmark history at multiplier 1.5. The noise processes scale each past position by a log-normal factor; the random walk makes the past positions persistent over dates with the same average log-variance as σ 0.10. Median past-date share History process Multiplier 1 Multiplier 1.25 Multiplier 1.5 Multiplier 1.75 Multiplier 2 Benchmark history 52% (16) 55% (16) 61% (14) 63% (16) 65% (16) Log-normal …"},{"id":"/projects/frtbtrace/results/#fd-h","page":"FRTBTrace: Full Results","section":"Finite-difference check of the origin ledger after the benchmark","url":"/projects/frtbtrace/results/#fd-h","kind":"section","text":"Largest normalised difference between the origin ledger and central finite differences on each smooth main book (60 dates × 96 trades), and the number of positions above $10^{ − 8}$, at two relative steps. Finite-difference check per book Book Positions Largest error, step 10⁻⁶ Above 10⁻⁸, step 10⁻⁶ Largest error, step 10⁻⁴ Above 10⁻⁸, step 10⁻⁴ Rebuilt K − frozen K Ordinary · 94101 5,760 1.8 × 10⁻¹⁰ 0 2.1 × 10⁻⁶ 18 1.4 × 10⁻¹⁴ Ordinary · 94202 5,760 1.7 × 10⁻¹⁰ 0 3.7 × 10⁻⁶ 7 0 Ordinary · 94303 5,760 8.1 × 10⁻¹⁰ 0 8.9 × 10⁻⁷ 26 0 Nonlinear · 94101 5,760 1.5 × 10⁻¹⁰ 0 6.2 × 10⁻⁶ 42 0 …"},{"id":"/projects/frtbtrace/results/#tie-sets-h","page":"FRTBTrace: Full Results","section":"Tie sets on the main books after the benchmark","url":"/projects/frtbtrace/results/#tie-sets-h","kind":"section","text":"The 4 main books at a tie, with the tied nodes and the smallest margin of a stress-ratio node on today’s book. Tie sets on the main books at a tie Book Capital K Tied nodes Smallest stress-ratio margin today Marginal set Regulatory near-tie · 94101 66.57 HIST/C_A G/0: 1.2 × 10⁻¹⁶ (floor active) construction fails: probe gradients fall outside the constructed set Regulatory near-tie · 94202 84.15 G/2, HIST/C_A G/2: 0 (tie) exact set: 4 vertices, dimension 2, largest spread 6.7% of K Regulatory near-tie · 94303 138.16 HIST/C_A G/3: 1.5 × 10⁻¹⁶ (floor active) construction fails: probe gradients …"},{"id":"/projects/frtbtrace/results/#repricing-h","page":"FRTBTrace: Full Results","section":"Certified selective repricing","url":"/projects/frtbtrace/results/#repricing-h","kind":"section","text":"Largest absolute difference from the exact engine’s marginal and origin allocations on each option book where certification applies. Certified selective repricing per book Book Status Marginal vs exact Origin vs exact Bit-identical Certificate radius F1 Favourable Convex 1-D · 94501 certified 0 0 yes 8.2 × 10⁻¹² F1 Favourable Convex 1-D · 94502 certified 1.1 × 10⁻¹⁶ 1.1 × 10⁻¹⁶ no 8.7 × 10⁻¹² F1 Favourable Convex 1-D · 94503 certified 2.2 × 10⁻¹⁶ 2.2 × 10⁻¹⁶ no 8.7 × 10⁻¹² F2 Nonlinear 1-D · 94501 certified 1.4 × 10⁻¹⁷ 1.4 × 10⁻¹⁷ no 7.1 × 10⁻¹² F2 Nonlinear 1-D · 94502 certified 2.8 × 10⁻¹⁷ …"},{"id":"/projects/frtbtrace/results/#files-h","page":"FRTBTrace: Full Results","section":"Files and SHA-256","url":"/projects/frtbtrace/results/#files-h","kind":"section","text":"164 files are the frozen result files of the post-review analyses, unchanged, with the SHA-256 recorded when they were frozen. The tables under tables/ collect per-book values from the frozen benchmark and post-review files named below. All 173 files Files and SHA-256 File Kind Rows Size SHA-256 fm2/fm2_books.csv frozen 60 22 kB fc003a7f498b72475d15709b2afb16b32be366d2f6555b143004dd827abf66f7 fm2/fm2_trades_tier_m_held_out_94101.csv frozen 96 11 kB bbb08760097980f18cab8cd1fe962f0e0d81d93afb2ed0d3e5ca46dd3829e8f5 fm2/fm2_trades_tier_m_held_out_94202.csv frozen 96 11 kB …"},{"id":"/projects/geoaft/details/","page":"GeoAFT: How It Works","section":"","url":"/projects/geoaft/details/","kind":"page","text":"How GeoAFT works: the intuition for adapting attention geometry, the method in one picture, synthetic and real-task results, a mechanism study with its controls, and the technical details."},{"id":"/projects/geoaft/details/#why-h","page":"GeoAFT: How It Works","section":"Why adapt relations?","url":"/projects/geoaft/details/#why-h","kind":"section","text":"Inside every attention head, tokens become queries and keys, and a compatibility rule, usually a scaled dot product, decides how strongly each query attends to each key. So a pretrained model has learned two things: representations, and a rule for comparing them. Parameter-efficient fine-tuning such as LoRA adapts the maps that produce queries and keys. The rule that compares them is inherited unchanged. GeoAFT asks what happens if we adapt that rule instead. Explainer (draft, October 2026). About two and a half minutes, silent: the idea and the synthetic results, recorded before the …"},{"id":"/projects/geoaft/details/#intuition-h","page":"GeoAFT: How It Works","section":"Same points, different relations","url":"/projects/geoaft/details/#intuition-h","kind":"section","text":"Changing the geometry changes what counts as similar. Hold one query and seven keys fixed. The dot product prefers the key furthest along the query’s direction. Euclidean distance prefers the nearest key. Taxicab (L1) distance prefers neighbours along the axes. An anisotropic Mahalanobis metric prefers neighbours along a direction it treats as cheap. The winner changes every time, and no point has moved. Figure 2. Try it. Each panel scores the same query $q$ against the same keys A–G with a different rule. Illustrative toy example, not trained-model behaviour."},{"id":"/projects/geoaft/details/#method-h","page":"GeoAFT: How It Works","section":"The method in one picture","url":"/projects/geoaft/details/#method-h","kind":"section","text":"GeoAFT keeps the pretrained score and adds a small, trainable geometry term on top of it: $$S_{ij} = s_{base} (q_i ,k_j ) + α_h g^¯ _ϕ (P_q q_i ,P_k k_j ),A_{ij} = softmax_{j ∈ 𝒱(i)} (S_{ij} )$$ Figure 3. The GeoAFT score. A structured geometry branch is centred over valid keys, scaled by a gate that starts at zero, and added before a single softmax. Starts from the pretrained model. Each gate $α_h$ is initialized at zero, so training begins from exactly the pretrained attention. Small and structured. What is trained is the geometry itself, a metric, an exponent or a projection, not a generic …"},{"id":"/projects/geoaft/details/#synthetic-h","page":"GeoAFT: How It Works","section":"Synthetic experiments controlled","url":"/projects/geoaft/details/#synthetic-h","kind":"section","text":"We first test GeoAFT where the right answer is known. A synthetic teacher generates attention from a known compatibility function over fixed representations, and every method adapts the same frozen dot-product base toward it. The score is oracle-gap recovery $R$: 0% means no improvement over the base, 100% means matching the oracle. It is not classification accuracy. Learned $L_p$ Target: an $L_p$ distance 99.983% Result. Near-oracle recovery. A fixed bank of ten $L_p$ geometries reached nearly the same. Mahalanobis Target: a Mahalanobis metric 99.991% Result. Near-oracle recovery. An exact …"},{"id":"/projects/geoaft/details/#real-h","page":"GeoAFT: How It Works","section":"Real tasks","url":"/projects/geoaft/details/#real-h","kind":"section","text":"On real tasks GeoAFT was used mostly as a score-level overlay: a frozen vision-language model and a strong few-shot classifier (the host) produce class scores, and GeoAFT adds a learned, gated residual to them. The test is whether this beats published results and, separately, whether the gain needs the geometry. Remote-sensing few-shot RSFS-8 · GeoRSCLIP ViT-B/32 · ProKeR host 84.48 · % at 1 shot Result. 84.48 / 88.20 / 91.47 at 1/2/4 shots, above the best published rows over the same 8 datasets (82.33 / 86.58 / 89.53: TaskRes, CLIP-LoRA, CLIP-LoRA). A projected-dot control, which has no …"},{"id":"/projects/geoaft/details/#mechanism-h","page":"GeoAFT: How It Works","section":"Mechanism study development data","url":"/projects/geoaft/details/#mechanism-h","kind":"section","text":"The real-task gains raise an obvious question: is the geometry doing the work, or would something simpler do the same? Three studies with designs fixed in advance compared each arm with the simplest control that could explain it. They ran on development splits only, and their results are descriptive. No geometry-specific improvement was demonstrated in the tested settings, and the mechanisms behind the remaining increments were not identified. Fixed class keys CoOp core-8 · CLIP ViT-B/16 and L/14 · CMPt host Control. A class bias, one number per class. Result. The bias alone came within 0.08 …"},{"id":"/projects/geoaft/details/#regimes-h","page":"GeoAFT: How It Works","section":"What the results mean","url":"/projects/geoaft/details/#regimes-h","kind":"section","text":"A geometry update can look different from a weight update and still compute the same function. So before asking whether geometry adaptation helps, we ask which kind of change it is. ### Exact reparameterization Established analytically The geometry describes a function a conventional scorer already represents. Mahalanobis is the example. ### Economical parameterization Supported in controlled experiments The same useful interaction, or a close approximation, with far fewer trained parameters. ### Distinct adaptation capacity Not shown on real tasks Changes a restricted conventional family …"},{"id":"/projects/geoaft/details/#limitations-h","page":"GeoAFT: How It Works","section":"Limitations and what didn’t work","url":"/projects/geoaft/details/#limitations-h","kind":"section","text":"Scope Synthetic tasks. The results recover known relations on fixed representations. The nonlinear teacher favours the matching geometry by construction, and flexible generic learners also approximated it well. They are not natural-task results. Remote-sensing result. A scoped result relative to the original published rows under a protocol fixed in advance: 8 of the 10 RSFS datasets, re-drawn splits (the authors’ splits cannot be reproduced), 1, 2 and 4 shots only, and one backbone. It compares point estimates with published numbers, with no interval. Our zero-shot accuracy sat +2.93 points …"},{"id":"/projects/geoaft/details/#benchmarks-h","page":"GeoAFT: How It Works","section":"Next studies and future directions","url":"/projects/geoaft/details/#benchmarks-h","kind":"section","text":"The mechanism study narrows where to look next. It tested fixed class keys, one attention layer and neighbour graphs; it did not test open keys, mid-layer placements or other training recipes. ### Do geometries matter where the keys are open? Coming soon In image-text retrieval every document is a new key and ranking is the score, so a pair geometry has room to differ from a projected dot product. The first study is remote-sensing retrieval on RSICD and RSITMD, after a leakage audit (one benchmark’s images come from the other, and RemoteCLIP was trained on both training splits) and with a …"},{"id":"/projects/geoaft/details/#definition-h","page":"GeoAFT: How It Works","section":"Notation and definition","url":"/projects/geoaft/details/#definition-h","kind":"section","text":"For token states $x_i$, one attention head forms queries $q_i = W_Q x_i$ and keys $k_j = W_K x_j$, and scores each pair with the scaled dot product $$s_{base} (q_i ,k_j ) = \\frac{q_i^⊤ k_j }{\\sqrt{d}},A_{ij} = softmax_{j ∈ 𝒱(i)} s_{base} (q_i ,k_j ),$$ where $𝒱(i)$ is the set of keys that query $i$ may attend to (its causal or padding mask). Most PEFT changes $(W_Q ,W_K ) → (W_Q + ΔW_Q , W_K + ΔW_K )$ and leaves $s$ unchanged. GeoAFT adds a structured, trainable residual to the score: $$S_{ij} = s_{base} (q_i ,k_j ) + α_h c(g_ϕ (P_q q_i ,P_k k_j ) − \\frac{1}{ 𝒱(i) }∑_{j^′ ∈ 𝒱(i)} g_ϕ (P_q q_i …"},{"id":"/projects/geoaft/details/#families-h","page":"GeoAFT: How It Works","section":"Families, centring and masks","url":"/projects/geoaft/details/#families-h","kind":"section","text":"With $u = P_q q$ and $v = P_k k$, the families used in the controlled experiments are: Family $g_ϕ (u,v)$ Trainable $ϕ$ Relation to dot-product scoring Learned $L_p$ $− ‖u − v‖_p$ exponent $p$ (bounded); optionally projections Not a bilinear form in general. With $p = 1$ it can produce centred patterns of maximal rank (§12). Mahalanobis $− (u − v)^⊤ LL^⊤ (u − v)$ factor $L$ Softmax-equivalent to bilinear plus key-quadratic (§12) Structured nonlinear compact nonlinear compatibility a few dozen parameters (46 in the reported run) Compared against a generic pair-MLP scorer The implementation …"},{"id":"/projects/geoaft/details/#qkvs-h","page":"GeoAFT: How It Works","section":"Q/K versus score adaptation","url":"/projects/geoaft/details/#qkvs-h","kind":"section","text":"Q/K adaptation does change attention scores, through the bilinear form $W_Q^⊤ W_K$. With low-rank updates of rank $r_Q$ and $r_K$, $$(W_Q + ΔW_Q )^⊤ (W_K + ΔW_K ) − W_Q^⊤ W_K = W_Q^⊤ ΔW_K + ΔW_Q^⊤ W_K + ΔW_Q^⊤ ΔW_K ,$$ which has rank at most $r_Q + r_K$. A structured geometry is not restricted in this way: for $N$ distinct points on a line, the row-centred L1 score matrix $[ − x_i − x_j ]$ has rank $N − 1$, the maximum possible after centring. An exact equivalence. Not every geometry is new capacity. Squared Mahalanobis expands as $$− (q − k)^⊤ M(q − k) = 2q^⊤ Mk − k^⊤ Mk − q^⊤ Mq,$$ and the …"},{"id":"/projects/geoaft/details/#protocol-h","page":"GeoAFT: How It Works","section":"Protocol, controls and full results","url":"/projects/geoaft/details/#protocol-h","kind":"section","text":"The controlled experiments test identifiability: can a method recover a known relation? Each fixes a set of representations and a target compatibility function. Methods are compared in paired cells on held-out synthetic queries and keys, and trainable parameter counts are recorded for every method. $$R = \\frac{L_{\\text{base}} − L_{\\text{method}} }{L_{\\text{base}} − L_{\\text{oracle}} },L = 𝔼_i KL(A_{i · }^{\\text{target}} ‖A_{i · }^{\\text{method}} ).$$ $L_{\\text{base}}$ is the loss of the unadapted model and $L_{\\text{oracle}}$ is the oracle reference loss. Normalizing by the gap makes results …"},{"id":"/projects/geoaft/details/#summary-h","page":"GeoAFT: How It Works","section":"In brief","url":"/projects/geoaft/details/#summary-h","kind":"section","text":"Design A gated residual adds a trainable distance, such as L1, learned $L_p$ or Mahalanobis, to the score a model already uses to match queries with keys. Its gate starts closed, so the adapted model begins as the pretrained one, and queries and keys are left untouched. Results On synthetic tasks with a known target relation, the overlay closed more than 99.9% of the gap to the oracle. On remote-sensing few-shot, in a scoped comparison, the overlay passed the best published rows at 1, 2 and 4 shots, and so did the same overlay with a plain dot product in place of the geometry. Open questions …"},{"id":"/projects/geoaft/details/#Accepted Research","page":"GeoAFT: How It Works","section":"Accepted Research","url":"/projects/geoaft/details/","kind":"section","text":"### Geometric Attention Fine-Tuning Is Representation-Relative: Autonomous ML Research with AI-Native Workflow Yuhe Sui, Jianing Zhang, Shufang Chen, Xiaotong Li, Wang Zimeng AutoMLR Workshop, NeurIPS 2026 · 2026 · Accepted [[OpenReview]](https://openreview.net/forum?id=9PwlVQ3gyj)"},{"id":"/projects/geoaft/details/#Related projects","page":"GeoAFT: How It Works","section":"Related projects","url":"/projects/geoaft/details/","kind":"section","text":"AI Native Workflow, GeoAttention The real-task and mechanism results come from the project’s second manuscript draft, its claim ledger and the study reports of November 2026, which are not yet public. The synthetic results come from the project’s controlled-task reports of October 2026. Back to top ↑"},{"id":"/projects/geoaft/","page":"GeoAFT","section":"","url":"/projects/geoaft/","kind":"page","text":"GeoAFT, Geometric Attention Fine-Tuning: adapting how a pretrained Transformer compares representations, and when that differs from ordinary weight adaptation."},{"id":"/projects/geoaft/#glance-h","page":"GeoAFT","section":"GeoAFT at a glance","url":"/projects/geoaft/#glance-h","kind":"section","text":"The idea LoRA-style methods change how queries and keys are produced. Geometric attention fine-tuning changes how they are compared: $$S_{ij} = s_{base} (q_i ,k_j ) + α_h g^¯ _ϕ (P_q q_i ,P_k k_j )$$ $g_ϕ$ is a small trainable geometry. The gate $α_h$ starts at zero, so training begins from exactly the pretrained attention. Experiments Synthetic tested Learned $L_p$ · 99.983% Mahalanobis · 99.991% Nonlinear · 99.934% Recovery of three known target relations, not classification accuracy. Real tasks tested Remote-sensing few-shot: a scoped result of 84.48 / 88.20 / 91.47 at 1/2/4 shots …"},{"id":"/projects/geoaft/#next-h","page":"GeoAFT","section":"Where this is going","url":"/projects/geoaft/#next-h","kind":"section","text":"### Do geometries matter where the keys are open? Image-text retrieval, where every document is a new key and ranking is the score, is the cleanest remaining test against a projected dot product. ### Can a graph metric reach the oracle’s headroom? On remote-sensing few-shot, oracle neighbour graphs leave several points of headroom that no label-free metric has reached yet. ### Would other placements or recipes change the reading? Only the last attention layer and one inherited training recipe were tested; mid-layer placements and recipes that train the geometry from the first step were not. …"},{"id":"/projects/geoaft/#Accepted Research","page":"GeoAFT","section":"Accepted Research","url":"/projects/geoaft/","kind":"section","text":"### Geometric Attention Fine-Tuning Is Representation-Relative: Autonomous ML Research with AI-Native Workflow Yuhe Sui, Jianing Zhang, Shufang Chen, Xiaotong Li, Wang Zimeng AutoMLR Workshop, NeurIPS 2026 · 2026 · Accepted [[OpenReview]](https://openreview.net/forum?id=9PwlVQ3gyj)"},{"id":"/projects/geoaft/#Related projects","page":"GeoAFT","section":"Related projects","url":"/projects/geoaft/","kind":"section","text":"AI Native Workflow, GeoAttention"},{"id":"/projects/geoaft/#Publications","page":"GeoAFT","section":"Publications","url":"/projects/geoaft/","kind":"section","text":"Geometric Attention Fine-Tuning Is Representation-Relative: Autonomous ML Research with AI-Native Workflow (2026). Yuhe Sui, Jianing Zhang, Shufang Chen, Xiaotong Li, Wang Zimeng. AutoMLR Workshop, NeurIPS 2026. Accepted. OpenReview"},{"id":"/projects/geoattention/","page":"GeoAttention","section":"","url":"/projects/geoattention/","kind":"page","text":"Research on attention geometry, representation-relative identifiability, and geometry-adaptive prediction."},{"id":"/projects/geoattention/#Related projects","page":"GeoAttention","section":"Related projects","url":"/projects/geoattention/","kind":"section","text":"GeoAFT, SoftRank"},{"id":"/projects/hedgefidelity/","page":"HedgeFidelity","section":"","url":"/projects/hedgefidelity/","kind":"page","text":"An early-stage research programme with derived research in progress."},{"id":"/projects/","page":"Projects, Competitions & Recognition","section":"","url":"/projects/","kind":"page","text":"Explore QRS research projects, competitions, and recognition in quantitative finance, machine learning, and mathematics."},{"id":"/projects/#All projects","page":"Projects, Competitions & Recognition","section":"All projects","url":"/projects/","kind":"section","text":"AI Native Workflow: Research on hierarchical, verification-gated and recoverable workflows for scaling long-horizon AI-assisted research and agent execution. Status: active. People: Yuhe Sui, Jianing Zhang, Shufang Chen, Danlin Chen, Wang Zimeng, Xiaotong Li. FRTBTrace: Active research on faithful, auditable, trade-level FRTB attribution. Status: active. People: Yuhe Sui, Yingzhi Tang. GeoAFT: Geometric Attention Fine-Tuning: adapting the rule a pretrained Transformer uses to compare representations, not only the representations themselves. Status: active. People: Yuhe Sui. GeoAttention …"},{"id":"/projects/mathresearchos/details/","page":"MathResearchOS: Usage Guide","section":"","url":"/projects/mathresearchos/details/","kind":"page","text":"MathResearchOS usage guide: install, create and run a case, family presets and model mixes, status and resume, human gates, manual hand-off, campaigns, Lean checks, where data is stored, safety limits and troubleshooting."},{"id":"/projects/mathresearchos/details/#install-h","page":"MathResearchOS: Usage Guide","section":"Install","url":"/projects/mathresearchos/details/#install-h","kind":"section","text":"You need Python 3.11 or newer. The package has no third-party dependencies. From a checkout of the repository: pip install -e . mathos --help This registers the mathos command. python -m mathresearchos does the same thing without installing, and the examples on this page work with either. Replace mathos with python -m mathresearchos if you did not install. For a live run you also need at least one model CLI, installed and logged in with your own account: codex, the Codex CLI, for the openai family. claude, the Claude Code CLI, for the claude family. Use both for a cross-family setup. …"},{"id":"/projects/mathresearchos/details/#solve-h","page":"MathResearchOS: Usage Guide","section":"Solve one problem","url":"/projects/mathresearchos/details/#solve-h","kind":"section","text":"A case is one objective plus everything the run produces. Put the problem statement, exactly as you want it solved, in a text file. The system stores it unchanged in OBJECTIVE.md and never rewrites it. Create the case The classic workflow (v1) has eight stages and a budget of 16 model calls: mathos create --mode solve --title \"First problem\" --objective-file problem.md The tiered workflow (v2) adds an explorer swarm, a separate refuter and auditors. --explorers sets the swarm size, from 2 to 32 (default 8), and the call budget becomes 16 plus the number of explorers. Use --text instead of …"},{"id":"/projects/mathresearchos/details/#how-h","page":"MathResearchOS: Usage Guide","section":"What happens in a run","url":"/projects/mathresearchos/details/#how-h","kind":"section","text":"A run walks a fixed graph of stages in dependency order. The v1 stages are specify, literature, explore, falsify, integrate, verify, report and verify_final. The v2 stages replace explore with explore_swarm and add triage and refute: the swarm runs N explorers, each forced onto a different method family, and triage merges their ideas with exact duplicates removed. The node fails, and is retried, if fewer than half of the explorers deliver. The audited stages (verify and verify_final) end in one of four verdicts: accept: the audit accepted the supplied evidence under the contract; the run …"},{"id":"/projects/mathresearchos/details/#follow-h","page":"MathResearchOS: Usage Guide","section":"Follow, pause and resume","url":"/projects/mathresearchos/details/#follow-h","kind":"section","text":"mathos list mathos status MATH-0001 mathos events MATH-0001 --last 20 status shows the case state, calls used against the budget, repair cycles, every stage with its status and attempt count, the next ready stage, the last verifier verdict, and the usage totals. A fresh v2 case looks like this: MATH-0002 — Demo v2 [solve] status=ready Calls 0/20; repair cycles 0/2 specify pending attempts=0 literature pending attempts=0 ... Ready: specify Usage: 0 tokens over 0 recorded call(s) Usage totals. Every model call writes a usage.json. status adds up the tokens by backend and counts calls that …"},{"id":"/projects/mathresearchos/details/#models-h","page":"MathResearchOS: Usage Guide","section":"Presets and mixes","url":"/projects/mathresearchos/details/#models-h","kind":"section","text":"Each stage has a role, and each role is served by a model. Three ways to assign them, from simplest to most flexible: Family presets Four built-in routes need no file. openai runs every role on the Codex CLI, claude on the Claude Code CLI, cross lets Claude generate and OpenAI verify, and cross-rev the reverse. The family defaults are gpt-6.1-sol for openai and claude-sonnet-5-5 for claude. The --dry-run output prints the model resolved for each role. Change a family default with the MATHOS_OPENAI_MODEL or MATHOS_CLAUDE_MODEL environment variable. mathos run MATH-0001 --route openai mathos …"},{"id":"/projects/mathresearchos/details/#pools-h","page":"MathResearchOS: Usage Guide","section":"Pools and other backends","url":"/projects/mathresearchos/details/#pools-h","kind":"section","text":"A pool is a JSON file that names backends and routes, for when presets and mixes are not enough. Backend types are codex, claude, openai_compat (an HTTP API such as DeepSeek, without tools) and manual (a human carries the prompt; see Manual hand-off). A route maps roles to backends. API keys are read from the environment variables the pool names and are never stored or logged. mathos run MATH-0002 --dry-run --pool examples/pool.example.json --route tiered-swarm examples/pool.example.json is a template: verify every model id with your own account before a live run. In the same run, a backend …"},{"id":"/projects/mathresearchos/details/#guide-h","page":"MathResearchOS: Usage Guide","section":"Reading the model selection guide","url":"/projects/mathresearchos/details/#guide-h","kind":"section","text":"docs/MODEL_SELECTION_GUIDE.md says which model to try for which role, and why. Its machine-readable twin is examples/role_recommendations.json. It is a set of priors to test, not a benchmark of this system; its own opening says the only direct evidence about the harness is one pilot problem. Start here. One family only: go straight to section 9 and paste a mix. Both CLIs: follow the thirteen-step decision procedure in section 7. Evidence tags. Every claim carries a tag: [P] primary (vendor documentation), [I] independent evaluation, [S] secondary (a lead, not a fact), [M] measured in this …"},{"id":"/projects/mathresearchos/details/#gates-h","page":"MathResearchOS: Usage Guide","section":"Human gates","url":"/projects/mathresearchos/details/#gates-h","kind":"section","text":"A case in the awaiting_human state does not resume itself. This happens after a replan or escalate verdict, an exhausted budget, a failed stage or a contract change. The case stays as it is until you decide. status shows the cause. Read status and events, and the stage’s output under runs/, and decide what is wrong. If the fix needs a change to the contract or workflow (not to the objective), edit DIC/ or the workflow, then accept it explicitly. The contract is hash-checked and a run halts if it differs from what was approved: mathos approve-contract MATH-0001 --accept Reopen from the …"},{"id":"/projects/mathresearchos/details/#handoff-h","page":"MathResearchOS: Usage Guide","section":"Manual hand-off","url":"/projects/mathresearchos/details/#handoff-h","kind":"section","text":"Some models exist only in a chat app, for example GPT-6 Pro in ChatGPT. The system cannot call them, and automating the website is likely against its terms. A manual backend lets a human carry the work instead. In a pool: {\"type\": \"manual\", \"model\": \"gpt-6-pro\", \"label\": \"ChatGPT, GPT-6 Pro\"}; in a mix: manual:gpt-6-pro. The pro-audit route in the example pool uses it as the v2 auditor. Run the case. When it reaches the manual stage it writes runs/<stage>-NNN/HANDOFF.md (instructions plus one self-contained message with every evidence file inlined) and stops at a human gate. Show the pending …"},{"id":"/projects/mathresearchos/details/#campaigns-h","page":"MathResearchOS: Usage Guide","section":"Campaigns","url":"/projects/mathresearchos/details/#campaigns-h","kind":"section","text":"A campaign runs several problems across several routes. Each round an orchestrator, either a frontier model or the zero-call round_robin builtin, assigns problems to routes; every assignment is an independent case, run in parallel. The orchestrator may only choose a (problem, route) pair or stop, within the budget. It cannot accept results or touch contracts. A spec is a JSON file with a name, the problems, the routes, an optional pool and a budget. examples/campaign.example.json is a small template, and the example pool it names must have its model ids verified for your account. Preview …"},{"id":"/projects/mathresearchos/details/#lean-h","page":"MathResearchOS: Usage Guide","section":"Lean check","url":"/projects/mathresearchos/details/#lean-h","kind":"section","text":"lean-check audits a Lean 4 file and reports kernel errors, uses of sorry, the axioms a theorem depends on, and the types of the statements. You install Lean (and Mathlib if the file needs it) yourself. Give the theorem to audit with --target, repeated for several, and the Lake project root if it is not the file’s folder: mathos lean-check Sqrt2.lean --target sqrt2_irrational mathos lean-check Sqrt2.lean --target sqrt2_irrational --project ~/lean/MyProject --out lean-report.json A clean report says the kernel accepted this formal statement. Whether the formal statement says what you meant is a …"},{"id":"/projects/mathresearchos/details/#storage-h","page":"MathResearchOS: Usage Guide","section":"Where data is stored","url":"/projects/mathresearchos/details/#storage-h","kind":"section","text":"Everything is plain files. --root defaults to the current folder, and cases/, campaigns/ and experiments/ are created relative to it. That makes a run easy to inspect, back up and diff. In the repository, cases/ and campaigns/ are untracked by git, because they hold your problems and model output. Path Holds cases/MATH-0001/ One case, written by mathos. Do not hand-edit while a run is active. OBJECTIVE.md Your exact input, preserved byte for byte. DIC/, EPS/INITIAL.md The frozen contract (intent, requests, plan) and the initial stage-graph description. Hash-checked. WORKFLOW.json, STATE.json …"},{"id":"/projects/mathresearchos/details/#safety-h","page":"MathResearchOS: Usage Guide","section":"Safety limits","url":"/projects/mathresearchos/details/#safety-h","kind":"section","text":"Calls are capped. Each case has a call budget (16 for v1; 16 plus the explorers for v2) and at most 2 repair cycles. A run that reaches the budget stops at a human gate. Dry run first. --dry-run and campaign --dry-run make no calls. A live campaign refuses to start without --confirm-live. The objective and contract are frozen. If either changes, the run halts. Accepted stage artifacts are hash-checked. No outward actions. A run does not publish anywhere, commit to GitHub, rent compute or change your objective. It writes inside its case folder. Narrow tools. Claude stages run with no MCP …"},{"id":"/projects/mathresearchos/details/#limitations-h","page":"MathResearchOS: Usage Guide","section":"Limitations and what an accept means","url":"/projects/mathresearchos/details/#limitations-h","kind":"section","text":"A verifier’s accept means its audit accepted the supplied evidence under the contract. It is not a Lean kernel certificate and not a guarantee that a statement is true. Two models agreeing, even from different families, is still an informal audit. For a result you intend to rely on, add a human read, a witness checker or the Lean kernel. Scope The runtime schedules and gates; the mathematical reasoning is done by the configured models, and no result is a formal theorem because a run completed. With one model family, every checker verdict is same-family and provisional. Different models …"},{"id":"/projects/mathresearchos/details/#troubleshooting-h","page":"MathResearchOS: Usage Guide","section":"Troubleshooting","url":"/projects/mathresearchos/details/#troubleshooting-h","kind":"section","text":"“Claude Code CLI not found”, or a Codex stage fails at once The CLI for that family is not installed or not on PATH, or you are not logged in. Run claude or codex once by hand, log in, then mathos resume. Use --route openai or claude if you only have one. “Case is locked by a run” Another run holds the case, or an earlier one crashed. Look at mathos status first. If the recorded process is gone, release the stale lock and then resume. The command refuses if the process is still alive: mathos recover-lock MATH-0001 --confirm-stale mathos resume MATH-0001 The run stopped and exits with code 2 …"},{"id":"/projects/mathresearchos/details/#summary-h","page":"MathResearchOS: Usage Guide","section":"In brief","url":"/projects/mathresearchos/details/#summary-h","kind":"section","text":"Design One objective becomes a case with a frozen contract and a stage graph. Models do the work, a verifier gates each audited stage, and everything is kept on disk, so a run can be paused, resumed and audited. Results One pilot problem went through the v2 workflow end to end with a correct final proof, which shows that the plumbing and the explorer swarm work. It measures no accuracy, and no held-out comparison has been run. Open questions Which model fits which role, how often checkers wrongly accept or reject, and how much a second family helps are all untested here. Limitations →"},{"id":"/projects/mathresearchos/details/#sources-h","page":"MathResearchOS: Usage Guide","section":"Sources","url":"/projects/mathresearchos/details/#sources-h","kind":"section","text":"This page follows the MathResearchOS repository’s README.md, START.md, AGENTS.md, docs/MODEL_SELECTION_GUIDE.md (verified 2026-11-11), docs/OS_DESIGN.md (the roadmap), skills/README.md, examples/, experiments/README.md and benchmarks/README.md, and the output of mathos --help and each subcommand’s --help. The package is version 0.1.0."},{"id":"/projects/mathresearchos/","page":"MathResearchOS","section":"","url":"/projects/mathresearchos/","kind":"page","text":"MathResearchOS: a command-line system that turns a mathematical objective into a recoverable, verifier-gated run across Codex and Claude models, keeping every attempt on disk. Install, quick start and a one-run figure."},{"id":"/projects/mathresearchos/#glance-h","page":"MathResearchOS","section":"MathResearchOS at a glance","url":"/projects/mathresearchos/#glance-h","kind":"section","text":"Quick start Install, create a case from a problem file, preview the run for free, then run it. The full guide covers each step. pip install -e . mathos create --mode solve --title \"First problem\" --objective-file problem.md mathos run MATH-0001 --dry-run mathos run MATH-0001 --route cross mathos status MATH-0001 Live runs call real models and can cost money; --dry-run never does. A live run needs a logged-in codex or claude CLI. Install details → Evidence so far Pilot run tested One public-benchmark problem (IMO-ProofBench, problem PB-Basic-008) through the v2 workflow with 8 explorers: 17 …"},{"id":"/projects/mathresearchos/#Jump to what you need","page":"MathResearchOS","section":"Jump to what you need","url":"/projects/mathresearchos/","kind":"section","text":"Solve one problem · create, dry run, run Choose models · presets, mixes, pools Follow and resume a run · status, events, usage Human gates · continue, hand-off Campaigns · many problems, many routes Lean check · kernel errors, sorry, axioms Where data is stored · cases, campaigns, experiments Troubleshooting · locks, gates, missing CLIs What an accept means, and the limitations →"},{"id":"/projects/mathresearchos/#next-h","page":"MathResearchOS","section":"Where this is going proposed","url":"/projects/mathresearchos/#next-h","kind":"section","text":"### Held-out model comparisons A benchmark harness with contamination-aware held-out problems; effort sweeps, a verifier canary with known-wrong proofs and explorer-yield counts, each planned before the run and reported in full. ### Obligation ledger and independent checkers A proof-obligation ledger the final verifier must cover, plus exact-arithmetic and Lean adapters, so more claims rest on a checkable certificate and less on a model’s audit. ### Longer research runs Retrieval-backed memory with a novelty ledger, so objectives that take many sessions do not repeat approaches already tried."},{"id":"/projects/mathresearchos/#Related projects","page":"MathResearchOS","section":"Related projects","url":"/projects/mathresearchos/","kind":"section","text":"AI Native Workflow"},{"id":"/projects/ntuinfo-com/","page":"ntuinfo.com","section":"","url":"/projects/ntuinfo-com/","kind":"page","text":"A bilingual English/Chinese full-stack web application with a quantitative, multi-criteria scoring framework (mental load, physical load, difficulty) that ranks 100+ NTU student clubs and surfaces algorithmically-driven recommendations for students."},{"id":"/projects/policyattention/details/","page":"PolicyAttention: How It Works","section":"","url":"/projects/policyattention/details/","kind":"page","text":"How PolicyAttention works: why softmax rather than linear attention, the actor, environment and critic errors, the exact reversal boundary and state-local mask, coverage relaxed, learned Transformers in repeated control, and the limitations."},{"id":"/projects/policyattention/details/#why-softmax-h","page":"PolicyAttention: How It Works","section":"Why softmax, not linear attention?","url":"/projects/policyattention/details/#why-softmax-h","kind":"section","text":"Transformers can run learning algorithms in context. For reinforcement learning, the constructions that improve a policy, and not only evaluate it, have used linear attention: its unnormalized bilinear products can carry a semi-gradient or actor–critic update. Standard softmax attention behaves differently. Its outputs are positive, normalized mixtures, and the constructive results for it have stopped at policy evaluation (temporal-difference learning). For one well-known control update that normalization is not an obstacle but the update itself. Negative-entropy policy mirror descent (PMD) …"},{"id":"/projects/policyattention/details/#parts-h","page":"PolicyAttention: How It Works","section":"Three calls, three errors","url":"/projects/policyattention/details/#parts-h","kind":"section","text":"Each round runs in a fixed order: the actor must form a policy before the environment can sample under it, and the critic may only evaluate that policy after the samples exist. The order separates three kinds of error. How should the policy change? Actor · softmax routing error $ζ_k$ Memories carry each state–action pair’s $log π$ and $Q$; a query routes to its own state’s memories and the softmax takes the PMD step. With a finite margin $κ$, other states’ memories keep a small weight; $ζ_k$ measures how far the row ends up from exact PMD. What happens under the new policy? Environment · …"},{"id":"/projects/policyattention/details/#explorer-h","page":"PolicyAttention: How It Works","section":"Why a stronger step can backfire","url":"/projects/policyattention/details/#explorer-h","kind":"section","text":"A larger step $η$ makes ideal PMD greedier, which helps. It also spreads the scores further apart, and a finite margin has to keep the other states’ memories down against that spread. In a two-state family where every quantity is exact, the competition reduces to one ratio, $ρ = ηc/((1 − γ)κ)$ for reward scale $c$: the implemented update improves the policy when $ρ&lt;1$ and makes it worse when $ρ > 1$. Figure 2. Try it. Two self-looping states with rewards $( − c,0)$ and $(c,0)$, a uniform prior and its exact $Q$, $c = 1$, $γ = 0.8$; the curve is the value gain at the worse state. Exact …"},{"id":"/projects/policyattention/details/#method-h","page":"PolicyAttention: How It Works","section":"The decoder in one picture","url":"/projects/policyattention/details/#method-h","kind":"section","text":"Figure 3. Two calls per round. One fixed decoder reads an actor packet, then, after the environment has sampled under the new policy, a critic packet. Causal masking means no critic token can see a transition before the policy that generated it exists. Small and fixed. 2 blocks, 2 heads, head width S+A+3 and model width 6S+6A+14, with a gated ReLU feed-forward map of 8 active units. The same weights serve both calls; the step size $η_k$ arrives as token content. Normalization-free. No layer normalization: the value channels must keep controlled amplitudes while the key channels carry …"},{"id":"/projects/policyattention/details/#where-h","page":"PolicyAttention: How It Works","section":"Where it runs","url":"/projects/policyattention/details/#where-h","kind":"section","text":"The two NeurIPS 2026 workshop papers split the work: one builds the loop and its guarantee and checks a learned Transformer against it; the other maps where the loop fails. Two ICAIF 2026 workshop papers take the update rule into synthetic finance settings. PTA Workshop, NeurIPS 2026 tested Construction, guarantee, learned realization The causal loop, the returned-policy bound, a learned pre-LN Transformer, repeated control by trained actors, and the decoder with the coverage oracle relaxed. OpenReview EvoRobust Workshop, NeurIPS 2026 tested Failure modes and robustness The exact reversal …"},{"id":"/projects/policyattention/details/#protocol-h","page":"PolicyAttention: How It Works","section":"How we test it","url":"/projects/policyattention/details/#protocol-h","kind":"section","text":"Every experiment uses small finite MDPs where the true values can be computed exactly, so each error is measured against the truth rather than estimated. Two kinds of evidence are kept apart. The exact construction. The fully specified decoder, run as written. On the two-state family every number is a deterministic computation; in the coverage study the decoder runs on 64 fresh random MDPs with $S = 4$, $A = 3$, $γ = 0.8$, $η = 0.8$ and $T = 20$ rounds, its protocol fixed in a file before the run. Learned Transformers. Ordinary pre-LN Transformers trained on generated MDPs with disjoint …"},{"id":"/projects/policyattention/details/#failure-h","page":"PolicyAttention: How It Works","section":"Results: the exact decoder","url":"/projects/policyattention/details/#failure-h","kind":"section","text":"Take the two-state family at margin $κ = 8$ and raise the step from 0.8 to 2.4. Ideal PMD gets better at every step. The implemented update, through the decoder’s own forward map, gets worse and then reverses. Step η = 0.8 ρ = 0.5 · below the boundary +0.916 of 0.950 Result. The implemented gain keeps most of the ideal gain; the actor’s row error is 0.014. Step η = 1.6 ρ = 1 · on the boundary 0.000 of 1.660 Result. Exactly no improvement: the leaked mass cancels the PMD step. Row error 0.664. Step η = 2.4 ρ = 1.5 · past the boundary −2.009 of 2.084 Result. The largest ideal gain becomes the …"},{"id":"/projects/policyattention/details/#coverage-h","page":"PolicyAttention: How It Works","section":"Relaxing the coverage oracle","url":"/projects/policyattention/details/#coverage-h","kind":"section","text":"The guarantee assumes the critic receives fresh samples for every state–action pair after each actor call. An acting agent does not get that: it sees one trajectory. The theorem says nothing once the oracle is removed, so we ran its own decoder there. Every arm gets the same budget of 12$m$ fresh transitions per round; only how they are spread differs. Figure 5. Same budget, different coverage. Normalized returned-policy loss after 20 rounds on 64 MDPs, one dot per MDP. Balanced is the oracle, with $m$ draws per pair; uniform pairs draws pairs at random; the on-policy stream is one continuing …"},{"id":"/projects/policyattention/details/#learned-h","page":"PolicyAttention: How It Works","section":"Results: learned Transformers","url":"/projects/policyattention/details/#learned-h","kind":"section","text":"Does an ordinary Transformer, trained without PMD labels, learn the same map? On held-out MDPs a pre-LN actor’s output is closest to PMD by a wide margin among five fixed rules, and it responds to the step size it is given. Closest rule Held-out row-L1 error to PMD 0.0357 Result. The next-closest fixed rule is at 0.112. Mean KL to PMD 0.0022; fitted step 0.755–0.810 for a supplied 0.8. Critic TD error on held-out MDPs 0.121 Result. Mean absolute TD error of the Bellman-trained critic; the largest error seen is 0.676. Repeated control 5 trained actors · 20 rounds 1.052× Result. Median loss …"},{"id":"/projects/policyattention/details/#stress-h","page":"PolicyAttention: How It Works","section":"Stress test and matched audit","url":"/projects/policyattention/details/#stress-h","kind":"section","text":"Are the learned errors uniformly small? A screen of a separately trained pre-LN checkpoint, 512 examples per condition from 8 generated MDPs, says no: on low-entropy inputs the mean row error to PMD is 0.059 but the largest is 1.977, close to the maximum possible of 2 (all conditions in §15). Two follow-ups separate what that screen can and cannot say. It is not the routing failure. This model’s actor packet for a state holds only that state’s memories, so the competing group of §3 does not exist and a state-local mask would change nothing. Large row error is not value loss. On a retrained …"},{"id":"/projects/policyattention/details/#limitations-h","page":"PolicyAttention: How It Works","section":"Limitations and what didn’t work","url":"/projects/policyattention/details/#limitations-h","kind":"section","text":"Scope A generative oracle, not trajectories. The guarantee assumes fresh samples for every state–action pair after each actor call, with at least $m_{min,k}$ per pair. Trajectory data do not provide this: pairs go unvisited, counts depend on the data, samples are Markov-dependent and successor actions go stale. Step sizes and packet caps are supplied from outside; the decoder does not choose its own schedule. Normalization-free. The exact construction has no layer normalization, and nothing is proved for pre-LN, RMSNorm, post-LN or final-LN models. The learned pre-LN model is compared with …"},{"id":"/projects/policyattention/details/#next-h","page":"PolicyAttention: How It Works","section":"Open questions","url":"/projects/policyattention/details/#next-h","kind":"section","text":"These come from the papers’ own scope sections and reviewers’ remaining concerns; none has been run. ### Learning without the oracle Run a learned critic on ordinary trajectory data, where pairs go unvisited and samples depend on each other, and measure what happens to the returned policy. The coverage study suggests where to look: how the critic treats pairs it has not seen. ### Closed-loop audits of learned models Measure a learned model’s actor and critic errors against the policy it actually executes, round after round, rather than on fixed inputs, so that the bound’s residuals are …"},{"id":"/projects/policyattention/details/#theory-h","page":"PolicyAttention: How It Works","section":"Definitions and the bound","url":"/projects/policyattention/details/#theory-h","kind":"section","text":"Take a finite discounted MDP with $S$ states, $A$ actions, $0 < γ&lt;1$ and $ r ≤ R_{max}$; write $B_Q = R_{max} /(1 − γ)$ and $F^π$ for the one-step Bellman operator under $π$. With $p_{k + 1} = PMD_{η_k } (π_k ,Q_k )$ the ideal update and $π^^ _{k + 1}$ the actor’s output, the two residuals are $$ζ_k = max_s ‖π^^ {k + 1} ( · ∣s) − p{k + 1} ( · ∣s)‖_1 ,$$ $$δ_k = ‖Q_{k + 1} − F^{π^^ _{k + 1} } Q_k ‖_∞ .$$ For the greedy set $G_k (s) = \\arg max_a Q_k (s,a)$, let $D_k (s) = − log π_k (G_k (s)∣s)$, $D^¯ k = max{s,a} E_{S^′ ∣s,a} D_k (S^′ )$ and $h_k = D^¯ _k /η_k + B_Q ζ_k$. Choose $b_0 ≥ ‖Q^⋆ …"},{"id":"/projects/policyattention/details/#witness-h","page":"PolicyAttention: How It Works","section":"The two-state family","url":"/projects/policyattention/details/#witness-h","kind":"section","text":"States $s_{ − }$ and $s_{ + }$ loop on themselves, with action rewards $( − c,0)$ and $(c,0)$. From a uniform prior and its exact $Q^π$, the query at each state sees all four state–action memories with logits $log \\frac{1}{2} + ηQ^π (s^¯ ,a) + κ1{s^¯ = s}$ and one-hot action values, and itself with logit $− ν$ and a uniform value. This row is exactly the actor call of the frozen decoder at $S = A = 2$, up to a common score shift. At $s_{ − }$, ideal PMD picks the better action with probability $σ(ηc)$, and the wrong-state group, which prefers the other action, has partition ratio …"},{"id":"/projects/policyattention/details/#tables-h","page":"PolicyAttention: How It Works","section":"Full tables","url":"/projects/policyattention/details/#tables-h","kind":"section","text":"Coverage relaxation in the normalization-free decoder $m$ Arm Unvisited pairs Min. count Critic error $δ$ Loss $L_T$ [95%] Paired difference to balanced 6 Balanced (oracle) 0.00 6.00 0.214 0.009 [0.007, 0.013] – 6 Uniform pairs 0.03 2.38 0.259 0.010 [0.006, 0.013] −0.000 [−0.001, 0.000] 6 On-policy stream 3.86 0.20 1.219 0.029 [0.026, 0.032] +0.018 [0.014, 0.022] 6 On-policy stream, carry 4.59 0.19 1.284 0.010 [0.005, 0.012] −0.001 6 Exploring stream 1.45 0.37 0.857 0.012 [0.010, 0.016] +0.001 24 Balanced (oracle) 0.00 24.00 0.106 0.009 [0.007, 0.013] – 24 On-policy stream 3.02 1.38 1.134 …"},{"id":"/projects/policyattention/details/#repro-h","page":"PolicyAttention: How It Works","section":"Reproducibility notes","url":"/projects/policyattention/details/#repro-h","kind":"section","text":"Decoder Every token coordinate, packet order, $Q/K/V/O$ matrix and feed-forward weight is listed in the EvoRobust supplement; at $S = A = 2$ the weights have 60 non-zero entries. All 1,803 grid cells replay through the full forward map, and the repository circuit agrees on all weights and actor outputs. Exact checks Direct softmax and Bellman solves match the partition and error–value identities on the 1,803 grid cells and on 2,928 further checks over reward scale, discount and margin, all to machine precision (errors below 10^−14). Coverage study 64 MDPs drawn once from a fixed seed, uniform …"},{"id":"/projects/policyattention/details/#summary-h","page":"PolicyAttention: How It Works","section":"In brief","url":"/projects/policyattention/details/#summary-h","kind":"section","text":"Design Policy mirror descent multiplies each action’s probability by the exponential of its value and renormalizes, which is what a softmax does. A small fixed decoder uses one attention row for that step and a second call for TD evaluation, and its errors are carried into a bound on the returned policy. Results In the exact decoder, a margin of 8 turns an ideal gain of 2.084 at step 2.4 into an implemented gain of −2.009, and masking other states removes the effect. Trained without PMD labels, a pre-LN Transformer lands within 0.0357 of PMD per row, and five trained actors control within …"},{"id":"/projects/policyattention/details/#sources-h","page":"PolicyAttention: How It Works","section":"Sources","url":"/projects/policyattention/details/#sources-h","kind":"section","text":"PolicyAttention: Softmax Attention Implements Policy Mirror Descent for Closed-Loop Control. Yuhe Sui, Yingzhi Tang, Shufang Chen. arXiv 2609.30500, 2026. [[arXiv]](https://arxiv.org/abs/2609.30500)"},{"id":"/projects/policyattention/details/#Accepted Research","page":"PolicyAttention: How It Works","section":"Accepted Research","url":"/projects/policyattention/details/","kind":"section","text":"### PolicyAttention: Robustness and Failure Modes of Softmax Policy Improvement Yuhe Sui, Yingzhi Tang, Xinyue Wu EvoRobust Workshop, NeurIPS 2026 · 2026 · Accepted [[OpenReview]](https://openreview.net/forum?id=VgswuGrqp6) ### PolicyAttention: When Softmax Attention Becomes Policy Improvement Yuhe Sui PTA Workshop, NeurIPS 2026 · 2026 · Accepted [[OpenReview]](https://openreview.net/forum?id=zbGWnk0kY3) The EvoRobust camera-ready version is titled PolicyAttention: When Stronger Softmax Policy Improvement Backfires. Results come from the camera-ready versions of the two NeurIPS workshop …"},{"id":"/projects/policyattention/icaif/details/","page":"In-Context PMD in Market Making: How It Works","section":"","url":"/projects/policyattention/icaif/details/","kind":"page","text":"How the ICAIF 2026 component diagnosis works: an exactly solvable market-making family, the in-context PMD loop and its exact swap, what the actor and the critic cost, the payoff against desk rules, and the limitations."},{"id":"/projects/policyattention/icaif/details/#why-h","page":"In-Context PMD in Market Making: How It Works","section":"Why take the controller apart?","url":"/projects/policyattention/icaif/details/#why-h","kind":"section","text":"A market maker keeps re-setting its quote skew as fees, volatility, liquidity and order-flow toxicity change. In-context reinforcement learning offers a controller that adapts without being re-engineered for each regime: a sequence model with frozen weights adapts at inference time by conditioning on recent experience. When such a controller does badly after a regime shift, the practitioner needs to know which learned component failed before deciding what to fix. End-to-end scores mix three things: how well the policy-improvement step is learned, how well the value estimate it relies on is …"},{"id":"/projects/policyattention/icaif/details/#market-h","page":"In-Context PMD in Market Making: How It Works","section":"A market we can solve exactly","url":"/projects/policyattention/icaif/details/#market-h","kind":"section","text":"The dealer holds inventory $q$ from −2 to 2 and observes order-flow imbalance $z ∈ { − 1,0, + 1}$, giving 15 states. Each step it sets a quote skew $u ∈ { − 1,0, + 1}$; at most one fill occurs. Buy pressure raises both the chance that the dealer's ask is hit and the chance that the price then rises: the adverse-selection channel, carried here by an observed state. The reward is spread income minus fees, plus mark-to-market, minus a mean–variance inventory penalty, with discount 0.8. There are 9 families of 64 paired markets: nominal (G0) and fee, volatility, liquidity and toxicity stress (F …"},{"id":"/projects/policyattention/icaif/details/#method-h","page":"In-Context PMD in Market Making: How It Works","section":"The loop and the swap in one picture","url":"/projects/policyattention/icaif/details/#method-h","kind":"section","text":"The in-context loop and the exact swap. The formulas are written out under Notation and metrics. Actor. Reads the policy $π_k$, the action values $Q_k$ and the step $η$, and returns $π_{k + 1}$. It is trained toward the PMD step, $softmax( log π_k + ηQ_k )$. Critic. Reads $Q_k$, the reward table and 6 sampled successors per state–action pair, and returns $Q_{k + 1}$. It is trained toward the average backup of those six samples. The arms. Exact runs exact PMD with the exact backup (exact TD-PMD, the reference). ActorOnly learns only the actor, CriticOnly only the critic, FullLoop both. The …"},{"id":"/projects/policyattention/icaif/details/#components-h","page":"In-Context PMD in Market Making: How It Works","section":"What each part costs after 20 rounds","url":"/projects/policyattention/icaif/details/#components-h","kind":"section","text":"Each cost is a paired difference in normalized loss against exact TD-PMD on the same market: the median of 320 paired values (5 runs × 64 markets) with a 95% hierarchical-bootstrap interval. Lower is better. Learned actor Pre-registered · nominal markets +0.0020 interval [−0.0002, +0.0043], which includes 0. Within the holds margin of exact TD-PMD on all nine families (ratios 0.990–1.086). Learned critic Pre-registered · nominal markets +0.0219 interval [+0.0186, +0.0248]. Positive on every family, from +0.0191 (F1) to +0.0580 (L2). The full loop's excess, +0.0235, is almost all the critic's. …"},{"id":"/projects/policyattention/icaif/details/#rounds-h","page":"In-Context PMD in Market Making: How It Works","section":"By round and by family","url":"/projects/policyattention/icaif/details/#rounds-h","kind":"section","text":"Excess loss over exact TD-PMD, round by round. Median of 320 paired values per round, on nominal (G0), severe volatility (V2) and severe illiquidity (L2) markets. Family ℓ(Exact) ActorOnly CriticOnly FullLoop SC1 · SampleAvg − Exact SC2 · CriticOnly − SampleAvg G0 nominal 0.133 +0.0020 [−0.0002, +0.0043] +0.0219 [+0.0186, +0.0248] +0.0235 [+0.0188, +0.0277] +0.0220* −0.0007 F1 fee, moderate 0.113 +0.0018 [−0.0010, +0.0042] +0.0191 [+0.0143, +0.0212] +0.0200 [+0.0164, +0.0254] +0.0197* −0.0002 F2 fee, severe 0.100 +0.0018 [−0.0009, +0.0043] +0.0221 [+0.0177, +0.0275] +0.0234 [+0.0194, +0.0297] …"},{"id":"/projects/policyattention/icaif/details/#rules-h","page":"In-Context PMD in Market Making: How It Works","section":"Where the loop pays off against desk rules","url":"/projects/policyattention/icaif/details/#rules-h","kind":"section","text":"HBEST is the best of 45 linear skew rules on 256 separate nominal markets (a = 1, b = −1, c = −0.5; mean capture 0.872 there). It leans against inventory and order flow and is not re-tuned per regime. HIMB skews against order flow alone ($u = − z$). Value-capture difference $C(FullLoop) − C(rule)$ at round 20, with 95% hierarchical-bootstrap intervals; every label shown is separated from 0 (†: not separated under a crossed bootstrap). Black dashes: exact TD-PMD in the loop's place. Fee and toxicity stress break HBEST. Its median capture falls from 0.931 nominally to 0.677 on F2 and 0.714 on …"},{"id":"/projects/policyattention/icaif/details/#adapt-h","page":"In-Context PMD in Market Making: How It Works","section":"Adapting after a shift","url":"/projects/policyattention/icaif/details/#adapt-h","kind":"section","text":"Is adapting in context better than keeping the old optimum? CARRY applies the nominal twin's exact optimal policy unchanged. From a random start, the loop is ahead of CARRY on I2 (+0.0218 [+0.0101, +0.0306]) after 20 rounds. The regime-switch test gives the loop a warmer start: 20 rounds on the nominal twin, then 20 on the severe market. The loop then ends above CARRY on I2 (+0.0328 [+0.0148, +0.0420]). The other severe families are reported under Limitations and what didn't work."},{"id":"/projects/policyattention/icaif/details/#meaning-h","page":"In-Context PMD in Market Making: How It Works","section":"What the results mean","url":"/projects/policyattention/icaif/details/#meaning-h","kind":"section","text":"Improve the critic stage first, including the backup it is trained toward. Its excess is positive on every family, while the learned actor stays within the holds margin of exact PMD. Fix the target, not only the fit. In the follow-up, the untrained six-sample average loses about as much as the learned critic, so fitting that target better cannot remove most of the cost. Fees and toxic order flow break the best nominal rule. There the loop beats it, in value capture on severe fee and toxicity stress."},{"id":"/projects/policyattention/icaif/details/#limitations-h","page":"In-Context PMD in Market Making: How It Works","section":"Limitations and what didn't work","url":"/projects/policyattention/icaif/details/#limitations-h","kind":"section","text":"Scope The market is stylized and exactly solvable (15 states, observed toxicity), and value capture says nothing about trading P&L. The controller also gets exact rewards, a generative sampler and an exact initial value table. Information budget: in every round the critic receives the exact expected reward table and six sampled successors for every state–action pair (270 samples per round), and every arm starts from the exact $Q^{π_0 }$. Fee and volatility stress change only the reward table, so on F and V the regime change reaches the controller through exact rewards. The adaptation tests …"},{"id":"/projects/policyattention/icaif/details/#open-h","page":"In-Context PMD in Market Making: How It Works","section":"Where this is going","url":"/projects/policyattention/icaif/details/#open-h","kind":"section","text":"### A better critic target Try targets better than the six-sample average and other sample budgets, and split the critic's excess between the noise of its six samples and the network's error. Exact component swaps with untrained controls can check each improvement before adaptation is claimed. ### A converged starting policy Run the adaptation tests from a converged nominal policy and for more than 20 rounds. ### Why the critic and not the actor Find a theory for why the critic, not the actor, limits control. Part 3 · Technical details"},{"id":"/projects/policyattention/icaif/details/#definition-h","page":"In-Context PMD in Market Making: How It Works","section":"Notation and metrics","url":"/projects/policyattention/icaif/details/#definition-h","kind":"section","text":"Negative-entropy policy mirror descent improves a full-support policy $π_k$ against an action-value estimate $Q_k$ with step $η > 0$, in every state $s$: $$π_{k + 1} ( · ∣s) = argmax_{ν ∈ Δ_A } η⟨ν,Q_k (s, · )⟩ − KL(ν‖π_k ( · ∣s))$$ whose solution is the softmax step the actor is trained toward: $$π_{k + 1} ( · ∣s) = softmax( log π_k ( · ∣s) + ηQ_k (s, · )).$$ Pairing it with a one-step evaluation $Q_{k + 1} = 𝒯^{π_{k + 1} } Q_k$ gives temporal-difference PMD (TD-PMD), where $$(𝒯^π Q)(s,u) = r(s,u) + γ𝔼_{s^′ } ⟨π( · ∣s^′ ),Q(s^′ , · )⟩.$$ The learned critic is trained toward the six-sample …"},{"id":"/projects/policyattention/icaif/details/#protocol-h","page":"In-Context PMD in Market Making: How It Works","section":"Protocol and controls","url":"/projects/policyattention/icaif/details/#protocol-h","kind":"section","text":"Pre-registration. The holds and class rules were committed before any learned result, the tests and statistics code before any locked output was read, and the follow-up protocol before any of its rows was computed. SampleAvg was registered after the main results were known. Holds rule. An arm holds on a family if its per-run ratio of median losses to exact TD-PMD is at most 1.5 in the median run and in at least 4 of 5 runs, fewer than 2 runs are systematically stalled (over 25% of markets stalled), and all numerical audits pass. On nominal markets ActorOnly, CriticOnly and FullLoop reach …"},{"id":"/projects/policyattention/icaif/details/#summary-h","page":"In-Context PMD in Market Making: How It Works","section":"In brief","url":"/projects/policyattention/icaif/details/#summary-h","kind":"section","text":"Design A frozen Transformer runs policy mirror descent in context on a 15-state dealer market that can be solved exactly: an actor takes the policy step and a critic estimates the next action values from 6 sampled transitions per state–action pair. Each learned part is replaced by its exact counterpart, one at a time, on 9 families of 64 paired markets, in 5 runs. Results After 20 rounds on nominal markets the learned actor's excess normalized loss is +0.0020 and the learned critic's is +0.0219, against +0.0235 for the full loop. An untrained average of the critic's six samples loses …"},{"id":"/projects/policyattention/icaif/details/#sources-h","page":"In-Context PMD in Market Making: How It Works","section":"Sources","url":"/projects/policyattention/icaif/details/#sources-h","kind":"section","text":"### Where Does Learned In-Context Policy Mirror Descent Pay Off in Market Making? A Component Diagnosis Xinyue Wu, Yuhe Sui, Shufang Chen, Yingzhi Tang ICAIF 2026 Workshop on AI-Driven Market Microstructure in Centralized and Decentralized Finance · Milan · Poster 03 [[Workshop listing]](https://icaif2026.org/workshop-papers/#paper-ai-market-microstructure-1245) [[Workshop]](https://icaif-ai-driven.github.io/) Numbers are taken from the paper's text and Table 1 and from the figure data of its Figs. 2 and 3."},{"id":"/projects/policyattention/icaif/","page":"In-Context PMD in Market Making: A Component Diagnosis","section":"","url":"/projects/policyattention/icaif/","kind":"page","text":"Where does learned in-context policy mirror descent pay off in market making? An ICAIF 2026 workshop paper that swaps the learned actor and critic for their exact counterparts in an exactly solvable dealer market."},{"id":"/projects/policyattention/icaif/#glance-h","page":"In-Context PMD in Market Making: A Component Diagnosis","section":"The paper at a glance","url":"/projects/policyattention/icaif/#glance-h","kind":"section","text":"The idea Policy mirror descent (PMD) improves a policy $π$ against action values $Q$ with a step $η$: $$π_{k + 1} = softmax( log π_k + ηQ_k )$$ One frozen Transformer runs both halves in context: an actor that takes this step and a critic that estimates the next $Q$ from 6 sampled transitions per state–action pair. Because our dealer market is exactly solvable, each half has an exact counterpart, and a failure becomes a set of measured component costs. Experiments Synthetic market tested Learned actor · +0.0020 Learned critic · +0.0219 Both learned · +0.0235 Excess normalized loss over exact …"},{"id":"/projects/policyattention/icaif/#next-h","page":"In-Context PMD in Market Making: A Component Diagnosis","section":"Where this is going from the paper","url":"/projects/policyattention/icaif/#next-h","kind":"section","text":"### A better critic target A critic that fitted its six-sample target perfectly would keep at least 70% of the cost, so the next step is a target better than the six-sample average, tried at other sample budgets. ### A converged starting policy Run the adaptation tests from a converged nominal policy and for more than 20 rounds. ### Why the critic and not the actor Find a theory for why the critic, not the actor, limits control. The directions in full →"},{"id":"/projects/policyattention/icaif/#Paper","page":"In-Context PMD in Market Making: A Component Diagnosis","section":"Paper","url":"/projects/policyattention/icaif/","kind":"section","text":"### Where Does Learned In-Context Policy Mirror Descent Pay Off in Market Making? A Component Diagnosis Xinyue Wu, Yuhe Sui, Shufang Chen, Yingzhi Tang ICAIF 2026 Workshop on AI-Driven Market Microstructure · 2026 · Accepted, Poster 03 [[Workshop listing]](https://icaif2026.org/workshop-papers/#paper-ai-market-microstructure-1245) This work is part of PolicyAttention."},{"id":"/projects/policyattention/","page":"PolicyAttention","section":"","url":"/projects/policyattention/","kind":"page","text":"PolicyAttention: one softmax attention row computes the policy mirror descent step exactly. A causal actor-environment-critic loop with a bound on the returned policy, learned Transformers checked against it, and where a stronger step backfires."},{"id":"/projects/policyattention/#glance-h","page":"PolicyAttention","section":"PolicyAttention at a glance","url":"/projects/policyattention/#glance-h","kind":"section","text":"The idea Negative-entropy policy mirror descent (PMD) moves a policy $π$ towards actions with high value $Q$, with step size $η$, state by state: $$π_{k + 1} = softmax( log π_k + ηQ_k )$$ An attention row whose scores are $log π + ηQ$ computes this exactly. The environment then supplies fresh samples under the new policy, a softmax critic evaluates it, and the errors of both add up to a bound on the loss of the policy the loop returns. Experiments Exact decoder tested Ideal / implemented gain, η = 0.8 · 0.950 / +0.916 · Ideal / implemented gain, η = 2.4 · 2.084 / −2.009 A larger step makes …"},{"id":"/projects/policyattention/#next-h","page":"PolicyAttention","section":"Where this is going open","url":"/projects/policyattention/#next-h","kind":"section","text":"### Learning without the oracle A learned critic run on ordinary trajectory data, where some pairs go unvisited and samples are dependent. ### Closed-loop audits of learned models Learned rollouts whose actor and critic errors are measured against the policy they actually execute. ### Routing failures in general models Whether the reversal seen in the exact decoder occurs in learned Transformers that see other states’ memories. The open questions in full →"},{"id":"/projects/policyattention/#Accepted Research","page":"PolicyAttention","section":"Accepted Research","url":"/projects/policyattention/","kind":"section","text":"### PolicyAttention: Robustness and Failure Modes of Softmax Policy Improvement Yuhe Sui, Yingzhi Tang, Xinyue Wu EvoRobust Workshop, NeurIPS 2026 · 2026 · Accepted [[OpenReview]](https://openreview.net/forum?id=VgswuGrqp6) ### PolicyAttention: When Softmax Attention Becomes Policy Improvement Yuhe Sui PTA Workshop, NeurIPS 2026 · 2026 · Accepted [[OpenReview]](https://openreview.net/forum?id=zbGWnk0kY3)"},{"id":"/projects/policyattention/#Preprint and ICAIF 2026","page":"PolicyAttention","section":"Preprint and ICAIF 2026","url":"/projects/policyattention/","kind":"section","text":"### PolicyAttention: Softmax Attention Implements Policy Mirror Descent for Closed-Loop Control Yuhe Sui, Yingzhi Tang, Shufang Chen arXiv 2609.30500 · 2026 [[arXiv]](https://arxiv.org/abs/2609.30500) ### PolicyAttention: A Certifiable and Testable Update Rule for Attention-Based Allocation Controllers IAFM'26 workshop, ICAIF 2026 · 2026 · Accepted ### Where Does Learned In-Context Policy Mirror Descent Pay Off in Market Making? A Component Diagnosis ICAIF 2026 Workshop on AI-Driven Market Microstructure · 2026 [[Project pages]](https://qrsntu.org/projects/policyattention/icaif/) …"},{"id":"/projects/policyattention/#Publications","page":"PolicyAttention","section":"Publications","url":"/projects/policyattention/","kind":"section","text":"PolicyAttention: Robustness and Failure Modes of Softmax Policy Improvement (2026). Yuhe Sui, Yingzhi Tang, Xinyue Wu. EvoRobust Workshop, NeurIPS 2026. Accepted. OpenReview PolicyAttention: When Softmax Attention Becomes Policy Improvement (2026). Yuhe Sui. PTA Workshop, NeurIPS 2026. Accepted. OpenReview"},{"id":"/projects/riskhedge/details/","page":"RiskHedge: How It Works","section":"","url":"/projects/riskhedge/details/","kind":"page","text":"How RiskHedge works: why not accept the cheap ranking, buying exact prices until the choice is fixed, the decision flow, results on 200 boundary-enriched synthetic instances, limitations, and the certificate in full."},{"id":"/projects/riskhedge/details/#why-h","page":"RiskHedge: How It Works","section":"Why not accept the cheap answer?","url":"/projects/riskhedge/details/#why-h","kind":"section","text":"A risk engine compares candidate hedges by the tail loss of the hedged book over many market scenarios and keeps the least risky few. Exact evaluation reprices every option in every scenario, so systems use price bounds, caches, proxies or learned surrogates instead. These can be accurate on average and still swap the last chosen hedge for the first rejected one when the two are close. The obvious approach is to rank by the approximate numbers and accept the result. Model validation describes how good an approximation is in aggregate, but it does not by itself establish that this hedge …"},{"id":"/projects/riskhedge/details/#explore-h","page":"RiskHedge: How It Works","section":"Buy exact prices until the decision is fixed","url":"/projects/riskhedge/details/#explore-h","kind":"section","text":"Each bar below is a hedge's risk interval: its exact risk lies somewhere inside. Buy exact prices and the bars narrow. The choice is certified once the three chosen bars sit entirely to the left of the other three. Switch on the midpoint shortcut to see a cheap ranking pick the wrong third hedge with nothing to warn you. Illustrative toy, not paper data. Six hedges, top three chosen; each batch is 8 exact primitives, the batch size the paper's gate uses."},{"id":"/projects/riskhedge/details/#method-h","page":"RiskHedge: How It Works","section":"The gate in one picture","url":"/projects/riskhedge/details/#method-h","kind":"section","text":"Decision flow. Redrawn from Fig. 1 of the FinAI-SPS paper; the refinement box says “primitives” where the paper's figure says “legs”, matching the paper's text. Teal is the certified path; the dashed ochre box is the uncertified midpoint baseline. Are the bounds usable? The price-bound provider must be available and valid, the bounds must belong to the current input, and the call must be in the registered scope. A stale input is recomputed; any other failure falls back to exact evaluation. Can any exact value change the choice? If every chosen hedge is better at its worst than every rejected …"},{"id":"/projects/riskhedge/details/#testing-h","page":"RiskHedge: How It Works","section":"How it was tested one synthetic Merton pipeline","url":"/projects/riskhedge/details/#testing-h","kind":"section","text":"The decision chooses the 3 least risky of 24 hedge packages by expected shortfall over 64 market scenarios, on a book that is long one stock. Exhaustive evaluation needs 320 shared exact option-pricing primitives; work is the fraction of those paid after the initial bounds. Baseline. The midpoint baseline gets the same input, bounds, risk measure and tie rule, replaces each interval by its midpoint, ranks and accepts. It pays no exact prices, so it is not work matched. Two stages. A discovery study (120 instances) required midpoint errors in at least two strata, found only 3 in one, and …"},{"id":"/projects/riskhedge/details/#results-h","page":"RiskHedge: How It Works","section":"Results","url":"/projects/riskhedge/details/#results-h","kind":"section","text":"Confirmation Pre-specified · 200 fresh, boundary-enriched instances 0/200 wrong or unsupported decisions by the gate, at a median 17.2% of exhaustive work (max 0.350). The midpoint baseline was silently wrong on 10/200. Guard faults Pre-specified · 60 injected states 60/60 rejected by the intended guard: 40 missing-provider and out-of-scope runs fell back exactly, 20 stale-input runs recomputed and certified. Work-matched Post hoc · same refinement order 11 wrong for an uncertified rule given about the same total work as the gate (8,600 vs 8,518 primitives). Among the budgets tried, zero …"},{"id":"/projects/riskhedge/details/#where-h","page":"RiskHedge: How It Works","section":"Where the shortcut fails, and what certainty costs","url":"/projects/riskhedge/details/#where-h","kind":"section","text":"By boundary risk. The 200 confirmation instances in five equal groups of boundary risk (initial uncertainty relative to the exact margin at the cut-off), frozen before reporting. The midpoint baseline fails only in the top group (10/40); the gate is never wrong, and its median work rises from 0 to 0.21–0.23 of exhaustive, then levels off. Descriptive. Work-matched comparison post hoc Same order, no certificate. Uncertified midpoint rules follow the gate's refinement order, pay a fixed budget of exact primitives per instance, then accept. Selected budgets from the paper's table; totals over …"},{"id":"/projects/riskhedge/details/#meaning-h","page":"RiskHedge: How It Works","section":"What the results mean","url":"/projects/riskhedge/details/#meaning-h","kind":"section","text":"Errors are silent. The baseline's output looks the same whether it is right or wrong. Every one of its 10 errors swapped only the third chosen hedge, all in the near-tie, wide-bound group (pre-specified Fisher test, p = 0.016). Ambiguity becomes work. 35 instances were certified from the initial bounds and 165 after refinement; none needed exhaustive pricing. The certificate adds stopping. A fixed budget either wastes work or leaves errors; the certificate says when each instance can stop."},{"id":"/projects/riskhedge/details/#companion-h","page":"RiskHedge: How It Works","section":"The companion paper EvoRobust, NeurIPS 2026","url":"/projects/riskhedge/details/#companion-h","kind":"section","text":"The EvoRobust paper, by the same authors, asks a related general question: which expensive tests must be run before a risk-sensitive choice is logically fixed? Its Merton option-pricing instantiation shows what certified price bounds can look like: Bounds for Merton European options on a declared domain (spot 90 to 110, volatility 0.1 to 0.3, no dividends), from a Taylor polynomial with an analytic remainder bound and an inspectable proof. A paid query returns a narrower certified interval, never a point. If intervals still overlap after every query, the status is unresolved and no decision …"},{"id":"/projects/riskhedge/details/#limitations-h","page":"RiskHedge: How It Works","section":"Limitations and what didn’t work","url":"/projects/riskhedge/details/#limitations-h","kind":"section","text":"Scope One synthetic pipeline. Everything comes from one Merton jump-diffusion option-hedging pipeline with 24 candidates, 64 scenarios and a top-3 choice, with four distinct exact decisions per study. There is no real portfolio data. A deliberately difficult population. The confirmation instances were enriched near the decision boundary, so 5.0% is a study-population rate, not a deployment error rate. All 10 baseline errors lie in one bin (B1). Their excess expected shortfall is 0.15–0.98%, and the paper attaches no materiality threshold to it. The first study stopped. The discovery study …"},{"id":"/projects/riskhedge/details/#open-h","page":"RiskHedge: How It Works","section":"Open questions","url":"/projects/riskhedge/details/#open-h","kind":"section","text":"### What does certification cost end to end? The work count leaves out building the cheap certified price bounds, and the paper measured no wall-clock time for the gate. A timing study of bound construction would show whether the exact pricing saved outweighs it. ### Does it hold beyond one synthetic book? All evidence comes from one synthetic Merton pipeline with four distinct exact decisions per study. Real portfolios, other pricers and other decisions are untested. ### Can learned models supply valid bounds? The conformal sets of the learned surrogate covered every primitive on only 95, 97 …"},{"id":"/projects/riskhedge/details/#definition-h","page":"RiskHedge: How It Works","section":"Notation and the certificate","url":"/projects/riskhedge/details/#definition-h","kind":"section","text":"Candidate $j$ has exact risk $q_j$: the empirical expected shortfall of the hedged book's scenario losses at tail mass 5%. The exact decision $D^⋆$ is the first $k$ candidates in the lexicographic order of $(q_j ,id_j )$. A shortcut holds an interval $[ℓ_j ,u_j ]$ per candidate, computed from primitive price enclosures by interval arithmetic. $$D\\text{is certified}⟺(u_d ,id_d ) < (ℓ_e ,id_e ) \\text{lexicographically for all}d ∈ D,e ∉ D.$$ Soundness. Assume (A1) every primitive enclosure contains the true model value for the current input, and (A2) the call is within the registered scope $1 ≤ …"},{"id":"/projects/riskhedge/details/#fulltable-h","page":"RiskHedge: How It Works","section":"Full results","url":"/projects/riskhedge/details/#fulltable-h","kind":"section","text":"Condition n Midpoint wrong Gate wrong Unsupported Median work Clean, all bins 200 10 (5.0%; 2.7–9.0%) 0 0 0.172 B1 near-tie × wide bounds 50 10 (20%; 11.2–33.0%) 0 0 0.239 B2–B5 150 0 0 0 0.036 Injected guard faults 60 not run 0 0 – Percentage intervals are Wilson 95% intervals. Work is the median fraction of the 320 shared primitives paid after the initial bounds (1 = exhaustive); the B4–B5 median is 0.0016. Of the fault runs, 40 fell back exactly and 20 recomputed and certified (median work 0.061). REFUSED was never emitted across both studies (0 of 740 gate records). Post hoc, not …"},{"id":"/projects/riskhedge/details/#summary-h","page":"RiskHedge: How It Works","section":"In brief","url":"/projects/riskhedge/details/#summary-h","kind":"section","text":"Design Hedges are ranked from cheap price bounds, but the top 3 is accepted only when every chosen hedge is better at its worst than every rejected hedge at its best. Otherwise the gate buys up to 8 exact primitives and retests, and failed guards or an exhausted budget fall back to exact evaluation. Each run leaves a record that a separate checker can replay. Results On 200 fresh, boundary-enriched synthetic instances the gate made 0 wrong or unsupported decisions at a median 17.2% of exhaustive pricing work. A midpoint ranking with no exact work was wrong on 10, all in one near-tie group. …"},{"id":"/projects/riskhedge/details/#sources-h","page":"RiskHedge: How It Works","section":"Sources","url":"/projects/riskhedge/details/#sources-h","kind":"section","text":"Paper: Certify the Decision, Not the Shortcut: Fail-Closed Screening for Financial Risk Decisions, Yingzhi Tang and Yuhe Sui, Financial AI Security, Privacy, and Safety Workshop (FinAI-SPS) at ICAIF 2026, poster. The workshop is non-archival and does not publish papers; the archive is available from the authors on request. Numbers and labels follow the camera-ready paper: Fig. 1 (decision flow), Sections 2 to 5, and Appendices C (registered criteria), D and H (post hoc audits and experiments) and G (boundary-risk quintiles, with its data file)."},{"id":"/projects/riskhedge/details/#Accepted Research","page":"RiskHedge: How It Works","section":"Accepted Research","url":"/projects/riskhedge/details/","kind":"section","text":"### Diverse Scenarios, Selective Evaluation: Certified Spectral-Risk Decisions under Costly Robustness Tests Yuhe Sui, Yingzhi Tang EvoRobust Workshop, NeurIPS 2026 · 2026 · Accepted [[OpenReview]](https://openreview.net/forum?id=OzOTmkkAWW) Back to top ↑"},{"id":"/projects/riskhedge/","page":"RiskHedge","section":"","url":"/projects/riskhedge/","kind":"page","text":"RiskHedge: a fail-closed gate for financial risk decisions that accepts a cheap hedge ranking only when a certificate shows exhaustive evaluation would choose the same hedges; otherwise it buys exact prices or falls back. ICAIF 2026 FinAI-SPS workshop paper."},{"id":"/projects/riskhedge/#glance-h","page":"RiskHedge","section":"RiskHedge at a glance","url":"/projects/riskhedge/#glance-h","kind":"section","text":"The idea Each candidate hedge $j$ has a risk interval $[ℓ_j ,u_j ]$ computed from certified price bounds. A proposed top-$k$ set $D$ is accepted only if $$(u_d ,id_d ) < (ℓ_e ,id_e )$$ for every chosen $d ∈ D$ and every rejected $e ∉ D$. Every chosen hedge is better at its worst than every rejected hedge at its best, so exact repricing cannot change the set; IDs break ties. Experiments Synthetic tested Gate wrong or unsupported · 0/200 Midpoint shortcut silently wrong · 10/200 Exact work, median · 17.2% 200 fresh instances from one synthetic Merton option-hedging pipeline, enriched near the …"},{"id":"/projects/riskhedge/#next-h","page":"RiskHedge","section":"Open questions from the paper’s limitations","url":"/projects/riskhedge/#next-h","kind":"section","text":"### What does certification cost end to end? The work count leaves out building the cheap certified price bounds, and no wall-clock time was measured in the paper. ### Does it hold beyond one synthetic book? Every result comes from one synthetic Merton pipeline with 24 hedges, 64 scenarios and a top-3 choice. ### Can learned models supply valid bounds? Statistical sets from a learned surrogate missed some prices, so the guarantee does not transfer to them. The questions in full →"},{"id":"/projects/riskhedge/#Workshop paper","page":"RiskHedge","section":"Workshop paper","url":"/projects/riskhedge/","kind":"section","text":"### Certify the Decision, Not the Shortcut: Fail-Closed Screening for Financial Risk Decisions Yingzhi Tang (Quantitative Research Society, Singapore; The Chinese University of Hong Kong, Shenzhen), Yuhe Sui (Quantitative Research Society, Singapore; Nanyang Technological University) Financial AI Security, Privacy, and Safety Workshop (FinAI-SPS) at ICAIF 2026 · poster · non-archival"},{"id":"/projects/riskhedge/#Accepted Research","page":"RiskHedge","section":"Accepted Research","url":"/projects/riskhedge/","kind":"section","text":"### Diverse Scenarios, Selective Evaluation: Certified Spectral-Risk Decisions under Costly Robustness Tests Yuhe Sui, Yingzhi Tang EvoRobust Workshop, NeurIPS 2026 · 2026 · Accepted [[OpenReview]](https://openreview.net/forum?id=OzOTmkkAWW) Project team Lead: Yuhe Sui Authors: Yingzhi Tang, Jianing Zhang, Mi Zeyuan Slicers: Wang Zimeng, Yingzhi Tang Scan to open this page"},{"id":"/projects/riskhedge/#Publications","page":"RiskHedge","section":"Publications","url":"/projects/riskhedge/","kind":"section","text":"Diverse Scenarios, Selective Evaluation: Certified Spectral-Risk Decisions under Costly Robustness Tests (2026). Yuhe Sui, Yingzhi Tang. EvoRobust Workshop, NeurIPS 2026. Accepted. OpenReview"},{"id":"/projects/softrank/details/","page":"SoftRank: How It Works","section":"","url":"/projects/softrank/details/","kind":"page","text":"How SoftRank works: why query-key radii depend on the coordinate frame, the visible interaction C = P(log A)P and the intrinsic size kappa, where the r/2 exponent comes from, certified brackets on BERT, GPT-2, Qwen2.5, ViT and Llama heads, and the limitations."},{"id":"/projects/softrank/details/#why-not-qk-h","page":"SoftRank: How It Works","section":"Why not measure the queries and keys?","url":"/projects/softrank/details/#why-not-qk-h","kind":"section","text":"An attention head computes logits $H = βQK^⊤$ and normalises each row with softmax. The obvious way to say how complex the head is, is to measure the two point clouds that produce the logits: how far the queries and keys spread (their radii, combined into $Γ = βρ_Q ρ_K$), or the spectrum of $W_q^⊤ W_k$. A bound written in those terms is correct for the factorization it is given. But the factorization is not unique. For any invertible matrix $S$, replacing $Q$ by $QS$ and $K$ by $KS^{ − ⊤}$ leaves every logit, and so the whole attention matrix, unchanged. The point clouds do change. In the …"},{"id":"/projects/softrank/details/#questions-h","page":"SoftRank: How It Works","section":"Three questions, three objects","url":"/projects/softrank/details/#questions-h","kind":"section","text":"What must be preserved? The approximation rank $r_ε (A)$ The least rank of any real matrix $B$ within maximum-row-$ℓ_1$ error $ε$ of $A$. That error is exactly the worst output error over all value vectors of norm at most one, in any normed space, so $r_ε (A)$ is the rank needed to preserve every bounded attention output. What can softmax see? The visible interaction $C = P_m ( log A)P_N$ Row softmax ignores any constant added to a row of logits, and terms that depend only on the key act as common base weights. Centring $log A$ on both sides removes the first and keeps the second apart. $C$ …"},{"id":"/projects/softrank/details/#explorer-h","page":"SoftRank: How It Works","section":"Coordinates against the operator","url":"/projects/softrank/details/#explorer-h","kind":"section","text":"The two sliders separate what changes the coordinates from what changes the head. The shear $t$ moves the queries and keys; the matrix below is recomputed from the moved vectors each time and does not change. The logit scale $β$ changes the head itself: the matrix sharpens, and the intrinsic size grows with it. Explorer: one operator, many frames. Here $κ(C) = 1$ exactly at $β = 1$: the original factorization reaches a radius product of 1, and the rectangular contrast $C_{11} − C_{12} − C_{21} + C_{22} = 4$ shows that no factorization can do better."},{"id":"/projects/softrank/details/#exponent-h","page":"SoftRank: How It Works","section":"Where the exponent comes from","url":"/projects/softrank/details/#exponent-h","kind":"section","text":"The bound rests on a cover of Gibbs rows: every softmax row is close, in $ℓ_1$, to one of a small set of rows, and the size of that set is a question about convex bodies in fixed dimension. Its exponent is set by the geometry of the support. For self-attention on the unit sphere in $ℝ^d$, the worst-case rank grows like $(1 + β)^{(d − 1)/2}$ with the temperature; on the full ball, with enough tokens, it grows like $β^{d/2}$. One radial degree of freedom adds exactly one half to the exponent. The intrinsic theorem inherits the same exponent, now with the visible dimension $r$ in place of the …"},{"id":"/projects/softrank/details/#measure-h","page":"SoftRank: How It Works","section":"Measuring the rank directly","url":"/projects/softrank/details/#measure-h","kind":"section","text":"The constant $C_r$ in the theorem is not known numerically, so on trained heads the rank is measured rather than predicted. Any explicit matrix of rank $k$ that is checked to lie within $ε$ proves $r_ε (A) ≤ k$; the upper search uses reweighted SVD and alternating-$ℓ_1$ factorization. Lower certificates quantify over every real competitor: Frobenius tails, truncated pseudoinverses, residual-aware bounds and contractive decoders. A failed attempt to approximate is never used as a lower bound. Numerical attention matrices carry a slack $χ$: $L_{ε + χ} (A^^ ) ≤ r_ε (A) ≤ U_{ε − χ} (A^^ )$. Every …"},{"id":"/projects/softrank/details/#brackets-h","page":"SoftRank: How It Works","section":"Results: brackets on learned heads","url":"/projects/softrank/details/#brackets-h","kind":"section","text":"The primary panel holds 2,302 operators: BERT-base at 256 × 256, the common-prefix blocks of GPT-2 and Qwen2.5-1.5B at 128 × 128, and two ViT-Base checkpoints at 197 × 197, from 64 fixed text sources and 64 ImageNet images. At three tolerances and with secondary decoder cells, the certificate pass produced 9,978 brackets. An independent recomputation found no failure, none of 458 targeted attacks on the lower ends succeeded, and 119 of 119 reconstructed upper witnesses passed the same check. BERT-base 256 × 256 · 512 operators 42.8% resolved; median upper ÷ lower 3.82 (lower 11, upper 57) …"},{"id":"/projects/softrank/details/#gap-h","page":"SoftRank: How It Works","section":"Constructions against certificates","url":"/projects/softrank/details/#gap-h","kind":"section","text":"A held-out panel of 1,152 operators (32 text sources and 32 images) asks how close practical low-rank constructions come to the lower certificate. Six fixed implementations were run at ε = 0.25; alternating $ℓ_1$ reached the lowest rank in every cell. The best construction needs 2.6–3.7 times the certified lower rank. Family medians with 95% intervals; truncated SVD needs 1.62 times the rank of alternating $ℓ_1$ under this error. The bottom bar sorts the 435,436 failed attempts into what the certificate can say about them. The gap is between a construction and a certificate; which end is …"},{"id":"/projects/softrank/details/#length-h","page":"SoftRank: How It Works","section":"Rank budgets as the block widens","url":"/projects/softrank/details/#length-h","kind":"section","text":"For Qwen2.5-1.5B the operator is the renormalised N × N common-prefix block of one 1,024-token pass, for 6 fixed heads and 32 arXiv documents, at widths N = 64 to 512. The question is a fixed budget: is rank 8, 16 or 32 enough at ε = 0.25? Fixed budgets are shown feasible less often as the block widens. Share of operators with a checked construction at the budget. Llama-3.2-1B was run blind, on 32 fresh documents, by agents that had not seen the Qwen results. On Qwen2.5 the pre-specified class is a decline at all three budgets: rank 16 drops from 98% to 47% of operators and rank 32 from 100% …"},{"id":"/projects/softrank/details/#regimes-h","page":"SoftRank: How It Works","section":"Other attention regimes","url":"/projects/softrank/details/#regimes-h","kind":"section","text":"The same certificates run unchanged on rectangular and encoder–decoder attention. FLAN-T5 encoder self-attention 256 × 256 3.81 median upper ÷ lower FLAN-T5 cross-attention 64 × 256 2.53 median upper ÷ lower FLAN-T5 decoder self-attention block 32 × 32 1.50 median upper ÷ lower BLIP-2 query → image 32 × 257 11 of 32 median upper rank; median lower 4.5"},{"id":"/projects/softrank/details/#native-h","page":"SoftRank: How It Works","section":"Native coordinates as a predictor","url":"/projects/softrank/details/#native-h","kind":"section","text":"The earlier, native-coordinate version of the geometry (native $Γ$, SVD-selected interaction dimensions and shape diagnostics) was tested as a predictor of the checked upper budget on held-out sources. Against a weak structural baseline it carries coarse information: held-out error falls by 0.0279 [0.0254, 0.0300] cap units. Against a calibrated baseline of logit, concentration and weight-space features, it adds nothing detectable: the aggregate gain in held-out error is −0.00005 cap units and the relative gain is −0.0035 [−0.0422, +0.0179]. No family excludes zero. Relative gain from adding …"},{"id":"/projects/softrank/details/#limitations-h","page":"SoftRank: How It Works","section":"Limitations and what didn’t work","url":"/projects/softrank/details/#limitations-h","kind":"section","text":"Scope The panels are fixed checkpoints with fixed head rosters: one BERT encoder, GPT-2, Qwen2.5-1.5B, two ViT-Base checkpoints, FLAN-T5-base, Llama-3.2-1B and the BLIP-2 Q-Former. The GPT-2 and Qwen2.5 panels use six of eight pre-specified non-local heads. Nothing is claimed for other models, larger language models or long context. The theorem assumes one common positive support. Causal masks need more theory, so decoder results come from common-prefix blocks, and the native-causal brackets are measurements, not uses of the theorem. “Block width” is the width of a common-prefix block, not a …"},{"id":"/projects/softrank/details/#next-steps-h","page":"SoftRank: How It Works","section":"Where this is going proposed","url":"/projects/softrank/details/#next-steps-h","kind":"section","text":"### Validated certificates A post-processing pass with rounding-error and residual bounds over the stored witnesses and constructions, so impossible, unresolved and feasible hold without the float64 qualifier. ### κ(T) on learned heads Primal and dual brackets for the intrinsic size on a representative subset, to test the theorem’s own quantity rather than its balanced-factor surrogate. ### Beyond one common support Theory for causal masks; and the open questions of the paper: equality of the intrinsic and native optima, joint sharpness in κ, residual and ε, and an efficient global algorithm …"},{"id":"/projects/softrank/details/#definitions-h","page":"SoftRank: How It Works","section":"Definitions and the theorem","url":"/projects/softrank/details/#definitions-h","kind":"section","text":"For an attention matrix $A ∈ ℝ^{m × N}$ and $0 < ε < 1$, $$r_ε (A) = min{rankB:max_i ∑j A{ij} − B_{ij} ≤ ε},$$ $$‖M‖{row,1} = sup{max_j ‖v_j ‖_E ≤ 1} max_i ‖∑j M{ij} v_j ‖_E .$$ On one common positive support, with $P_m = I − \\frac{1}{m}11^⊤$, the visible interaction and the projective residual of a centred $T$ are $$C = P_m ( log A)P_N ,$$ $$q(E) = inf_b max_i osc(E_{i · } − b^⊤ ),$$ $$τ(T) = 2 tanh (\\frac{q(C − T)}{4}).$$ The residual rests on the sharp inequality, with $σ$ the softmax map, $$‖σ(x + h) − σ(x)‖1 ≤ 2 tanh (osc(h)/4).$$ The size is a minimum over factorizations, attained in …"},{"id":"/projects/softrank/details/#laws-h","page":"SoftRank: How It Works","section":"Support-geometry laws","url":"/projects/softrank/details/#laws-h","kind":"section","text":"For self-attention $A_β (X)_{ij} ∝ e^{β⟨x_i ,x_j ⟩}$ with $n$ tokens, write $ℜ$ for the worst case of $r_ε$ over configurations. For fixed $d ≥ 2$ and $ε$, on the sphere, and on the ball when $β ≥ β_0 (d,ε)$ and $n ≥ C_d e^{β/8}$: $$ℜ_ε^{sph} (n,d,β)≍min{n,(1 + β)^{(d − 1)/2} },$$ $$ℜ_ε (n,d,β)≍β^{d/2} .$$ The lower bounds come from decoding constructions (well-separated sphere centres; a discrete Gaussian on a lattice in the ball) whose attention is close to a block projection, so any good approximant must be invertible on the messages. The ball law needs exponentially many tokens, so it is …"},{"id":"/projects/softrank/details/#tables-h","page":"SoftRank: How It Works","section":"Full tables","url":"/projects/softrank/details/#tables-h","kind":"section","text":"Brackets on the primary panel at ε = 0.25 Family Shape Operators Resolved Median L Median U Median U/L BERT-base 256 × 256 512 42.8% 11 57 3.82 GPT-2 128 × 128 382 99.7% 2 6 3.00 Qwen2.5-1.5B 128 × 128 384 77.1% 3 9 2.63 ViT-Base (ImageNet-1k) 197 × 197 512 59.0% 6 25 3.41 ViT-Base (ImageNet-21k) 197 × 197 512 61.9% 5 21 3.08 Held-out construction benchmark at ε = 0.25 Family Median lower certificate Median best construction Ratio (95% interval) BERT-base 11.25 57.5 3.73 [3.48, 3.89] GPT-2 2 6 2.58 [2.50, 3.00] Qwen2.5-1.5B 3 9.25 2.58 [2.42, 2.78] ViT-Base (ImageNet-1k) 5 24.5 3.47 [3.00 …"},{"id":"/projects/softrank/details/#repro-h","page":"SoftRank: How It Works","section":"Reproducibility notes","url":"/projects/softrank/details/#repro-h","kind":"section","text":"Certificate pass 3,326 operators at tolerances 0.15, 0.25 and 0.35: 9,978 brackets, every upper end an explicit matrix checked in maximum-row-$ℓ_1$; independent recomputation with no failure; 0 of 458 targeted lower-end attacks succeeded; 119/119 reconstructed upper witnesses pass. Numerics Certificates and constructions in float64 without interval enclosure, with the slack $χ$ of each numerical attention matrix charged to both ends. Protocols Each study fixed its panel, tolerances and decision rules in a frozen protocol before its run of record, and a separate verifier rechecked its numbers …"},{"id":"/projects/softrank/details/#summary-h","page":"SoftRank: How It Works","section":"In brief","url":"/projects/softrank/details/#summary-h","kind":"section","text":"Design The complexity of a head is the rank its normalised operator needs to keep every bounded output within ε. The quantities that control it are taken from the doubly centred log-attention and minimised over factorizations, so no query–key frame is preferred. Results The bound carries the dimension exponent of the support geometry, and that exponent is attained. On trained encoders, decoders and vision transformers, the target can be bracketed directly, and practical constructions sit a factor of a few above what the certificates exclude. Open questions Whether the theorem’s own size …"},{"id":"/projects/softrank/details/#sources-h","page":"SoftRank: How It Works","section":"Sources","url":"/projects/softrank/details/#sources-h","kind":"section","text":"Paper: Intrinsic Interaction Geometry Controls the Low-Rank Complexity of Softmax Attention, Yuhe Sui, Jianing Zhang, Yingzhi Tang, arXiv 2608.28150 (v1 28 August 2026, v2 22 September 2026). [[arXiv]](https://arxiv.org/abs/2608.28150) Extended abstract: The Approximation Rank of Softmax Attention: Sharp Geometric Laws and Robust Interaction Dimension, Yuhe Sui, Jianing Zhang, NeurReps Workshop (Symmetry and Geometry in Neural Representations), NeurIPS 2026, accepted. [[OpenReview]](https://openreview.net/forum?id=0zgsZ8FjVz)"},{"id":"/projects/softrank/details/#Accepted Research","page":"SoftRank: How It Works","section":"Accepted Research","url":"/projects/softrank/details/","kind":"section","text":"### The Approximation Rank of Softmax Attention: Sharp Geometric Laws and Robust Interaction Dimension Yuhe Sui, Jianing Zhang NeurReps Workshop, NeurIPS 2026 (extended abstract) · 2026 · Accepted [[OpenReview]](https://openreview.net/forum?id=0zgsZ8FjVz) Numbers on this page come from the project’s study records: the bracketing study, the held-out construction benchmark, the block-width studies on Qwen2.5 and Llama, the FLAN-T5 and BLIP-2 studies, and the native and intrinsic predictor tests. Where a newer study or the current text of the paper supersedes the extended abstract, this page …"},{"id":"/projects/softrank/","page":"SoftRank","section":"","url":"/projects/softrank/","kind":"page","text":"SoftRank: the approximation rank of softmax attention, measured on the operator rather than on one choice of query and key coordinates. A gauge-invariant bound from the softmax-visible interaction, a sharp r/2 exponent, and certified brackets on trained heads. NeurReps 2026."},{"id":"/projects/softrank/#glance-h","page":"SoftRank","section":"SoftRank at a glance","url":"/projects/softrank/#glance-h","kind":"section","text":"The idea Softmax cannot see anything that adds the same number to a whole row of logits, and the logits cannot see how they are split between queries and keys. What is left is the doubly centred log-attention $C = P( log A)P$. If a rank-$r$ part $T$ of $C$ leaves a residual $τ(T) < ε$, then $$r_ε (A) ≤ C_r (1 + \\frac{κ(T)}{(ε − τ(T))^2 })^{r/2} ,$$ where $κ(T)$ is the smallest radius product over all factorizations of $T$. Nothing in the bound depends on the coordinate frame, and no smaller exponent than $r/2$ works in the worst case. Experiments Learned attention heads tested Certified rank …"},{"id":"/projects/softrank/#next-h","page":"SoftRank","section":"Where this is going proposed","url":"/projects/softrank/#next-h","kind":"section","text":"### Validated certificates Rounding-error and residual bounds for every stored witness, so each verdict holds beyond float64. ### The intrinsic size on real heads Primal and dual brackets for κ(T) on a representative set of heads, in place of the balanced-factor surrogate. ### Causal masks A theory for row-dependent supports, so decoder self-attention is covered without common-prefix blocks. What comes next, in full →"},{"id":"/projects/softrank/#Papers","page":"SoftRank","section":"Papers","url":"/projects/softrank/","kind":"section","text":"### Intrinsic Interaction Geometry Controls the Low-Rank Complexity of Softmax Attention Yuhe Sui, Jianing Zhang, Yingzhi Tang arXiv 2608.28150 · v1 28 August 2026, v2 22 September 2026 [[arXiv]](https://arxiv.org/abs/2608.28150)"},{"id":"/projects/softrank/#Accepted Research","page":"SoftRank","section":"Accepted Research","url":"/projects/softrank/","kind":"section","text":"### The Approximation Rank of Softmax Attention: Sharp Geometric Laws and Robust Interaction Dimension Yuhe Sui, Jianing Zhang NeurReps Workshop, NeurIPS 2026 (extended abstract) · 2026 · Accepted [[OpenReview]](https://openreview.net/forum?id=0zgsZ8FjVz) Scan to open this page"},{"id":"/projects/softrank/#Publications","page":"SoftRank","section":"Publications","url":"/projects/softrank/","kind":"section","text":"The Approximation Rank of Softmax Attention: Sharp Geometric Laws and Robust Interaction Dimension (2026). Yuhe Sui, Jianing Zhang. NeurReps Workshop, NeurIPS 2026 (extended abstract). Accepted. OpenReview arXiv"},{"id":"/publications/","page":"Publications","section":"","url":"/publications/","kind":"page","text":"Browse publications and preprints by QRS researchers, with author, year, and venue filters."},{"id":"/publications/#Publications","page":"Publications","section":"Publications","url":"/publications/","kind":"section","text":"Diverse Scenarios, Selective Evaluation: Certified Spectral-Risk Decisions under Costly Robustness Tests (2026). Yuhe Sui, Yingzhi Tang. EvoRobust Workshop, NeurIPS 2026. Accepted. OpenReview Geometric Attention Fine-Tuning Is Representation-Relative: Autonomous ML Research with AI-Native Workflow (2026). Yuhe Sui, Jianing Zhang, Shufang Chen, Xiaotong Li, Wang Zimeng. AutoMLR Workshop, NeurIPS 2026. Accepted. OpenReview NTU-QRS AlphaAllocator: Bounded Transformer News Overlays for Chinese Macro-Asset Allocation (2026). Yuhe Sui. NLPCC 2026 Shared Task 4 · Poster + Oral. OpenReview …"},{"id":"/research-academy/","page":"QRS Research Academy: Cohorts, Outcomes and Applications","section":"","url":"/research-academy/","kind":"page","text":"A selective QRS research programme, from guided research to independent research leadership: selection process, how the Academy works, cohorts and applications for 2026 Fall #4."},{"id":"/research-academy/#ac-status-title","page":"QRS Research Academy: Cohorts, Outcomes and Applications","section":"2026 Fall #4","url":"/research-academy/#ac-status-title","kind":"section","text":"Upcoming intake Research cycle December 2026 – January 2027 Target venue Relevant AAMAS 2027 workshops Eligibility and how to apply 2026 Fall #4 Selection How it works Cohorts Roles Research FAQ"},{"id":"/research-academy/#apply-title","page":"QRS Research Academy: Cohorts, Outcomes and Applications","section":"Recruitment: 2026 Fall #4","url":"/research-academy/#apply-title","kind":"section","text":"Upcoming intake Research cycle December 2026 – January 2027. We particularly welcome early-stage undergraduate and graduate students seeking to undertake original research. Exceptional pre-university students will also be considered. Prior research or publication experience is not required; selection emphasises intellectual curiosity, analytical rigour, and the potential to develop into independent researchers. Who should apply Early-stage undergraduate and graduate students who want to carry out original research. Exceptional pre-university students, considered individually. Students at any …"},{"id":"/research-academy/#selection-title","page":"QRS Research Academy: Cohorts, Outcomes and Applications","section":"Selection Process","url":"/research-academy/#selection-title","kind":"section","text":"Selection has four stages. Shortlisted applicants are invited to each next stage, and dates are sent directly. ### Application and background review The committee reads your application form and résumé: projects, research experience, and availability for the research cycle. ### Online assessment Shortlisted applicants take two short, timed online tests: quantitative reasoning, and qualitative reasoning (reading comprehension, interpretation and logic). ### Research assessment and interview Invited applicants choose one research question and write a short research note on it. Correct partial …"},{"id":"/research-academy/#process-title","page":"QRS Research Academy: Cohorts, Outcomes and Applications","section":"How the Academy Works","url":"/research-academy/#process-title","kind":"section","text":"Five stages from guided contributions to independent research. ### Research Orientation Literature review, identifying open questions, and evaluating potential research directions. ### Research Formulation Defining a tractable question, its novelty, and a theoretical or empirical approach. ### Research Execution Developing methods, performing experiments or proofs, establishing baselines, and critically evaluating evidence. ### Academic Communication Preparing manuscripts, conducting internal peer review, and identifying appropriate publication venues. ### Continued Research Opportunities to …"},{"id":"/research-academy/#cohorts-title","page":"QRS Research Academy: Cohorts, Outcomes and Applications","section":"Cohorts","url":"/research-academy/#cohorts-title","kind":"section","text":"Each cohort's research cycle, target venue and outcome. ### 2026 Fall #1 Completed Inaugural cohort Target venue: NeurIPS 2026 workshops Outcome: Five works accepted to NeurIPS 2026 workshops Members: Jianing Zhang, Xiaotong Li, Yingzhi Tang Members and alumni ### 2026 Fall #2 Completed Target venue: ICAIF 2026 workshops Outcome: Six works accepted to ICAIF 2026 workshops Members: Shufang Chen, Wang Zimeng, Xinyue Wu, Jingshu Liu, Yizhe Chia, Annie Huaiyu Wang Members and alumni ### 2026 Fall #3 Working Target venue: AAAI Workshops ### 2026 Fall #4 Upcoming intake Research cycle December 2026 …"},{"id":"/research-academy/#roles-title","page":"QRS Research Academy: Cohorts, Outcomes and Applications","section":"Project Roles and Progression","url":"/research-academy/#roles-title","kind":"section","text":"Each research programme organises its work around three project-level roles. They describe a person's responsibilities within one project, not an organisation-wide title. Project roles Lead Owns the overall scientific direction of the parent project. Authors Core contributors to the parent research programme. Slicers Lead derived research directions with a distinct question, application, evaluation setting, or extension. Example: PolicyAttention Lead: Yuhe Sui Authors: Shufang Chen, Yingzhi Tang, Xinyue Wu Slicers: Shufang Chen, Xinyue Wu Academy member and QRS Researcher Academy member …"},{"id":"/research-academy/#research-title","page":"QRS Research Academy: Cohorts, Outcomes and Applications","section":"Research Directions","url":"/research-academy/#research-title","kind":"section","text":"Programmes that Academy members join, with their accepted works and members. Attention geometry and representation learning GeoAttention Research on attention geometry, representation-relative identifiability, and geometry-adaptive prediction. Academy members and alumni: Jianing Zhang (author); Xiaotong Li (author) SoftRank Theoretical research on softmax-attention approximation rank, support geometry, and robust interaction dimension. NeurReps Workshop, NeurIPS 2026 (extended abstract) arXiv preprint Academy members and alumni: Jianing Zhang (author); Yingzhi Tang (author); Jingshu Liu …"},{"id":"/research-academy/#faq-title","page":"QRS Research Academy: Cohorts, Outcomes and Applications","section":"Frequently Asked Questions","url":"/research-academy/#faq-title","kind":"section","text":"Do I need prior publications or research experience? No. Prior research or publication experience is not required. Selection emphasises intellectual curiosity, analytical rigour, and the potential to develop into an independent researcher. Can Year 1–2 undergraduates and graduate students apply? Yes. We particularly welcome early-stage undergraduate and graduate students who want to undertake original research. Are pre-university students eligible? Exceptional pre-university students will also be considered. Can applicants from other universities, or from outside Singapore, take part? Yes. …"},{"id":"/research-academy/#ac-closing-title","page":"QRS Research Academy: Cohorts, Outcomes and Applications","section":"Apply for 2026 Fall #4","url":"/research-academy/#ac-closing-title","kind":"section","text":"The research cycle runs December 2026 – January 2027. Prior research or publication experience is not required. Apply to QRS Research Academy · Meet our researchers"},{"id":"/research-academy/members/","page":"Research Academy Members","section":"","url":"/research-academy/members/","kind":"page","text":"Meet QRS Research Academy members and alumni by cohort, with their research areas, accepted works, and researchers promoted from the Academy."},{"id":"/research-academy/members/#2026-fall-1","page":"Research Academy Members","section":"QRS Research Academy, 2026 Fall #1","url":"/research-academy/members/#2026-fall-1","kind":"section","text":"Completed Target venue: NeurIPS 2026 workshops. Five works accepted to NeurIPS 2026 workshops Jianing Zhang Researcher, Quantitative Research Society Research areas: AI Native Workflow, GeoAttention, SoftRank Accepted works: AutoMLR Workshop, NeurIPS 2026; NeurReps Workshop, NeurIPS 2026 Xiaotong Li Research Academy Member Research areas: AI Native Workflow, GeoAttention Accepted works: AutoMLR Workshop, NeurIPS 2026 Yingzhi Tang Researcher, Quantitative Research Society Research areas: PolicyAttention, RiskHedge Slicer — RiskHedge Accepted works: EvoRobust Workshop, NeurIPS 2026; EvoRobust …"},{"id":"/research-academy/members/#2026-fall-2","page":"Research Academy Members","section":"QRS Research Academy, 2026 Fall #2","url":"/research-academy/members/#2026-fall-2","kind":"section","text":"Completed Target venue: ICAIF 2026 workshops. Six works accepted to ICAIF 2026 workshops Shufang Chen Research Academy Member Slicer — PolicyAttention Accepted works: AutoMLR Workshop, NeurIPS 2026 Wang Zimeng Research Academy Member · NUS Sub-branch Coordinator Slicer — RiskHedge Accepted works: AutoMLR Workshop, NeurIPS 2026 Xinyue Wu Research Academy Member Slicer — PolicyAttention Accepted works: EvoRobust Workshop, NeurIPS 2026 Jingshu Liu Research Academy Member Slicer — SoftRank Yizhe Chia Research Academy Member Slicer — AI Native Workflow Annie Huaiyu Wang Research Academy Member …"},{"id":"/research-academy/members/#2026-fall-4","page":"Research Academy Members","section":"QRS Research Academy, 2026 Fall #4","url":"/research-academy/members/#2026-fall-4","kind":"section","text":"Upcoming intake Target venue: Relevant AAMAS 2027 workshops. Members will be listed here once the cohort is selected. Research cycle: December 2026 – January 2027. Apply now"},{"id":"/service/","page":"Service","section":"","url":"/service/","kind":"page","text":"QRS supports academic workshops and research communities with web, publicity, outreach, and organisational infrastructure."},{"id":"/service/#Workshop & Research Community Support","page":"Service","section":"Workshop & Research Community Support","url":"/service/","kind":"section","text":"QRS supports academic workshops, research communities, and student-led scientific initiatives with lightweight web, publicity, outreach, and organisational infrastructure."},{"id":"/service/#What We Can Help With","page":"Service","section":"What We Can Help With","url":"/service/","kind":"section","text":"Support may include: Workshop website creation and maintenance Calls for papers and submission-information pages Speaker, programme, and accepted-paper pages Publicity graphics and digital materials Schedule and attendee-information pages Outreach to relevant student and research communities Lightweight coordination support where appropriate"},{"id":"/service/#workshop-explorer","page":"Service","section":"Workshop Explorer","url":"/service/#workshop-explorer","kind":"section","text":"An independent QRS directory of conference workshops for researchers deciding where to submit. Search calls for papers by research area, paper type, page limit, deadline and publication policy, with submission requirements and official links for each workshop. Unconfirmed or conflicting details are marked as such. AAAI 2027 Workshop Explorer · All conferences"},{"id":"/service/#neurips-planner","page":"Service","section":"NeurIPS 2026 Planner","url":"/service/#neurips-planner","kind":"section","text":"An independent QRS planner for NeurIPS 2026 in Sydney, Atlanta and Paris: every session in venue time, search across authors, organisations and papers, a personal plan with clash warnings, hotels and a venue guide. Details the programme has not published are marked as such. NeurIPS 2026 Attendee Guide · Schedule"},{"id":"/service/#Our Approach","page":"Service","section":"Our Approach","url":"/service/","kind":"section","text":"Our aim is to reduce the operational overhead of running research activities while helping organisers maintain a clear and professional public presence. Support is collaborative and scoped according to the needs of each workshop or research community."},{"id":"/service/#Work With Us","page":"Service","section":"Work With Us","url":"/service/","kind":"section","text":"Researchers, workshop organisers, and academic communities interested in working with QRS are welcome to contact us. contact@qrsntu.org"},{"id":"/service/workshops/aaai-2027/","page":"AAAI 2027 Workshop Explorer","section":"","url":"/service/workshops/aaai-2027/","kind":"page","text":"Search and filter the AAAI 2027 workshops by research area, paper type, page limit, deadline and archival status, with submission rules and official CFP links."},{"id":"/service/workshops/aaai-2027/#wx-topics-title","page":"AAAI 2027 Workshop Explorer","section":"Browse by topic","url":"/service/workshops/aaai-2027/#wx-topics-title","kind":"section","text":"3 · Theory and optimisation · Mathematical foundations / theoretical ML · Optimization / learning algorithms · Causal inference / interventions 14 · Agents and decision-making · Reinforcement learning / decision-making · Multi-agent systems / agentic AI · Social choice / mechanism design · Human–AI interaction / collaboration 3 · Language and reasoning · LLM reasoning / post-training · NLP / information retrieval · Neuro-symbolic / structured reasoning 7 · Perception and embodiment · Attention / representation learning · Multimodal / vision-language learning · Robotics / embodied systems 6 · …"},{"id":"/service/workshops/aaai-2027/#about-data-title","page":"AAAI 2027 Workshop Explorer","section":"About this directory","url":"/service/workshops/aaai-2027/#about-data-title","kind":"section","text":"Sources and method Every workshop named in the official AAAI directory was checked against its organisers' website, call for papers and submission site, last on 12 Nov 2026; every change found is logged. General dates and policies come from the AAAI workshop programme. AAAI's workshop programme overview states 47 workshops, but its public directory names 45. The other two could not be identified from AAAI sources and are not listed. What the colours mean TopicThe rule on the left of each card shows the workshop's main topic: · Theory and optimisation · Agents and decision-making · Language …"},{"id":"/service/workshops/aaai-2027/updates/","page":"AAAI 2027 Workshop Updates","section":"","url":"/service/workshops/aaai-2027/updates/","kind":"page","text":"What changed in the AAAI 2027 workshop data: moved deadlines, OpenReview due times that differ from the published deadline, and points where official sources disagree."},{"id":"/service/workshops/aaai-2027/updates/#deadlines-title","page":"AAAI 2027 Workshop Updates","section":"Deadline changes","url":"/service/workshops/aaai-2027/updates/#deadlines-title","kind":"section","text":"Submission deadlines that organisers have moved since the directory was first compiled. The explorer keeps the old date struck through beside the new one. Workshop Previous deadline Now Change Recorded SAFE: Synthetic and Adversarial Forensics 2 Nov 2026 23:59 AoE 4 Nov 2026 23:59 ET extended 5 Nov 2026 Emerging AI Technologies for Music 6 Nov 2026 23:59 AoE 13 Nov 2026 23:59 AoE extended 12 Nov 2026 EMC² 8 Jan 2027 23:59 PST 25 Dec 2026 23:59 PST moved earlier 1 Nov 2026"},{"id":"/service/workshops/aaai-2027/updates/#openreview-title","page":"AAAI 2027 Workshop Updates","section":"OpenReview due times","url":"/service/workshops/aaai-2027/updates/#openreview-title","kind":"section","text":"Due times read from each workshop's OpenReview submission site through OpenReview's public API, last on 12 Nov 2026, compared with the deadline the workshop publishes. Where no time or zone is published, the comparison assumes 23:59 Anywhere on Earth. OpenReview usually keeps a submission open for 30 minutes after its due time; the table uses the due time. Workshops on other submission systems are not listed. Workshop Published deadline OpenReview due (UTC) Difference Earlier readings Generative AI and Disinformation 20 Nov 2026 AoE 15 Nov 2026, 12:59 Earlier by about 6 days Unchanged since 1 …"},{"id":"/service/workshops/aaai-2027/updates/#log-title","page":"AAAI 2027 Workshop Updates","section":"Log of findings","url":"/service/workshops/aaai-2027/updates/#log-title","kind":"section","text":"Everything recorded at each check, newest first: changed dates and times, details published later, points where official sources disagree, and earlier notes now resolved. 12 Nov 2026 Details · All workshopsRechecked all 45 workshops against their organisers’ pages and re-read every OpenReview site. EAIM extended its deadline to 13 Nov; no other published deadline moved. Two sites could not be read: QC+AI (expired security certificate) and Agentic-Software (page shows only a title). AICS, which showed only a bot check last time, could be read and its dates are unchanged. Dates and times · …"},{"id":"/service/workshops/","page":"Workshop Explorer","section":"","url":"/service/workshops/","kind":"page","text":"An independent QRS directory of conference workshops: search calls for papers by research area, paper type, page limit, deadline and publication policy."},{"id":"/yh/","page":"Yuhe Sui","section":"","url":"/yh/","kind":"person","text":"President & Founder, QRS@NTU; Principal Researcher, Quantitative Research Society"},{"id":"/yh/#About","page":"Yuhe Sui","section":"About","url":"/yh/","kind":"section","text":"Yuhe studies attention mechanisms, focusing on their geometry, approximation behaviour, and statistical efficiency. Research interests include adapting attention through post-training and fine-tuning, and applying these methods to quantitative finance, reinforcement learning, and sequential decision-making. Projects · Publications"},{"id":"/yh/#Projects","page":"Yuhe Sui","section":"Projects","url":"/yh/","kind":"section","text":"AI Native Workflow: Research on hierarchical, verification-gated and recoverable workflows for scaling long-horizon AI-assisted research and agent execution. Status: active. People: Yuhe Sui, Jianing Zhang, Shufang Chen, Danlin Chen, Wang Zimeng, Xiaotong Li. FRTBTrace: Active research on faithful, auditable, trade-level FRTB attribution. Status: active. People: Yuhe Sui, Yingzhi Tang. GeoAFT: Geometric Attention Fine-Tuning: adapting the rule a pretrained Transformer uses to compare representations, not only the representations themselves. Status: active. People: Yuhe Sui. GeoAttention …"},{"id":"/yh/#Publications","page":"Yuhe Sui","section":"Publications","url":"/yh/","kind":"section","text":"Diverse Scenarios, Selective Evaluation: Certified Spectral-Risk Decisions under Costly Robustness Tests (2026). Yuhe Sui, Yingzhi Tang. EvoRobust Workshop, NeurIPS 2026. Accepted. OpenReview Geometric Attention Fine-Tuning Is Representation-Relative: Autonomous ML Research with AI-Native Workflow (2026). Yuhe Sui, Jianing Zhang, Shufang Chen, Xiaotong Li, Wang Zimeng. AutoMLR Workshop, NeurIPS 2026. Accepted. OpenReview NTU-QRS AlphaAllocator: Bounded Transformer News Overlays for Chinese Macro-Asset Allocation (2026). Yuhe Sui. NLPCC 2026 Shared Task 4 · Poster + Oral. OpenReview …"},{"id":"/yz/","page":"Yingzhi Tang","section":"","url":"/yz/","kind":"person","text":"Researcher, Quantitative Research Society"},{"id":"/yz/#About","page":"Yingzhi Tang","section":"About","url":"/yz/","kind":"section","text":"Yingzhi studies Financial Engineering with a minor in Artificial Intelligence at The Chinese University of Hong Kong, Shenzhen. Her interests span quantitative finance, machine learning, and robust decision-making. Her experience includes quantitative factor research, factor timing, and machine-learning-based trading strategies, alongside work on AI agent systems as a quantitative developer intern at UBS. At QRS, she contributes to PolicyAttention and RiskHedge, exploring the reliability of attention-based policy improvement and decision-making under uncertainty. Projects · Publications"},{"id":"/yz/#Projects","page":"Yingzhi Tang","section":"Projects","url":"/yz/","kind":"section","text":"FRTBTrace: Active research on faithful, auditable, trade-level FRTB attribution. Status: active. People: Yuhe Sui, Yingzhi Tang. PolicyAttention: Research on softmax policy improvement, its robustness, and its failure modes. Status: active. People: Yuhe Sui, Shufang Chen, Yingzhi Tang, Xinyue Wu. RiskHedge: Research on spectral-risk decisions, diverse scenarios, and selective robustness evaluation. Status: active. People: Yuhe Sui, Yingzhi Tang, Jianing Zhang, Mi Zeyuan. SoftRank: Theoretical research on softmax-attention approximation rank, support geometry, and robust interaction dimension. …"},{"id":"/yz/#Publications","page":"Yingzhi Tang","section":"Publications","url":"/yz/","kind":"section","text":"Diverse Scenarios, Selective Evaluation: Certified Spectral-Risk Decisions under Costly Robustness Tests (2026). Yuhe Sui, Yingzhi Tang. EvoRobust Workshop, NeurIPS 2026. Accepted. OpenReview PolicyAttention: Robustness and Failure Modes of Softmax Policy Improvement (2026). Yuhe Sui, Yingzhi Tang, Xinyue Wu. EvoRobust Workshop, NeurIPS 2026. Accepted. OpenReview"},{"id":"/site-map/","page":"Site Map","section":"","url":"/site-map/","kind":"page","text":"Find all public QRS pages, including programmes, events, research publications, mathematics notes, and member profiles."},{"id":"course:BR2207","page":"Math Notes","section":"BR2207 Quantitative Analysis","url":"/math_notes/br2207/","kind":"course","text":"NTU past-year papers and notes for BR2207 Quantitative Analysis: Finals 2022-23 to 2024-25 (3 years, 0 with solutions)."},{"id":"course:BR2210","page":"Math Notes","section":"BR2210 Financial Markets and Products","url":"/math_notes/br2210/","kind":"course","text":"NTU past-year papers and notes for BR2210 Financial Markets and Products: Finals 2022-23 to 2024-25 (3 years, 0 with solutions)."},{"id":"course:BR2211","page":"Math Notes","section":"BR2211 Financial and Risk Analytics I","url":"/math_notes/br2211/","kind":"course","text":"NTU past-year papers and notes for BR2211 Financial and Risk Analytics I: Finals 2022-23 to 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EvoRobust Workshop, NeurIPS 2026, 2026."},{"id":"publication:geoaft-ai-native-workflow-automlr-2026","page":"Publications","section":"Geometric Attention Fine-Tuning Is Representation-Relative: Autonomous ML Research with AI-Native Workflow","url":"/projects/ai-native-workflow/","kind":"publication","text":"Yuhe Sui, Jianing Zhang, Shufang Chen, Xiaotong Li, Wang Zimeng. AutoMLR Workshop, NeurIPS 2026, 2026."},{"id":"publication:alphaallocator-nlpcc-2026","page":"Publications","section":"NTU-QRS AlphaAllocator: Bounded Transformer News Overlays for Chinese Macro-Asset Allocation","url":"/projects/alphaallocator/","kind":"publication","text":"Yuhe Sui. NLPCC 2026 Shared Task 4 · Poster + Oral, 2026."},{"id":"publication:policyattention-evorobust-2026","page":"Publications","section":"PolicyAttention: Robustness and Failure Modes of Softmax Policy Improvement","url":"/projects/policyattention/","kind":"publication","text":"Yuhe Sui, Yingzhi Tang, Xinyue Wu. EvoRobust Workshop, NeurIPS 2026, 2026."},{"id":"publication:policyattention-pta-2026","page":"Publications","section":"PolicyAttention: When Softmax Attention Becomes Policy Improvement","url":"/projects/policyattention/","kind":"publication","text":"Yuhe Sui. PTA Workshop, NeurIPS 2026, 2026."},{"id":"publication:approximation-rank-neurreps-ea-2026","page":"Publications","section":"The Approximation Rank of Softmax Attention: Sharp Geometric Laws and Robust Interaction Dimension","url":"/projects/softrank/","kind":"publication","text":"Yuhe Sui, Jianing Zhang. NeurReps Workshop, NeurIPS 2026 (extended abstract), 2026."},{"id":"event:gmmg-singapore-2026","page":"Events","section":"Global Market Making Games 2026 — Singapore Qualifier","url":"/gmmg/","kind":"event","text":"2026-10-16. Singapore (venue to be announced). An individual global market-making competition open to university students across Singapore."},{"id":"event:imc-tech-race-ntu-2026","page":"Events","section":"IMC Tech Race @ NTU","url":"/events/","kind":"event","text":"2026-09-02. Nanyang Technological University. An on-campus coding race by IMC featuring 20 rapid computer-science problems, a live leaderboard, networking with IMC technologists, and prizes."},{"id":"event:sg-hk-quant-trading-hackathon-2026","page":"Events","section":"Singapore vs Hong Kong Quant Trading Hackathon","url":"/events/","kind":"event","text":"2026-02-23 to 2026-04-21. Singapore & Hong Kong / online. A cross-border university quantitative-trading competition in which Singapore and Hong Kong teams built and deployed live crypto trading strategies, with city qualifiers followed by a SG-vs-HK final."}]}