Search: “numerical-continuation”

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The Router Within: Eliciting Native Skill Routing from a Frozen LLM

Gavel reads skill-routing signals from a frozen LLM's forward passes with two linear maps, beating retrieval pipelines by up to 21.9 points.

Gavel (Glance And Verdict) shows a frozen agent LLM already contains skill-routing signals in its forward passes, read out via two trained linear maps without loading skill text into context. A glance step scores the full library using mid-layer states and per-skill banks built in one forward pass; a verdict step fuses the model's own likelihood and yes/no judgment as a product of experts. Trained once, it transfers zero-shot to three public benchmarks and SkillTraj (372 simulated agent trajectories); on Qwen3-32B it beats progressive disclosure and retrieve-and-rerank pipelines adding 1.2B-16B external parameters by up to 13.4 points (21.9 mid-rollout).

arXiv cs.AI / cs.LG / cs.CL·Sep 14, 17:58 UTC · 2d agoAI research 2 sources1

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Variational Continuation for Double Pendulum Periodic Orbits

Researchers introduce a Hessian-based, integrator-free method using automatic differentiation to continue periodic orbits in the double pendulum, uncovering previously unreported orbit families.

A new arXiv paper presents a variational, Hessian-based framework for numerically continuing periodic orbits in dynamical systems, parametrizing candidate loops as Fourier series and minimizing deviation from the governing differential equations. Automatic differentiation replaces hand-derived Jacobians, and flat directions of the loss landscape guide the continuation search. The method is demonstrated on the double pendulum, mapping bifurcations along orbit families, including periodic orbits where neither pendulum mass is ever simultaneously at rest.

arXiv cs.AI / cs.LG / cs.CL·Sep 4, 16:42 UTC · 12d agoAI research

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Towards a Deterministic Math Solver for Clinical Language Models

Paper shows handing arithmetic to a deterministic Python solver beats direct model calculation at 32B but not reliably at 7B on MedCalc-Bench.

Researchers test a Program-Solve interface where clinical LLMs write case-specific Python executed by a restricted local solver instead of doing arithmetic directly. On MedCalc-Bench Verified (1,100 cases, 55 calculators), Qwen2.5-32B-AWQ scored 90.53% with solver handoff versus 83.47% with direct arithmetic (+7.05 points), while Qwen2.5-7B gained an unreliable +3.29 points with a confidence interval spanning zero. The authors audited the benchmark against clinical guidelines and flagged 16 of 55 calculators for version, use, or coefficient concerns.

Hugging Face daily papers·Sep 8, 20:00 UTC · 8d agoAI research1

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Learning to Solve Hard Problems in RL for LLMs by Never Giving Up

Paper introduces Never Give Up adaptive sampling, fixing RL's 'Matthew Effect' where compute is wasted on easy problems and hard problems see little improvement.

Researchers identify a 'Matthew Effect' in reinforcement learning for LLMs, where RL yields large gains on easy problems but minimal improvement on hard ones because compute is misallocated. They propose Never Give Up (NGU), an adaptive sampling method that keeps generating samples for a problem until one is correct, using asynchronous RL to filter easy problems cheaply and concentrate compute on hard ones. NGU improves performance per compute on the Deepscaler math benchmark and iteratively solves the Manufactoria coding task where standard GRPO with per-test reward fails.

Hugging Face daily papers·Sep 10, 20:00 UTC · 6d agoAI research

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MAxBench: A Multinomial Concept Recovery Benchmark

MAxBench evaluates multinomial concept recovery methods, finding affine subspaces steer most reliably but none consistently beats prompting.

MAxBench is a geometry-agnostic evaluation framework for multinomial concept representations in language models, based on sampling from recovered concept representations. It compares 10 localization methods covering 5 geometry types across 6 concepts and 4 models. Findings show affine subspaces steer more reliably than rank-one or linear subspaces due to better non-zero offsets, manifold steering is competitive where applicable, and no method consistently outperforms prompting.

arXiv cs.AI / cs.LG / cs.CL·Sep 11, 17:08 UTC · 5d agoAI research

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Discrete Beckmann Transport Models for One-Step Language Modeling and Reasoning

DBTM achieves one-step text generation via a time-independent transport map trained directly from data, removing pretrained teacher distillation.

Discrete Beckmann Transport Models (DBTM) build a time-independent flow whose autonomous transport map provably carries any point in ambient space to a fixed point on simplex vertices in a single step. The fixed-point property is characterized by a conservation equation whose residual can be minimized directly from data, eliminating the need for a teacher flow, distillation, and time conditioning. A partial-context interpolant extension turns additional function evaluations into refinement steps rather than ODE integration steps. On language modeling and reasoning tasks, DBTM's one- and few-step generation improves quality and accuracy over discrete diffusion and continuous flow baselines.

arXiv cs.AI / cs.LG / cs.CL·Sep 14, 17:19 UTC · 2d agoAI research1

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Unsolved Problem by Fields Medalist Breached by Two High School Students

Two high school students used Claude Opus 5 and GPT-5.6 Sol to help solve an open Lorentzian polynomials problem, posting a 75-page arXiv proof.

Aayush Bathija and Prince Rohatgi of Oak Park High School, mentored by UCLA postdoc Daniel Soskin, published the 75-page paper 'Bounded Ratios for Lorentzian Polynomials' (arXiv 2609.05341), solving an open problem in Fields Medalist June Huh's Lorentzian polynomial theory. The main structural theorem extends bounded coefficient-ratio characterization from quadratic to arbitrary-degree polynomials via discrete convexity conditions. The students used Claude Opus 5 and GPT-5.6 Sol for exploration and proof ideas but independently verified all arguments; the result follows an open letter from 25 Fields Medalists voicing concerns about AI's impact on mathematical rigor.

Hacker News · security·Sep 14, 12:23 UTC · 2d agoAI researchHN 22↑ · 19 comments

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Procedural Graphs: Self-Evolving Execution Structures for LLM Agents

Researchers introduce Procedural Graphs, self-evolving (procedure, relation, procedure) structures guiding LLM agent tool use and planning.

Procedural Graphs organize procedural knowledge into (procedure, relation, procedure) triplets to guide LLM agent actions, addressing drift such as lost objectives, out-of-order tool calls, and repeated unproductive steps. At each decision step the framework localizes the active node and a guidance model translates the surrounding subgraph into step-level situational guidance. An LLM refiner edits graph topology by contrasting failed with successful trajectories, and across datasets, task types and LLMs the approach outperforms memory-based baselines and matches or surpasses hand-designed graphs.

arXiv cs.AI / cs.LG / cs.CL·Sep 8, 17:59 UTC · 8d agoAI research1

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Procedural Graphs: Self-Evolving Execution Structures for LLM Agents

Procedural Graph framework stores procedural knowledge as triplets and self-evolves via LLM refinement, beating memory-based baselines across datasets, tasks, and LLMs.

The Procedural Graph organizes procedural knowledge into (procedure, relation, procedure) triplets; at each decision step the framework localizes the agent's active node and a guidance model translates the surrounding subgraph into step-level guidance that biases the solver's next action. An LLM refiner contrasts failed with successful trajectories and edits the graph's topology and attributes, retaining rejected edits to discourage repetition. Starting from a minimal skeleton, the loop builds graphs that match or surpass hand-designed ones and can repair flawed expert priors, delivering consistent gains over memory-based baselines across multiple datasets, task types, and LLMs.

Hugging Face daily papers·Sep 7, 20:00 UTC · 9d agoAI research1

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How Model Growth, Recursion, and Boundary Operators Influence Scaling Exponents

Researchers show model growth via looped transformers improves scaling exponents; a 7.4B architecture matches GPT-3 13B with roughly 20x less compute.

The paper shows that architectural interventions, contrary to conventional wisdom, can modify pre-training scaling exponents and yield exponential performance gains with compute. Looped transformers with increasing loop counts provide a model growth mechanism; a 7.4B model-growth architecture matches GPT-3 13B on CORE with roughly 20x less compute, with efficiency gains that increase with scale. A boundary operator that normalizes and injects an earlier block also improves compute efficiency, and in data-constrained multi-epoch settings increasing loops with scale is compute-optimal.

arXiv cs.AI / cs.LG / cs.CL·Sep 16, 17:36 UTC · 14h agoAI research

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I wrote an AI textbook — how long until AI can do it better?

AI researcher Nathan Lambert argues LLMs remain weak at long-form technical writing, questioning whether models can autonomously organize scientific knowledge for breakthroughs.

Nathan Lambert describes writing a post-training textbook, Reinforcement Learning from Human Feedback, and finds today's LLMs weak at organizing long-form technical content despite becoming superhuman at coding and math. He notes GPT 5.5 Pro found deep typos across a 200-300 page manuscript while Claude models proved more useful as editors. He argues that compressing knowledge through writing is a prerequisite for autonomous scientific insight and tempers expectations for near-term AI-driven open science.

Interconnects·Aug 12, 13:01 UTC · Aug 12, 2026AI research

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AIJon: Automated Generation of Annotations for Fuzzing

AIJON uses LLMs to auto-generate IJON-style fuzzing annotations, matching human-expert quality on the Magma benchmark.

Researchers replicate IJON experiments and propose AIJON, a system that uses LLMs to automatically generate expert-style annotations for coverage-guided fuzzing at scale. On the Magma benchmark, LLM-generated annotations performed comparably to human-generated ones, though annotation-based fuzzing was not strictly better than AFL++. The paper analyzes how annotations affect fuzzer energy distribution across campaigns.

arXiv cs.CR·Sep 16, 10:50 UTC · 20h agoResearch

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TasmScan: Continuation-Aware Taint Analysis for TVM Bytecode with Savelist Abstraction

TasmScan introduces source-free taint analysis for TON smart-contract bytecode, detecting 95.3% of defects with 96.8% precision and 17x speedup.

TasmScan is the first bytecode-level static analysis framework for the TON Virtual Machine, enabling cross-continuation data flow reasoning without source code by modeling savelist semantics through forward register analysis with formal over-approximation guarantees. It lifts bytecode into a typed intermediate representation (TASIR) and performs path-sensitive taint analysis. On a 208-contract benchmark with human-confirmed ground truth it detects 95.3% of defects across five classes at 96.8% precision, and resolves 294,546 dynamic continuation targets with 100% precision across 2,921 registry contracts. It achieves a 17x median speedup over symbolic-execution baselines.

arXiv cs.CR·Sep 15, 11:01 UTC · 1d agoResearch1

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Double descent is the principle of least action

A statistical mechanics analysis explains double descent: finite-time diffusion induces effective weight decay that regularizes models as parameters grow.

The paper models stochastic gradient-based training as a particle diffusing over the training-loss energy landscape at an induced temperature, sampling parameters via a Boltzmann distribution. Finite training time carries an effective weight decay, making every parameter a quadratic degree of freedom governed by the equipartition theorem. Adding parameters at fixed training loss lowers the temperature and the L2 norm of the stationary path, increasing effective regularization and explaining the double descent phenomenon.

arXiv cs.AI / cs.LG / cs.CL·Sep 16, 17:17 UTC · 14h agoAI research

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Locus: A Framework for Exploring and Optimizing Point Addition Hardware for Zero-Knowledge Proofs

Locus framework automates ASIC and FPGA point-addition designs for elliptic curves, achieving 2.71x speedups and 3.11x area reductions for ZKPs.

Locus is a framework that automatically generates ASIC and FPGA implementations of elliptic curve point addition (PADD) for supported equation forms, enabling exploration of over 1,000 design points. On a 12nm technology node, its designs achieve a 2.71x geomean speedup and 3.11x geomean area reduction versus prior ASICs, plus 34.67x geomean speedup over CPU. Integrated into a prior ZKP accelerator at iso-area, it yields a 3.15x geomean speedup on end-to-end proof generation. The framework is open source on GitHub.

arXiv cs.CR·Sep 16, 15:53 UTC · 15h agoResearch

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A*-Thought-V2: Efficient Latent Reasoning via Geometric Dynamics of LLM

A*-Thought-V2 compresses chain-of-thought into latent tokens using geometric hidden-state dynamics, cutting computation while improving accuracy on Qwen models.

A*-Thought-V2 models chain-of-thought as a hidden-state trajectory and interleaves explicit text with continuous latent tokens, compressing steps whose transitions deviate from the question-to-solution direction. Trained via stepwise embedding forcing and label forcing with soft multi-modal supervision, it was evaluated on Qwen3.5-9B and Qwen3.6-27B across six benchmarks. Reported results include up to 2.6% average accuracy gain, up to 50% shorter responses, 2.29x higher Accuracy per Computation Unit, 94.6% faster preprocessing, and up to 80.3% faster training.

Hugging Face daily papers·Sep 7, 13:56 UTC · 9d agoAI research

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Proximity Gaps for Gabidulin Codes and Applications

Researchers prove proximity-gap bounds for rank-metric and Gabidulin codes, enabling the first polynomial commitment scheme framework based on rank-metric error-correcting codes.

The paper proves every linear rank-metric code admits a proximity gap for deltas up to (d-1)/(3n) with error at most q^(e+1)/q^m, and improves the gap to (d-1)/(2n) for Gabidulin codes with error at most 10q^(n-1)/q^m, matching bounds for Reed-Solomon codes. A constructed infinite family of constant-rate Gabidulin codes shows the (d-1)/(2n) bound is tight, and a counterexample establishes a lower bound on the error at the d/(3n) gap. Applications include an IOPP for interleaved Gabidulin codes adapted from the Ligero IOPP and a q-linearized polynomial commitment scheme adapted from Ligero-based PCS, reportedly the first PCS framework based on rank-metric codes.

arXiv cs.CR·Sep 9, 07:45 UTC · 8d agoResearch

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StochBench: A Domain-Specific Benchmark for Stochastic Processes in Lean

StochBench introduces 450 graduate-level stochastic-processes problems in Lean 4; an Opus 4.8-based agent proved 34.9% under a 15-minute limit.

StochBench is a Lean 4 benchmark of 450 graduate stochastic-processes problems, each paired with its natural-language source, covering Markov chains, renewal processes, martingales, Brownian motion, stochastic calculus, weak convergence, and Poisson and continuous-time Markov processes. The benchmark addresses field-specific applied mathematics underrepresented in Mathlib, unlike competition-math-dominated suites such as IMO and Putnam collections. An Opus 4.8-based agent achieved a 34.9% proof rate (157/450) under a 15-minute per-problem limit, showing the benchmark remains challenging for advanced provers.

Hugging Face daily papers·Sep 7, 20:00 UTC · 9d agoAI research

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AI models' written reasoning steps correspond to distinct internal patterns, a new study finds

KAIST and Naver AI Lab researchers show LLM reasoning steps like extraction and computation map to distinct activation patterns, strongest in middle layers.

Researchers at KAIST and Naver AI Lab defined eight recurring reasoning operations, including extraction, decomposition, formula recall, deduction, and computation, and showed they correspond to separable activation patterns in Qwen2.5-7B, Qwen3-8B, and Gemma4-31B on math tasks, with GPT-5 labeling solution segments. The separation peaks in middle layers, holds even when a computation step produces a wrong answer, and goes beyond surface-level token choice. Findings replicated on Llama-3-8B, and classifiers trained on Qwen3-8B transferred to GPQA-Diamond and MATH-500. The authors note that using internal states for error detection or mid-generation steering remains future work.

The Decoder·Sep 12, 13:39 UTC · 4d agoAI research2

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LongAgent: History-Guided Agentic Search for Longitudinal Outcome Prediction

LongAgent autonomously searches variable sets and temporal windows to predict longitudinal medical outcomes, beating the strongest non-agent baseline on synthetic data.

The paper proposes LongAgent, an agent-based method that searches over combinations of variable sets, temporal windows and aggregation functions for outcome prediction on heterogeneous medical longitudinal data. It uses a history memory of previous searches and numerical evidence to guide exploration. On synthetic data it achieves mean RMSE 1.7376, improving over the best non-agent baseline by 0.0151 (95% CI [0.0045, 0.0260]; p=0.0273), and performs comparably to the best baseline on a real clinical dataset.

arXiv cs.AI / cs.LG / cs.CL·Sep 14, 16:51 UTC · 2d agoAI research

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Characterizing Language Generation in the Limit: Finite Witnesses and a Separation-Width Hierarch

New work characterizes language generation in the limit via finite witnesses, proves a full separation-width hierarchy, and formalizes all results in Lean.

The paper fully characterizes when language generation in the limit is possible for arbitrary families over a countable universe: each target must admit a finite positive witness such that targets activated by any finite sample share an infinite common intersection. It defines positive separation width and proves every level of the resulting hierarchy occurs, with countable families admitting singleton witnesses and unions of families with infinite common cores requiring unbounded finite witnesses. The characterization, a universal normalization, and a diagonal capture lemma are machine-checked in the Lean proof assistant, with the development maintained on GitHub.

arXiv cs.AI / cs.LG / cs.CL·Sep 9, 17:54 UTC · 7d agoAI research1

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Beyond the Turing threshold: Productive grammars generate essentially undecidable languages

A theoretical paper designs formal grammars that emulate Post's productive sets, generating languages that are provably beyond Turing decidability.

The paper elaborates on Emil Post's productive sets, which are not even semi-computable, and builds formal grammars that emulate their construction over natural numbers. The resulting languages are shown to be essentially undecidable, placing them beyond Turing decidability. This is pure computability and formal language theory with limited direct security relevance.

arXiv cs.CR·Sep 10, 11:20 UTC · 6d agoResearch1

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Show HN: LLM Attention Visualization

A developer released a browser-based tool that visualizes which past tokens influence each LLM output token using aggregated, value-weighted attention scores.

A Show HN project presents a React application built on Transformers.js that renders per-token attention influence by aggregating attention weights scaled by value-vector magnitudes across all attention heads and layers. To expose internal tensors, the author instrumented the ONNX computation graph, hosted a modified model on Hugging Face, and pre-generated prompts to avoid long model downloads in the browser. Demos with a 600-million-parameter model show how verbatim copying draws heavily on source tokens and how single outputs blend information from multiple phrases.

Hacker News · AI·Sep 8, 16:59 UTC · 8d agoAI tools & infraHN 41↑ · 9 comments

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Opaque recurrence, and other AI terms that you should probably know

TechCrunch updates its plain-English glossary defining common AI terms from AGI and agents to chain-of-thought reasoning.

TechCrunch maintains a regularly updated glossary of AI terminology, defining terms such as AGI, AI agents, API endpoints, chain of thought, coding agents, compute, deep learning, and diffusion. It highlights 'opaque recurrence', the reasoning technique in OpenAI's new Astra model that has drawn attention from AI safety researchers. The piece is an educational living document rather than new research or a product announcement.

TechCrunch · AI·Sep 7, 19:24 UTC · 9d agoAI industry1

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Hierarchical NeRF with JAX3D for Volumetric Rendering, Novel-View Synthesis, and 3D Reconstruction

MarkTechPost tutorial implements a hierarchical NeRF in JAX using jax3d volume-rendering primitives for novel-view synthesis and 3D reconstruction.

The tutorial builds an end-to-end hierarchical Neural Radiance Field using JAX, Flax, Optax, and jax3d's volume-rendering functions (sample_along_rays, volume_rendering, sample_piecewise_constant_pdf). It implements positional encoding, skip connections, separate coarse and fine networks, and view-direction conditioning with hierarchical importance sampling. Training uses JAX JIT compilation, Adam optimization, exponential learning-rate decay, and gradient clipping. Evaluation covers PSNR, depth and opacity visualization, 360-degree rendering, and marching-cubes geometry extraction.

MarkTechPost·Sep 13, 19:46 UTC · 3d agoAI research

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When LLM Decompilers Recompile More and Preserve Less

Researchers show LLM decompiler outputs can recompile yet diverge behaviorally, proposing the Decompile-Diverge fuzzing oracle to catch hidden changes.

The paper demonstrates that LLM-based decompilers can produce code that recompiles and passes all shipped tests yet diverges on other legitimate inputs—4.9% overall and up to 13% for one system—and can make disclosed vulnerabilities vanish without a visible crash. Across 300 real GitHub functions and 287 CVE-grounded functions, a refinement LLM lifted Ghidra's build rate from 75% to 90% while Matched rate fell from 74% to 62%, with up to one tenth of vulnerabilities showing Crash Absence. Decompile-Diverge detects these gaps by synthesizing drivers, growing fuzzing corpora from the reference, and rerunning decompiled code on identical inputs.

arXiv cs.CR·Sep 4, 17:16 UTC · 12d agoResearch

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What Else Needs Fixing? Exploring Cost-Effective Test-Time Compute for Revision Propagation in Artifacts Generated Through Conversation

A new benchmark shows LLMs reach 68.3-93% accuracy propagating local revisions across conversationally generated artifacts, with parallel-sample selection most cost-effective.

The paper introduces a benchmark for revision propagation: when users request a local change, LLMs must identify dependencies and update all affected parts of an artifact generated through conversation, where context lives in the chat history. Nine revision methods, including sequential reflection and parallel sampling variants, were evaluated on gpt-oss-20b/120b, gpt-5.4-mini, and qwen3.5-9b/27b/122b. Baselines scored 68.3-93% accuracy, and selecting among three parallel samples via LLM-based or medoid selection improved accuracy by 2.2-9.7% as the most cost-effective test-time compute strategy. Code and dataset are released.

Hugging Face daily papers·Sep 2, 20:00 UTC · 14d agoAI research

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Long-Lived Characters, Local Inference: Incremental Memory Maintenance for Game NPCs

Researchers present incremental KV-cache memory maintenance for long-lived game NPCs running locally on a quantized Qwen hybrid model.

The paper studies incremental memory maintenance for long-lived game NPCs deployed locally with a quantized Qwen hybrid recurrent-attention language model. The runtime removes superseded attention KV entries, computes replacement records at the true sequence tail, and preserves the continuing recurrent state and unchanged KV. Experiments across eight scripted maintenance rounds show true-tail updates preserve current-state and historical bindings, while slot-preserving alternatives repeat a double-subtraction error.

arXiv cs.AI / cs.LG / cs.CL·Sep 16, 17:09 UTC · 14h agoAI research

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A*-Thought-V2: Efficient Latent Reasoning via Geometric Dynamics of LLM

A*-Thought-V2 compresses redundant chain-of-thought steps into latent tokens guided by hidden-state geometry, improving accuracy up to 2.6% while halving response length.

A*-Thought-V2 models chain-of-thought as a hidden-state trajectory projected into a 3D PCA space and compresses steps whose transitions deviate from the question-to-solution direction into continuous latent tokens, keeping aligned steps explicit. Training uses stepwise embedding forcing and label forcing with soft multi-modal vocabulary supervision. On Qwen3.5-9B and Qwen3.6-27B across six in-domain and out-of-domain benchmarks it improves average accuracy by up to 2.6%, cuts response length by up to half, and raises Accuracy per Computation Unit 2.29x while reducing preprocessing and training time by 94.6% and up to 80.3%.

arXiv cs.AI / cs.LG / cs.CL·Sep 7, 17:56 UTC · 9d agoAI research

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