Chain-of-thought prompting, by including intermediate reasoning steps in few-shot examples, elicits strong reasoning abilities in large language models on arithmetic, commonsense, and symbolic tasks.
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Measuring Mathematical Problem Solving With the MATH Dataset
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abstract
Many intellectual endeavors require mathematical problem solving, but this skill remains beyond the capabilities of computers. To measure this ability in machine learning models, we introduce MATH, a new dataset of 12,500 challenging competition mathematics problems. Each problem in MATH has a full step-by-step solution which can be used to teach models to generate answer derivations and explanations. To facilitate future research and increase accuracy on MATH, we also contribute a large auxiliary pretraining dataset which helps teach models the fundamentals of mathematics. Even though we are able to increase accuracy on MATH, our results show that accuracy remains relatively low, even with enormous Transformer models. Moreover, we find that simply increasing budgets and model parameter counts will be impractical for achieving strong mathematical reasoning if scaling trends continue. While scaling Transformers is automatically solving most other text-based tasks, scaling is not currently solving MATH. To have more traction on mathematical problem solving we will likely need new algorithmic advancements from the broader research community.
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- abstract Many intellectual endeavors require mathematical problem solving, but this skill remains beyond the capabilities of computers. To measure this ability in machine learning models, we introduce MATH, a new dataset of 12,500 challenging competition mathematics problems. Each problem in MATH has a full step-by-step solution which can be used to teach models to generate answer derivations and explanations. To facilitate future research and increase accuracy on MATH, we also contribute a large auxiliary pretraining dataset which helps teach models the fundamentals of mathematics. Even though we are
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representative citing papers
Sliding-window transformers without positional encodings are Turing complete because the sliding window breaks permutation symmetry and suffices to simulate Post machines via a constant-size histogram state.
A nine-dimension algebraic complexity framework shows that LLMs suffer a scale-invariant working memory bottleneck, collapsing at 20-30 parallel branches regardless of parameter count from 8B to 235B.
Only two of seven LLMs produce positive returns on live Polymarket data, with MiMo-V2-Flash at 17.6% CWR and Gemini-3-Flash at 6.2% CWR while the other five lose money.
User-turn generation reveals that LLMs' interaction awareness is largely decoupled from task accuracy, remaining near zero in deterministic settings even as accuracy scales to 96.8% on GSM8K.
SARL rewards reasoning topology to improve label-free RL, outperforming baselines with gains up to 44.7% on math and 34.6% on open-ended tasks while maintaining more stable training.
LLaDA is a scalable diffusion-based language model that matches autoregressive LLMs like LLaMA3 8B on tasks and surpasses GPT-4o on reversal poem completion.
SWE-Gym supplies 2438 executable real-world Python tasks to train SWE agents and verifiers, yielding up to 19% gains and new open-weight SOTA of 32% on SWE-Bench Verified.
ErrorRadar is a new benchmark of 2,500 multimodal K-12 math problems for MLLM error step identification and categorization, where GPT-4o trails human experts by ~10%.
LiveBench is a contamination-limited LLM benchmark with auto-scored challenging tasks from recent sources across math, coding, reasoning and more, where top models score below 70%.
MiniF2F is a new cross-system benchmark containing 488 Olympiad-level mathematics problems formalized in Metamath, Lean, Isabelle, and HOL Light, together with baseline results from a GPT-3-based prover.
ELDR reduces median TPOT by 5.9-13.9% in PD-disaggregated MoE serving via expert signatures from prefill, K-means partitioning, and locality-band routing with KV-co-indexed signature cache.
Online IL overcomes an information-theoretic bottleneck that offline IL faces in non-realizable settings even at horizon 1, under a new structural characterization of reward-relative misspecification.
TRL extends tandem training to RLVR pipelines, matching GRPO solo reasoning on Qwen3-4B math tasks while improving handoff robustness, reducing distributional drift, and increasing CoT legibility for the junior.
TAC is a bandit curriculum for multi-domain RLVR that prioritizes domains whose gradient updates align with and benefit other domains, yielding up to 2.8-point macro accuracy gains over learnability-only baselines on Qwen3-1.7B and Llama3.2-3B.
SGPO extracts strategies from strong-model responses, builds autonomous and guided trajectories, and applies token-level forward-KL distillation with adaptive weighting to outperform SFT and RL baselines by 2.2 points on math benchmarks.
Verifiable search procedures cannot be learned as forward chain-of-thought by language models; they instead learn memorization, verification, or require precomputed catalogs.
MergeProbe forecasts LoRA adapter mergeability from first-few-percent training signals and outperforms interference-aware baselines on retention while adding low overhead on a five-domain benchmark.
Coordination control in LLM teams adds accuracy only where round-0 majority is unreliable, task recoverable, and free interaction fails to repair it, matching contingency theory predictions across models and regimes.
GraphPO represents reasoning rollouts as a DAG to merge semantically equivalent paths, share suffixes, and assign separate efficiency and correctness advantages for lower variance and better performance than chain or tree baselines.
TAPO constructs learnable micro-reflective trajectories from contrastive model rollouts during RL training to provide explicit error diagnoses and corrections, reporting consistent gains over GRPO on AIME and HMMT math benchmarks.
Heterogeneous agents achieve dense latent KV-cache communication via lightweight cross-model transformation and two-phase training, outperforming text at lower compute in context-aware settings and enabling context-unaware transfer.
SWITCH uses explicit <swi> and </swi> boundary tokens to make latent chain-of-thought compatible with on-policy RL (GRPO) and open to causal mechanistic probing, outperforming prior hidden-state recurrence methods.
EBA clusters sampled LLM generations in representation space to estimate agreement, outperforming random selection with stable scaling and showing that central positions correlate with higher generation quality.
citing papers explorer
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Chain-of-Thought Prompting Elicits Reasoning in Large Language Models
Chain-of-thought prompting, by including intermediate reasoning steps in few-shot examples, elicits strong reasoning abilities in large language models on arithmetic, commonsense, and symbolic tasks.
-
Rethinking the Role of Positional Encoding: Sliding-Window Transformers without PE Remain Turing Complete
Sliding-window transformers without positional encodings are Turing complete because the sliding window breaks permutation symmetry and suffices to simulate Post machines via a constant-size histogram state.
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Beyond Accuracy: Diagnosing Algebraic Reasoning Failures in LLMs Across Nine Complexity Dimensions
A nine-dimension algebraic complexity framework shows that LLMs suffer a scale-invariant working memory bottleneck, collapsing at 20-30 parallel branches regardless of parameter count from 8B to 235B.
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PolyBench: Benchmarking LLM Forecasting and Trading Capabilities on Live Prediction Market Data
Only two of seven LLMs produce positive returns on live Polymarket data, with MiMo-V2-Flash at 17.6% CWR and Gemini-3-Flash at 6.2% CWR while the other five lose money.
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Beyond the Assistant Turn: User Turn Generation as a Probe of Interaction Awareness in Language Models
User-turn generation reveals that LLMs' interaction awareness is largely decoupled from task accuracy, remaining near zero in deterministic settings even as accuracy scales to 96.8% on GSM8K.
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SARL: Label-Free Reinforcement Learning by Rewarding Reasoning Topology
SARL rewards reasoning topology to improve label-free RL, outperforming baselines with gains up to 44.7% on math and 34.6% on open-ended tasks while maintaining more stable training.
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Large Language Diffusion Models
LLaDA is a scalable diffusion-based language model that matches autoregressive LLMs like LLaMA3 8B on tasks and surpasses GPT-4o on reversal poem completion.
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Training Software Engineering Agents and Verifiers with SWE-Gym
SWE-Gym supplies 2438 executable real-world Python tasks to train SWE agents and verifiers, yielding up to 19% gains and new open-weight SOTA of 32% on SWE-Bench Verified.
-
ErrorRadar: Benchmarking Complex Mathematical Reasoning of Multimodal Large Language Models Via Error Detection
ErrorRadar is a new benchmark of 2,500 multimodal K-12 math problems for MLLM error step identification and categorization, where GPT-4o trails human experts by ~10%.
-
LiveBench: A Challenging, Contamination-Limited LLM Benchmark
LiveBench is a contamination-limited LLM benchmark with auto-scored challenging tasks from recent sources across math, coding, reasoning and more, where top models score below 70%.
-
MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics
MiniF2F is a new cross-system benchmark containing 488 Olympiad-level mathematics problems formalized in Metamath, Lean, Isabelle, and HOL Light, together with baseline results from a GPT-3-based prover.
-
ELDR: Expert-Locality-Aware Decode Routing for PD-Disaggregated MoE Serving
ELDR reduces median TPOT by 5.9-13.9% in PD-disaggregated MoE serving via expert signatures from prefill, K-means partitioning, and locality-band routing with KV-co-indexed signature cache.
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When Does Online Imitation Learning Help in LLM Post-Training? The Role of (Non-)Realizability Beyond Horizon
Online IL overcomes an information-theoretic bottleneck that offline IL faces in non-realizable settings even at horizon 1, under a new structural characterization of reward-relative misspecification.
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Tandem Reinforcement Learning with Verifiable Rewards
TRL extends tandem training to RLVR pipelines, matching GRPO solo reasoning on Qwen3-4B math tasks while improving handoff robustness, reducing distributional drift, and increasing CoT legibility for the junior.
-
Transferability for General Reasoning: An Automated Curriculum for Multi-Domain RLVR
TAC is a bandit curriculum for multi-domain RLVR that prioritizes domains whose gradient updates align with and benefit other domains, yielding up to 2.8-point macro accuracy gains over learnability-only baselines on Qwen3-1.7B and Llama3.2-3B.
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Beyond Trajectory Imitation: Strategy-Guided Policy Optimization for LLM Reasoning
SGPO extracts strategies from strong-model responses, builds autonomous and guided trajectories, and applies token-level forward-KL distillation with adaptive weighting to outperform SFT and RL baselines by 2.2 points on math benchmarks.
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A Verifiable Search Is Not a Learnable Chain-of-Thought
Verifiable search procedures cannot be learned as forward chain-of-thought by language models; they instead learn memorization, verification, or require precomputed catalogs.
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Predicting Mergeability of Parameter-Efficient Fine-Tuning Updates
MergeProbe forecasts LoRA adapter mergeability from first-few-percent training signals and outperforms interference-aware baselines on retention while adding low overhead on a five-domain benchmark.
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Leadership as Coordination Control: Behavioral Signatures and the Recovery-Advantage Boundary in Multi-Agent LLM Teams
Coordination control in LLM teams adds accuracy only where round-0 majority is unreliable, task recoverable, and free interaction fails to repair it, matching contingency theory predictions across models and regimes.
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GraphPO: Graph-based Policy Optimization for Reasoning Models
GraphPO represents reasoning rollouts as a DAG to merge semantically equivalent paths, share suffixes, and assign separate efficiency and correctness advantages for lower variance and better performance than chain or tree baselines.
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Learning from Your Own Mistakes: Constructing Learnable Micro-Reflective Trajectories for Self-Distillation
TAPO constructs learnable micro-reflective trajectories from contrastive model rollouts during RL training to provide explicit error diagnoses and corrections, reporting consistent gains over GRPO on AIME and HMMT math benchmarks.
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See What I See, Know What I Think: Dense Latent Communication Across Heterogeneous Agents
Heterogeneous agents achieve dense latent KV-cache communication via lightweight cross-model transformation and two-phase training, outperforming text at lower compute in context-aware settings and enabling context-unaware transfer.
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Demystifying Hidden-State Recurrence: Switchable Latent Reasoning with On-Policy Reinforcement Learning
SWITCH uses explicit <swi> and </swi> boundary tokens to make latent chain-of-thought compatible with on-policy RL (GRPO) and open to causal mechanistic probing, outperforming prior hidden-state recurrence methods.
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Agreement in Representation Space for Open-Ended Self-Consistency
EBA clusters sampled LLM generations in representation space to estimate agreement, outperforming random selection with stable scaling and showing that central positions correlate with higher generation quality.
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INFRAMIND: Infrastructure-Aware Multi-Agent Orchestration
INFRAMIND is an infrastructure-aware multi-agent orchestration framework that uses RL on a hierarchical constrained MDP to jointly optimize topology, model selection, and scheduling under dynamic load.
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Unified Energy for Invariant and Independent Decoding in Diffusion Language Models
The paper introduces Uni-E, a unified energy for DLMs that accounts for model capacity, dependency and invariance, can be computed exactly, and corrects distribution shifts from dependency and invariance.
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The Hidden Bias of Process Reward Models:PRISM for Rewarding the Right Reasoning
PRISM is a contrastive, policy-aware training framework for process reward models that reduces false positives by 22% on PRMBench and boosts downstream accuracy up to 33% in Best-of-N selection by learning reliable relative comparisons instead of pointwise labels.
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From Correctness to Utility: Gain-Based Prefix Evaluation for LLM Reasoning
Prefix gain measured via student-model solve-rate improvement is used to train a Prefix Utility Model (PUM) that supplies stronger supervision than correctness-based process rewards for mathematical reasoning.
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OrderGrad: Optimizing Beyond the Mean with Order-Statistic Policy Gradient Estimation
OrderGrad supplies unbiased likelihood-ratio and reparameterization gradient estimators for finite-sample L-statistics by applying a rank-based reward transformation usable in standard policy-gradient updates.
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Elmes*: Automated Construction of Fine-Grained Evaluation Rubrics for Large Language Models in Long-Tail Educational Scenarios
Elmes* automates fine-grained rubric construction for LLM educational evaluation via multi-agent interactions and a self-evolving SceneGen module, producing the Edu-330 benchmark that demonstrates multidimensional differences in model teaching performance.
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Less is MoE: Trimming Experts in Domain-Specialist Language Models
Fisher-MoE prunes sparse intermediate dimensions in MoE FFNs ranked by Fisher importance, delivering 50% compression that preserves capability while cutting memory ~45% and raising throughput 21%.
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STRIDE: Training Data Attribution via Sparse Recovery from Subset Perturbations
STRIDE formulates TDA as sparse recovery using steering operators that mimic subset training effects in activation space, claiming SOTA LLM pre-training attribution at 13x prior speed.
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Conformal Language Modeling via Posterior Sampling
Conformal language modeling samples from posterior approximations conditioned on high-scoring regions to achieve risk control with higher utility than post-hoc filtering in open-ended text generation.
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Testing LLM Arithmetic Reasoning Generalization with Automatic Numeric-Remapping Attacks
An automatic numeric-remapping attack generator reveals 12-26 point accuracy drops on GSM8K for three LLMs while MAWPS and MultiArith stay near 98%.
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Extreme Low-Bit Inference in Reasoning Models: Failure Modes and Targeted Recovery
2-bit quantized reasoning models exhibit process failures like loops and delayed commitment that degrade end-to-end performance, but FP16 planning and loop rescue recover accuracy on MATH-500 from 17.2% to 74.2% for Qwen3-8B while retaining speed gains.
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OmniOPD: Logit-Free On-Policy Distillation via Speculative Verification
OmniOPD replaces token-level logit matching in on-policy distillation with Monte Carlo chunk-level semantic verification and a peak-entropy scheduler.
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D$^3$: Dynamic Directional Graph-Constrained Data Scheduling for LLM Training
D³ introduces a dynamic directional graph-constrained framework that models sample interactions via loss dependencies to derive an optimized training sequence for LLMs.
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Bastion: Budget-Aware Speculative Decoding with Tree-structured Block Diffusion Drafting
BASTION is a budget-aware speculative decoding framework with adaptive tree-structured block diffusion drafting that reports up to 6.61x speedup and 39% improvement over block-diffusion baselines.
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Compositional Generalization in Autoregressive Models via Logit Composition
Logit composition of autoregressive models is projective under factorized conditionals, preserved under smooth reparameterizations, and maintains length generalization when assumptions hold uniformly.
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RLVR Datasets and Where to Find Them: Tracing Data Lineage for Better Training Data
ATLAS traces RLVR data to 20 atomic sources, most datasets are variants, and DAPO++ curated with SCA improves RLVR performance while Q predicts training effectiveness.
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Evaluating Interactive Reasoning in Large Language Models: A Hierarchical Benchmark with Executable Games
The paper introduces a multi-turn interactive benchmark using 474 executable games to evaluate LLMs on evidence acquisition, belief updating, contextual robustness, and metacognitive adaptation, revealing large performance gaps and sensitivity to perturbations.
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ARBITER: Reasoning Trajectory Basins and Majority Vote Failures in Test-Time Sampling
ARBITER models reasoning trajectory basins in test-time sampling and uses model-internal signals to correct majority-vote failures, recovering part of the oracle gap on math benchmarks.
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CurveRL: Principled Distribution-Aware Context Reweighting for LLM Reasoning
CurveRL derives a quantile-coordinate reweighting rule from a utility functional on pass rates and shows it outperforms GRPO on reasoning benchmarks.
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X-Token: Projection-Guided Cross-Tokenizer Knowledge Distillation
X-Token proposes projection-guided P-KL and H-KL losses to fix uncommon-token suppression and over-conservative matching in logit-based cross-tokenizer distillation, yielding gains over GOLD on Llama-3.2-1B.
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CopT: Contrastive On-Policy Thinking with Continuous Spaces for General and Agentic Reasoning
CopT reverses CoT by eliciting a draft answer first then using continuous-embedding contrastive verification and on-policy thinking to reflect and correct, yielding up to 23% higher accuracy and 57% fewer tokens without training.
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Detecting and Mitigating the Correct-Answer Extinction Window in Test-Time Reinforcement Learning with Majority Voting
TTRL gains are reinterpreted as mostly sharpening rather than learning, with an identified extinction window causing net corruption; TTRL-Guard mitigates via FRS, MPS, and RCSU for improved pass@1.
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Learning How to Cube
A neuro-symbolic post-training pipeline lets a 4B transformer learn cubing heuristics that reach pass@5 of 53 on 100 SAT competition instances, matching the strongest symbolic baseline.
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Factorization-Error-Free Discrete Diffusion Language Model via Speculative Decoding
FeF-DLLM achieves factorization-error-free generation in discrete diffusion language models via prefix-conditioned posterior factorization and speculative decoding, delivering 5.04 pp higher accuracy and 3.86x faster inference on GSM8K, MATH, HumanEval, and MBPP.
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Good Agentic Friends Do Not Just Give Verbal Advice: They Can Update Your Weights
TFlow enables multi-agent LLMs to collaborate via transient low-rank LoRA perturbations derived from sender activations, yielding up to 8.5 accuracy gains and 83% token reduction versus text-based baselines on Qwen3-4B models.
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Query-Conditioned Test-Time Self-Training for Large Language Models
QueST adapts LLMs at test time by generating query-specific problem-solution pairs for self-supervised fine-tuning, improving reasoning performance without external data.