GRPO's group-mean baseline assigns identical advantages to all tokens under output-only rewards, inducing gradient sparsity and an intrinsic rank-2 structure proven from the zero-sum constraint and confirmed by SVD on Nemotron-4B gradients.
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In recent years, large language models have greatly improved in their ability to perform complex multi-step reasoning. However, even state-of-the-art models still regularly produce logical mistakes. To train more reliable models, we can turn either to outcome supervision, which provides feedback for a final result, or process supervision, which provides feedback for each intermediate reasoning step. Given the importance of training reliable models, and given the high cost of human feedback, it is important to carefully compare the both methods. Recent work has already begun this comparison, but many questions still remain. We conduct our own investigation, finding that process supervision significantly outperforms outcome supervision for training models to solve problems from the challenging MATH dataset. Our process-supervised model solves 78% of problems from a representative subset of the MATH test set. Additionally, we show that active learning significantly improves the efficacy of process supervision. To support related research, we also release PRM800K, the complete dataset of 800,000 step-level human feedback labels used to train our best reward model.
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- abstract In recent years, large language models have greatly improved in their ability to perform complex multi-step reasoning. However, even state-of-the-art models still regularly produce logical mistakes. To train more reliable models, we can turn either to outcome supervision, which provides feedback for a final result, or process supervision, which provides feedback for each intermediate reasoning step. Given the importance of training reliable models, and given the high cost of human feedback, it is important to carefully compare the both methods. Recent work has already begun this comparison, bu
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Shared token budgets between visible chain-of-thought and answers create a coupling tax that makes non-thinking competitive on math benchmarks, with a truncation decomposition predicting the crossover and split budgets improving results.
MedPRMBench is the first fine-grained benchmark for process reward models in medical reasoning, featuring 6500 questions, 13000 chains, 113910 step labels, and a baseline that improves downstream QA accuracy by 3.2-6.7 points.
A Lean-verified multi-agent system produces a catalogue of 14,116 quantum codes with transversal diagonal gates for small parameters, extracts infinite families, and resolves specific distance-3 cases with constructions and no-go proofs.
ExCyTIn-Bench is the first benchmark of 7542 questions from Microsoft Sentinel threat investigation graphs, where the best LLM agent achieves a reward of 0.606.
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.
Flow models reach 99.2% Sudoku accuracy in 7 passes and 96.1% on out-of-distribution Sudoku-Extreme by selecting dynamically stable candidates and training with self-conditioning plus DPO to avoid failed outputs.
GILP trains a parameterized backbone for valid actions and state predictions, then uses a consistency gate with LLM drafts to reduce hallucinated-state rate from 0.176 to 0.035 on GPT-4o-mini while raising success from 0.668 to 0.838.
VCT abstracts non-linear LLM operations into authenticated state transitions via atomic Q&A hash chains, session Merkle roots, and account-level roots with joint signatures, plus protocols for deletions and concurrency detection.
Verifiable search procedures cannot be learned as forward chain-of-thought by language models; they instead learn memorization, verification, or require precomputed catalogs.
ICT framework applies JS divergence to token logits to select critical tokens for selective RLVR updates, claiming 4.58% average pass@4 gains on Qwen2.5 models across seven reasoning benchmarks.
DivInit improves agentic search breadth scaling by selecting diverse first-turn queries from a single model generation, delivering 5-7 point gains on multi-hop QA across five models and eight benchmarks at matched compute.
This paper introduces a taxonomy of four LLM failure modes on research math proofs and empirically shows premise smuggling in all eight audited Gemini outputs, with a new audit instrument achieving 100% precision.
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.
Establishes a quadratic lower bound on query complexity for sampling from large classes of distributions given approximate density oracles, answers an open question on optimality of random walks, and shows circumvention for bounded classes as an abstraction of TTT.
AR-OPD disentangles privileged supervision via anchored residual guidance to reduce hindsight leakage in on-policy distillation, reporting gains of 2.3 points over full privileged OPD and 7.9 over SFT on reasoning tasks.
A paired-image benchmark reveals that many MLLMs fail to update predictions when task-critical visual evidence changes, even when they answer individual images correctly.
Introduces CHARM framework that detects cascading hallucinations in agentic RAG at 89.4% rate with 5.3% false positives and reduces error propagation by 82.1% on multi-hop QA benchmarks.
ChemCoTBench-V2 is a new rule-verifiable benchmark with 5,620 samples across 18 tasks that evaluates LLM chemical reasoning traces using deterministic chemistry rules and reference traces rather than final answers alone.
ResMerge improves merging of RL expert LLMs via a stable residual consensus backbone plus gated head correction, outperforming task-vector and spectral baselines in capability preservation.
Chunk-Level Guided Generation uses off-the-shelf large LLMs to score fixed-length chunks from small models via likelihoods, matching trained PRM performance on math benchmarks without reward-model training.
PEFT-Arena reveals distinct stability-plasticity profiles across PEFT methods, with orthogonal finetuning achieving the best Pareto frontier under comparable parameter budgets, supported by weight-space spectral and activation-space retention analyses.
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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ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving
ToRA trains language models on interactive tool-use trajectories with imitation learning and output shaping to integrate reasoning and external tools, yielding 13-19% gains on math datasets and new highs like 44.6% on MATH for a 7B model.
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Predict, Reuse, and Repair: Accelerating Dynamic Sparse Attention for Long-Context LLM Decoding
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Nothing from Something: Can a Language Model Discover 0?
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Order Is Not Control
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Evaluating Research-Level Math Proofs via Strict Step-Level Verification
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Selective-Advantage Entropy-Adaptive Horizon GRPO: Asymmetric Token-Level Discounting for Efficient Reinforcement Learning of Language Models
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Evaluating Reasoning Fidelity in Visual Text Generation
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AXIOM: A Trust-First Neuro-Symbolic Execution Architecture for Verifiable Mathematical Reasoning
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Mechanistically Interpreting the Role of Sample Difficulty in RLVR for LLMs
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Prefix-Safe Bayesian Belief Tracking for LLM Reasoning Reliability:Separating Calibration from Ranking
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Less is More: Early Stopping Rollout for On-Policy Distillation
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Stabilizing Recurrent Dynamics for Test-Time Scalable Latent Reasoning in Looped Language Models
STARS trains looped language models with Jacobian spectral radius regularization and random loop sampling to drive latent states toward asymptotically stable fixed points, yielding reliable test-time scaling on arithmetic and mathematical reasoning tasks.
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Cassandra: Enabling Reasoning LLMs at Edge via Self-Speculative Decoding
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Hide to Guide: Learning via Semantic Masking
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StepGap hybrid checker detects typed evidence gaps in multi-hop QA steps with sF1 72.0 and boosts downstream model EM by 3.3 points when used as GRPO reward.
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CaptchaMind: Training CAPTCHA Solvers via Reinforcement Learning with Explicit Reasoning Supervision
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LambdaPO: A Lambda Style Policy Optimization for Reasoning Language Models
LambdaPO introduces pairwise preference-based advantage estimation and a semantic density reward to extract more optimization signal from trajectory groups than GRPO's monolithic baseline.
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R2V Agent: Teaching SLMs When to Ask for Help
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YFPO: A Preliminary Study of Yoked Feature Preference Optimization with Neuron-Guided Rewards for Mathematical Reasoning
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Learning to Foresee: Unveiling the Unlocking Efficiency of On-Policy Distillation
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On-Policy Distillation with Best-of-N Teacher Rollout Selection
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Robust Multi-Agent LLMs under Byzantine Faults
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Matrix-Decoupled Concentration for Autoregressive Sequences: Dimension-Free Guarantees for Sparse Long-Context Rewards
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Decodable but Not Corrected by Fixed Residual-Stream Linear Steering: Evidence from Medical LLM Failure Regimes
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DeepImagine: Learning Biomedical Reasoning via Successive Counterfactual Imagining
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Language as a Latent Variable for Reasoning Optimization
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Prioritizing the Best: Incentivizing Reliable Multimodal Reasoning by Rewarding Beyond Answer Correctness
Groupwise Ranking Reward reduces reasoning-answer inconsistency in multimodal models and raises reliability-conditioned accuracy from 47.4% to 54.7% over standard RLVR.
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Reducing Credit Assignment Variance via Counterfactual Reasoning Paths
Introduces IBPO, a counterfactual credit assignment method that turns sparse terminal rewards into process-level advantage estimates for more stable LLM reasoning training.
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Targeted Exploration via Unified Entropy Control for Reinforcement Learning
UEC-RL improves RL reasoning performance in LLMs and VLMs by activating exploration on hard prompts and stabilizing entropy, delivering a 37.9% relative gain over GRPO on Geometry3K.
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Correct Prediction, Wrong Steps? Consensus Reasoning Knowledge Graph for Robust Chain-of-Thought Synthesis
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From Pixels to Digital Agents: An Empirical Study on the Taxonomy and Technological Trends of Reinforcement Learning Environments
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Goldilocks RL: Tuning Task Difficulty to Escape Sparse Rewards for Reasoning
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Hard Negative Sample-Augmented DPO Post-Training for Small Language Models
A six-dimensional MathVerifier supplies hard negatives and per-sample weights that improve DPO performance on math reasoning for a 1.5B Qwen2.5 model over standard SFT and unweighted DPO.
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Rethinking Expert Trajectory Utilization in LLM Post-training for Mathematical Reasoning
Sequential SFT followed by RL, guided by the Plasticity-Ceiling Framework, achieves higher performance ceilings in LLM mathematical reasoning than synchronized methods by optimizing data scale and transition timing.
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DiffAdapt: Difficulty-Adaptive Reasoning for Token-Efficient LLM Inference
DiffAdapt detects problem difficulty via entropy in reasoning traces and applies one of three fixed inference strategies per question, cutting token usage up to 22.4% with comparable or better accuracy across five models and eight benchmarks.