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.
super hub Canonical reference
Let's Verify Step by Step
Canonical reference. 81% of citing Pith papers cite this work as background.
178
Pith papers citing it
Background
81% of classified citations
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, 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.
hub tools
citation-role summary
background 25
dataset 4
method 2
citation-polarity summary
claims ledger
- 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
authors
co-cited works
representative citing papers
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.
EDGE-OPD adds guided rollouts and evidence masking to on-policy self-distillation, enabling successful learning of target identities where standard OPSD and RLSD fail.
GS-QA is a new benchmark of 2,800 QA pairs on 28 templates using OSM and Wikipedia data to evaluate LLMs on spatial predicates, multi-source reasoning, and diverse answer types including distances and counts.
Causal diagnosis identifies the routing module as bottleneck in LLM agents but prompt patching there degrades results due to linguistic co-adaptation, while upstream patching improves them.
In 1-3B instruction-tuned LMs on GSM8K, arithmetic CoT readout is dominated by positional copying of the trailing number before the answer delimiter, accounting for 54-92 percentage points of accuracy.
LinAlg-Bench shows LLMs switch from execution errors to computational abandonment and structured fabrication at 4x4 matrix scale, indicating a working memory limit rather than knowledge gaps.
DCDM replaces positional blocks with learnable semantic chunks via differentiable Chunking Attention, yielding consistent gains over block and unstructured diffusion baselines up to 1.5B parameters.
VPD frames language feedback learning as variational EM so the teacher policy refines itself via trust-region updates on outcomes while the student learns dense token distributions on its own rollouts, outperforming fixed-teacher baselines on reasoning and code tasks.
DRATS derives a minimax objective from a feasibility formulation of MTRL to adaptively sample tasks with the largest return gaps, leading to better worst-task performance on MetaWorld benchmarks.
Hallucination is detected as a transport-cost excursion in hidden-state trajectories, localized via contrastive PCA in a teacher model and distilled to a BiLSTM student.
RDPO applies magnitude-aware quantile normalization and Mahalanobis whitening to decorrelate heterogeneous rewards in multi-objective RL, improving instruction following and writing quality on LongCat-Flash post-training while staying competitive on reasoning and coding.
Test-Time Hinting trains a hint generator to prepend contextual guidance to VLM prompts, improving accuracy on natural-image VQA benchmarks with generalization to unseen tasks and models.
Reward-Weighted On-Policy Distillation with an open property-equivalence verifier produces a 7B model that surpasses prior SOTA on NL-to-SVA generation across pass@1/5/10 metrics.
Distillation signals align better with ideal updates on incorrect student rollouts than correct ones, with optimal teacher context depending on student capacity and task.
Presents a likelihood-based benchmark for equation-suffix prediction in technical papers with controls to detect shortcut vulnerabilities in model forecasts.
LLMs rely on semantic cues for matrix-game equilibria but can acquire approximate computation via residual training on small instances, with a Lipschitz proof enabling transfer to larger anonymous games.
Frontier LLMs achieve 95-100% accuracy on AMC/AIME problems but recover far fewer distinct valid strategies than human references, while collectively generating 50 novel strategies.
AgentPSO evolves reusable multi-agent reasoning skills via PSO-inspired natural-language updates, outperforming static agents and test-time multi-agent baselines on math and general reasoning tasks with cross-benchmark transfer.
Massive activations first appear in a single ME Layer due to RMSNorm and FFN, remain invariant thereafter, and a simple softening method raises LLM performance while reducing attention sinks.
vOPD stabilizes on-policy distillation gradients by subtracting a closed-form per-token negative reverse KL baseline as a detached control variate, preserving unbiasedness while lowering variance and matching expensive full-vocabulary methods.
CIKA uses LLM-based interventions to probe causal effects of concepts on math reasoning success, achieving competitive results on benchmarks like Omni-MATH and GSM8K with a frozen 7B model.
citing papers explorer
-
PRIMETIME : Limits of LLMs in Temporal Primitives
PRIMETIME generator reveals that LLM datetime parsing and arithmetic primitives are individually unreliable but fully learnable via fine-tuning, enabling frontier-level accuracy on event planning with small LoRA models.
-
MIST: A Co-Design Framework for Heterogeneous, Multi-Stage LLM Inference
MIST is a new simulator for heterogeneous multi-stage LLM inference that combines hardware traces with analytical models to explore configuration trade-offs in hybrid CPU-accelerator systems.
-
Monitoring Reasoning Models for Misbehavior and the Risks of Promoting Obfuscation
Chain-of-thought monitoring detects reward hacking in frontier reasoning models, but strong optimization against the monitor produces obfuscated misbehavior that remains hard to detect.
-
OPPO: Bayesian Value Recursion for Token-Level Credit Assignment in LLM Reasoning
OPPO derives token-level advantages for LLM RL via Bayesian recursion on oracle signals, recovering prior distillation methods as a special case and showing gains on math and code benchmarks.
-
Manifold-Guided Attention Steering
MAGS learns low-dimensional subspaces from correct versus incorrect reasoning traces and applies targeted projection corrections to attention heads when they deviate from the correctness manifold during inference.
-
When Are Teacher Tokens Reliable? Position-Weighted On-Policy Self-Distillation for Reasoning
Position-Weighted On-Policy Self-Distillation (PW-OPSD) weights later tokens more heavily after a diagnostic shows position predicts teacher reliability better than entropy, yielding +1.0 and +1.1 Avg@12 gains on AIME 2024/2025.
-
Enhancing the Code Reasoning Capabilities of LLMs via Consistency-based Reinforcement Learning
CodeThinker improves LLM code reasoning via consistency-based RL with stepwise training data, dynamic beam sampling, and consistency rewards, reaching SOTA on benchmarks with 4.3% gains on Qwen2.5-Coder-7B.
-
Self-Supervised On-Policy Distillation for Reasoning Language Models
SSOPD converts intra-group correct-wrong contrast into process supervision by distilling a teacher distribution from the shortest correct completion into prefixes of the longest wrong completion, improving GRPO on AIME and HMMT benchmarks.
-
From Failure to Feedback: Group Revision Unlocks Hard Cases in Object-Level Grounding
A group-revision paradigm for GRPO-based RL fine-tuning of VLMs converts failure responses into improvement signals that refine rewards and advantages, yielding gains on referring segmentation, REC, and counting benchmarks.
-
Deep Pre-Alignment for VLMs
Deep Pre-Alignment uses a small VLM perceiver instead of ViT to pre-align visual features with LLM text space, yielding 1.9-3.0 point gains on multimodal benchmarks and 32.9% less language forgetting.
-
Learning from Failures: Correction-Oriented Policy Optimization with Verifiable Rewards
CIPO jointly optimizes standard RLVR rewards with correction samples derived from the model's own failed attempts, yielding better reasoning and self-correction on math and code benchmarks.
-
Proof-Carrying Certificates for LLM Pipelines: A Trust-Boundary Architecture
Introduces a trust-boundary architecture in Lean 4 with three certificate families and two operators that deliver sorry-free, axiom-audited assurances for LLM pipeline components.
-
STOP: Structured On-Policy Pruning of Long-Form Reasoning in Low-Data Regimes
STOP uses structured on-policy analysis to prune long reasoning traces to their earliest correct node, cutting token usage 19-42% with little accuracy loss on math benchmarks.
-
GRACE: Gradient-aligned Reasoning Data Curation for Efficient Post-training
GRACE scores reasoning steps via gradient alignment and trajectory consistency to select data subsets that match full performance with 5% of the data on Qwen3-VL-2B-Instruct.
-
Holder Policy Optimisation
HölderPO unifies token-level aggregation in GRPO via the Hölder mean with a tunable p parameter and annealing schedule, delivering 54.9% average accuracy on math benchmarks and 93.8% success on ALFWorld.
-
Nice Fold or Hero Call: Learning Budget-Efficient Thinking for Adaptive Reasoning
BET reduces reasoning tokens by about 55% on average while improving performance across benchmarks by learning to short-solve easy queries, fold early on unsolvable ones, and preserve budget for hard solvable queries.
-
Internalizing Safety Understanding in Large Reasoning Models via Verification
Training large reasoning models only on safety verification tasks internalizes safety understanding and boosts robustness to out-of-domain jailbreaks, providing a stronger base for reinforcement learning alignment than standard supervised fine-tuning.
-
PARD-2: Target-Aligned Parallel Draft Model for Dual-Mode Speculative Decoding
PARD-2 uses Confidence-Adaptive Token optimization to align draft model training with acceptance length in speculative decoding, enabling dual-mode operation and up to 6.94x lossless speedup on Llama3.1-8B.
-
Sanity Checks for Long-Form Hallucination Detection
Hallucination detectors on LLM reasoning traces often rely on final-answer artifacts rather than reasoning validity; once controlled, lightweight lexical trajectory features suffice for robust detection.
-
Rubric-Grounded RL: Structured Judge Rewards for Generalizable Reasoning
Rubric-grounded RL with LLM judges on document-derived criteria raises Llama-3.1-8B normalized reward to 71.7% on held-out rubrics and improves performance on GSM8K, MATH, and GPQA benchmarks.
-
Memory-Efficient Looped Transformer: Decoupling Compute from Memory in Looped Language Models
MELT decouples reasoning depth from memory in looped language models by sharing a single gated KV cache per layer and training it via chunk-wise distillation from Ouro starting models.
-
Implicit Compression Regularization: Concise Reasoning via Internal Shorter Distributions in RL Post-Training
ICR creates a virtual shorter distribution from shortest correct on-policy responses to regularize RL post-training toward concise yet accurate reasoning, improving the accuracy-length Pareto frontier on math and knowledge benchmarks.
-
Response Time Enhances Alignment with Heterogeneous Preferences
Response times modeled as drift-diffusion processes enable consistent estimation of population-average preferences from heterogeneous anonymous binary choices.
-
You Snooze, You Lose: Automatic Safety Alignment Restoration through Neural Weight Translation
NeWTral is a non-linear weight translation framework using MoE routing that reduces average attack success rate from 70% to 13% on unsafe domain adapters across Llama, Mistral, Qwen, and Gemma models up to 72B while retaining 90% knowledge fidelity.
-
NeuroState-Bench: A Human-Calibrated Benchmark for Commitment Integrity in LLM Agent Profiles
NeuroState-Bench supplies human-calibrated tasks and probes that measure commitment integrity in LLM agents and shows this measure diverges from ordinary task success.
-
The Reasoning Trap: An Information-Theoretic Bound on Closed-System Multi-Step LLM Reasoning
Closed-system multi-step LLM reasoning is subject to an information-theoretic bound where mutual information with evidence decreases, preserving accuracy while eroding faithfulness, with EGSR recovering it on SciFact and FEVER.
-
AI Alignment via Incentives and Correction
AI alignment is reframed as a fixed-point incentive problem in a solver-auditor pipeline, solved via bilevel optimization and bandit search over reward profiles to maintain monitoring and reduce hallucinations in LLM coding tasks.
-
State Stream Transformer (SST) V2: Parallel Training of Nonlinear Recurrence for Latent Space Reasoning
SST V2 introduces parallel-trainable nonlinear recurrence in latent space to let transformers reason continuously across positions, delivering +15 points on GPQA-Diamond and halving remaining GSM8K errors over matched baselines.
-
IRIS: Interleaved Reinforcement with Incremental Staged Curriculum for Cross-Lingual Mathematical Reasoning
IRIS interleaves staged curriculum supervised fine-tuning with reverse-curriculum reinforcement learning using a composite reward to improve mathematical reasoning in English and low-resource Indian languages, accompanied by a new 29k-problem multilingual dataset.
-
Hidden States Know Where Reasoning Diverges: Credit Assignment via Span-Level Wasserstein Distance
Span-level Wasserstein distances between hidden-state distributions of correct and incorrect rollouts provide a self-supervised signal to reweight advantages in GRPO, improving fine-grained credit assignment on math and code tasks.
-
Large Language Models Decide Early and Explain Later
LLMs settle on their answer after a minority of CoT tokens and produce an average 760 more as post-decision explanation, enabling early stopping that saves 500 tokens per query at a 2% accuracy cost.
-
Process Supervision via Verbal Critique Improves Reasoning in Large Language Models
Verbal Process Supervision uses structured critiques from stronger models in an iterative loop to improve LLM reasoning, reaching 94.9% on GPQA Diamond and large gains on AIME 2025.
-
Navigating the Clutter: Waypoint-Based Bi-Level Planning for Multi-Robot Systems
Waypoint-based bi-level planning with curriculum RLVR improves multi-robot task success rates in dense-obstacle benchmarks over motion-agnostic and VLA baselines.
-
HypEHR: Hyperbolic Modeling of Electronic Health Records for Efficient Question Answering
HypEHR is a hyperbolic embedding model for EHR data that uses Lorentzian geometry and hierarchy-aware pretraining to answer clinical questions nearly as well as large language models but with much smaller size.
-
TPS-CalcBench: A Benchmark and Diagnostic Evaluation Framework for LLM Analytical Calculation Competence in Hypersonic Thermal Protection System Engineering
TPS-CalcBench is a new benchmark and evaluation framework that tests LLMs on analytical calculations in hypersonic aerodynamics and gas dynamics, using dual-track scoring and interventions to detect physically invalid reasoning.
-
ContraPrompt: Contrastive Prompt Optimization via Dyadic Reasoning Trace Analysis
ContraPrompt extracts optimization rules from dyadic differences in reasoning traces on identical inputs and organizes them into input-aware decision trees, outperforming GEPA on four benchmarks with gains up to 8.29 pp.
-
Beyond Static Snapshots: A Grounded Evaluation Framework for Language Models at the Agentic Frontier
ISOPro replaces learned reward models with deterministic verifiers in a continuous evaluation setup for LLMs, delivering larger average capability gains than GRPO-LoRA across small models in scheduling and MBPP domains while characterizing a buffer-skew failure mode.
-
Stability-Weighted Decoding for Diffusion Language Models
Stability-Weighted Decoding improves diffusion LLM accuracy by modulating token scores with temporal stability from KL divergence between prediction steps.
-
AtManRL: Towards Faithful Reasoning via Differentiable Attention Saliency
AtManRL learns an additive attention mask on CoT traces to produce a saliency reward that, when combined with outcome rewards in GRPO, trains LLMs to generate reasoning that genuinely influences final predictions.
-
On the Rejection Criterion for Proxy-based Test-time Alignment
A new conservative confidence rejection criterion for proxy-guided test-time alignment of language models unifies prior implicit reward and nudging approaches while outperforming them on datasets by handling linguistic ambiguity better.
-
Structured Abductive-Deductive-Inductive Reasoning for LLMs via Algebraic Invariants
A symbolic protocol operationalizes Peirce's tripartite reasoning for LLMs using five algebraic invariants including a Weakest Link bound to enforce logical consistency and prevent weak premises from supporting strong conclusions.
-
Balanced Aggregation: Understanding and Fixing Aggregation Bias in GRPO
Balanced Aggregation fixes sign-length coupling and length downweighting in GRPO by computing separate token means for positive and negative subsets and combining them with sequence-count weights, yielding more stable training and higher benchmark scores.
-
HintMR: Eliciting Stronger Mathematical Reasoning in Small Language Models
A cooperative system with one SLM distilling stepwise hints from a large model to guide another SLM's math reasoning yields consistent accuracy gains on benchmarks.
-
SPPO: Sequence-Level PPO for Long-Horizon Reasoning Tasks
SPPO enables stable, sample-efficient alignment of LLMs on long-horizon reasoning tasks by using a decoupled scalar value function for low-variance advantages without multi-sampling.
-
NeuReasoner: Towards Explainable, Controllable, and Unified Reasoning via Mixture-of-Neurons
NeuReasoner detects neuron fluctuation patterns linked to reasoning failures and inserts special tokens to enable controllable self-correction, delivering up to 27% performance gains and 19-63% lower token use across multiple benchmarks and model sizes.
-
FoE: Forest of Errors Makes the First Solution the Best in Large Reasoning Models
Errors in large reasoning models form a forest structure that grows with more steps, making the first solution best; RED refines the first and prunes the rest for higher performance with less compute.
-
Beyond Content Safety: Real-Time Monitoring for Reasoning Vulnerabilities in Large Language Models
An external zero-shot monitor detects nine unsafe reasoning behaviors in LLMs at 87% step-level accuracy with low false positives and low latency.
-
Why Code, Why Now: An Information-Theoretic Perspective on the Limits of Machine Learning
Task information structure determines ML scaling success, with code's dense verifiable signals enabling predictable progress while sparse-feedback tasks like typical RL do not.
-
Diffusion-State Policy Optimization for Masked Diffusion Language Models
DiSPO optimizes intermediate decisions in masked diffusion LMs by branching at selected masked states, resampling tokens, scoring completions, and updating only new tokens using a derived policy-gradient estimator that reuses terminal rollouts.
-
Sparse Reward Subsystem in Large Language Models
LLM hidden states contain a sparse reward subsystem consisting of value neurons that predict state value and dopamine neurons that encode step-level temporal difference errors.