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.
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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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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.
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.
LaTER reduces LLM token usage 16-33% on reasoning benchmarks by exploring in latent space then switching to explicit CoT verification, with gains like 70% to 73.3% on AIME 2025 in the training-free version.
citing papers explorer
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The Coupling Tax: How Shared Token Budgets Undermine Visible Chain-of-Thought Under Fixed Output Limits
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: A Fine-grained Benchmark for Process Reward Models in Medical Reasoning
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.
-
Co-Designing Quantum Codes with Transversal Diagonal Gates via Multi-Agent Systems
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: Evaluating LLM agents on Cyber Threat Investigation
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: Internalizing Privileged Context with Evidence Guided On-Policy Distillation
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.
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GS-QA: A Benchmark for Geospatial Question Answering
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.
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Diagnosis Is Not Prescription: Linguistic Co-Adaptation Explains Patching Hazards in LLM Pipelines
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.
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The Readout Shortcut: Positional Number Copying Dominates Arithmetic CoT Readout in Small Language Models
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.
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LinAlg-Bench: A Forensic Benchmark Revealing Structural Failure Modes in LLM Mathematical Reasoning
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.
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Dynamic Chunking for Diffusion Language Models
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.
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Learning from Language Feedback via Variational Policy Distillation
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.
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Distributionally Robust Multi-Task Reinforcement Learning via Adaptive Task Sampling
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.
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Where Does Reasoning Break? Step-Level Hallucination Detection via Hidden-State Transport Geometry
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.
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Multi-Objective and Mixed-Reward Reinforcement Learning via Reward-Decorrelated Policy Optimization
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 for Black-Box Vision-Language Models
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.
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Reward-Weighted On-Policy Distillation with an Open Property-Equivalence Verifier for NL-to-SVA Generation
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.
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Unmasking On-Policy Distillation: Where It Helps, Where It Hurts, and Why
Distillation signals align better with ideal updates on incorrect student rollouts than correct ones, with optimal teacher context depending on student capacity and task.
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Likelihood scoring for continuations of mathematical text: a self-supervised benchmark with tests for shortcut vulnerabilities
Presents a likelihood-based benchmark for equation-suffix prediction in technical papers with controls to detect shortcut vulnerabilities in model forecasts.
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Equilibrium Residuals Expose Three Regimes of Matrix-Game Strategic Reasoning in Language Models
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.
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Beyond Accuracy: Evaluating Strategy Diversity in LLM Mathematical Reasoning
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.
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A Single Layer to Explain Them All:Understanding Massive Activations in Large Language Models
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.
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KL for a KL: On-Policy Distillation with Control Variate Baseline
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.
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Mathematical Reasoning via Intervention-Based Time-Series Causal Discovery Using LLMs as Concept Mastery Simulators
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.
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LaTER: Efficient Test-Time Reasoning via Latent Exploration and Explicit Verification
LaTER reduces LLM token usage 16-33% on reasoning benchmarks by exploring in latent space then switching to explicit CoT verification, with gains like 70% to 73.3% on AIME 2025 in the training-free version.
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Star Elastic: Many-in-One Reasoning LLMs with Efficient Budget Control
Star Elastic trains N nested submodels in a single post-training job on a parent reasoning LLM, supporting elastic budget control that matches or exceeds independent baselines while cutting training compute by up to 360x.
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Maximizing Rollout Informativeness under a Fixed Budget: A Submodular View of Tree Search for Tool-Use Agentic Reinforcement Learning
InfoTree casts intermediate state selection in tree search as monotone submodular maximization under fixed rollout budgets, yielding closed-form UUCB terms and lifting mixed-outcome ratios while outperforming flat GRPO and prior tree variants on nine benchmarks.
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Decoding-Time Debiasing via Process Reward Models: From Controlled Fill-in to Open-Ended Generation
Decoding-time use of process reward models for bias mitigation raises fairness scores by up to 0.40 on a bilingual benchmark while preserving fluency across four LLMs and extends to open-ended generation with low overhead.
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RMGAP: Benchmarking the Generalization of Reward Models across Diverse Preferences
RMGAP benchmark shows state-of-the-art reward models reach at most 49.27% Best-of-N accuracy when forced to select responses matching diverse preferences.
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Selector-Guided Autonomous Curriculum for One-Shot Reinforcement Learning from Verifiable Rewards
SGAC replaces reward-variance heuristics with a multi-feature learnable selector emphasizing output entropy, yielding 68% accuracy on Hendrycks MATH with Qwen2.5-Math-1.5B versus 64-66% baselines.
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BoostLoRA: Growing Effective Rank by Boosting Adapters
BoostLoRA grows effective adapter rank linearly via iterative boosting on hard examples with orthogonal low-rank updates, outperforming both single-shot ultra-low-rank adapters and full fine-tuning on math and code tasks with zero added inference overhead.
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Training Computer Use Agents to Assess the Usability of Graphical User Interfaces
uxCUA is a trained computer use agent that assesses GUI usability more accurately than larger models by learning to prioritize and execute important user interactions on labeled interface datasets.
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Co-Evolving LLM Decision and Skill Bank Agents for Long-Horizon Tasks
COSPLAY co-evolves an LLM decision agent with a skill bank agent to improve long-horizon game performance, reporting over 25.1% average reward gains versus frontier LLM baselines on single-player benchmarks.
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Fine-Tuning Small Reasoning Models for Quantum Field Theory
Small 7B reasoning models were fine-tuned on synthetic and curated QFT problems using RL and SFT, yielding performance gains, error analysis, and public release of data and traces.
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Navigating the Conceptual Multiverse
The conceptual multiverse system with a verification framework for decision structures helps users in philosophy, AI alignment, and poetry build clearer working maps of open-ended problems by making implicit LLM choices explicit and changeable.
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IG-Search: Step-Level Information Gain Rewards for Search-Augmented Reasoning
IG-Search computes step-level information gain rewards from policy probabilities to improve credit assignment in RL training for search-augmented QA, yielding 1.6-point gains over trajectory-level baselines on multi-hop tasks.
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AI Achieves a Perfect LSAT Score
Language models achieve a perfect LSAT score, with experiments showing that internal thinking phases and a fine-tuned process reward model are key to high performance on logical reasoning questions.
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Backdoors in RLVR: Jailbreak Backdoors in LLMs From Verifiable Reward
RLVR can be backdoored with under 2% poisoned data using an asymmetric reward trigger, implanting jailbreaks that cut safety performance by 73% on average without harming benign tasks.
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Structural Evaluation Metrics for SVG Generation via Leave-One-Out Analysis
Element-level leave-one-out analysis yields per-element quality scores and four structural metrics (purity, coverage, compactness, locality) that quantify SVG modularity and enable artifact detection.
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Demystifying OPD: Length Inflation and Stabilization Strategies for Large Language Models
OPD for LLMs suffers length inflation and repetition collapse; StableOPD uses reference divergence and rollout mixing to prevent it and improve math reasoning performance by 7.2% on average.
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QaRL: Rollout-Aligned Quantization-Aware RL for Fast and Stable Training under Training--Inference Mismatch
QaRL aligns quantized rollouts with training in LLM RL and uses TBPO with dual clipping to stabilize optimization, delivering +5.5 improvement over standard quantized-rollout baselines on Qwen3-30B math problems while retaining speed benefits.
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Generate, Filter, Control, Replay: A Comprehensive Survey of Rollout Strategies for LLM Reinforcement Learning
This survey introduces the Generate-Filter-Control-Replay (GFCR) taxonomy to structure rollout pipelines for RL-based post-training of reasoning LLMs.
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Sampling for Quality: Training-Free Reward-Guided LLM Decoding via Sequential Monte Carlo
Sequential Monte Carlo sampling from a reward-augmented sequence distribution improves LLM performance on HumanEval by up to 54.9% and MATH500 by up to 8.8%, outperforming standard sampling and GRPO.
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WMF-AM: Probing LLM Working Memory via Depth-Parameterized Cumulative State Tracking
WMF-AM is a depth-parameterized benchmark that measures LLMs' cumulative state tracking ability without scratchpads, validated on 28 models across arithmetic and non-arithmetic tasks with ablations confirming the construct.
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Drift and selection in LLM text ecosystems
Recursive LLM text generation drives public corpora toward shallow equilibria via drift unless normative selection for quality sustains deeper structure with a bounded divergence.
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Pramana: Fine-Tuning Large Language Models for Epistemic Reasoning through Navya-Nyaya
Fine-tuning LLMs on Navya-Nyaya's six-phase reasoning structure yields 100% semantic correctness on held-out logical problems despite only 40% strict format adherence.
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ModeX: Evaluator-Free Best-of-N Selection for Open-Ended Generation
ModeX selects the modal semantic output from multiple LLM generations via a similarity graph and recursive spectral clustering without needing reward models or evaluators.
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Schoenfeld's Anatomy of Mathematical Reasoning by Language Models
ThinkARM abstracts LLM reasoning traces into Schoenfeld episodes and shows that exploration steps correlate with correctness while efficiency methods selectively suppress evaluative feedback.
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d-TreeRPO: Towards More Reliable Policy Optimization for Diffusion Language Models
d-TreeRPO uses tree rollouts for fine-grained verifiable rewards and time-scheduled self-distillation to reduce probability estimation gaps in diffusion LLMs, delivering substantial gains on Sudoku, Countdown, GSM8K, and Math500 benchmarks.
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Reinforcement Learning for Reasoning in Large Language Models with One Training Example
One training example via RLVR boosts LLM math reasoning from 17.6% to 35.7% average across six benchmarks.
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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.