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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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
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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.
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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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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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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.
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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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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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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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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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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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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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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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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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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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TRINITY: An Evolved LLM Coordinator
A compact 0.6B-parameter coordinator with a 10K-parameter head uses evolutionary strategy to dynamically delegate roles to LLMs, achieving SOTA results such as 86.2% on LiveCodeBench.
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SCOPE-RL: Stable and Quantitative Control of Policy Entropy in RL Post-Training
SCOPE-RL adds a regularization term built from high-temperature positive samples to quantitatively control entropy dynamics and maintain exploration in RL post-training of reasoning LLMs.
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Entropy After </Think> for reasoning model early exiting
Entropy After </Think> (EAT) enables early exiting in reasoning LLMs by tracking entropy stabilization after a </think> token, cutting token use 12-22% on MATH500 and AIME2025 with no accuracy loss.
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HyperAdapt: Simple High-Rank Adaptation
HyperAdapt performs parameter-efficient fine-tuning by row- and column-wise diagonal scaling to induce high-rank updates with only n+m trainable parameters.
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SPaCe: Unlocking Sample-Efficient Large Language Models Training With Self-Pace Curriculum Learning
SPaCe uses semantic clustering to shrink training sets and a multi-armed bandit to adaptively select samples, matching or beating baselines on reasoning benchmarks with up to 100x fewer examples.
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Muon is Scalable for LLM Training
Muon optimizer with weight decay and update scaling achieves ~2x efficiency over AdamW for large LLMs, shown via the Moonlight 3B/16B MoE model trained on 5.7T tokens.
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Process Reinforcement through Implicit Rewards
PRIME enables online process reward model updates in LLM RL using implicit rewards from rollouts and outcome labels, yielding 15.1% average gains on reasoning benchmarks and surpassing a stronger instruct model with 10% of the data.
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Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning
Process advantage verifiers trained to predict step-level progress under a distinct prover policy improve LLM reasoning accuracy by over 8% and sample efficiency by 5-6x over outcome reward models.
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Training Language Models to Self-Correct via Reinforcement Learning
SCoRe uses multi-turn online RL with regularization on self-generated traces to improve LLM self-correction, achieving 15.6% and 9.1% gains on MATH and HumanEval for Gemini models.
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Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMs
Step-DPO performs preference optimization on individual reasoning steps rather than complete answers, producing nearly 3% accuracy gains on MATH for 70B+ parameter models with 10K preference pairs.
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FBOS-RL: Feedback-Driven Bi-Objective Synergistic Reinforcement Learning
FBOS-RL is a feedback-driven bi-objective RL framework that combines Feedback-Guided Exploration Enhancement with Exploitation-oriented Policy Alignment and Exploration-oriented Capability Cultivation to raise training speed and final performance over GRPO under fixed rollout budgets.
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R2V Agent: Teaching SLMs When to Ask for Help
R2V-Agent combines an SLM policy trained via BC and DPO with a step-level risk-calibrated router using Brier scores and CVaR to escalate to LLM only on high residual failure risk, improving success-cost tradeoffs on HumanEval+, TextWorld, and TerminalBench.
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Matrix-Decoupled Concentration for Autoregressive Sequences: Dimension-Free Guarantees for Sparse Long-Context Rewards
Develops a McDiarmid-type concentration inequality for causal autoregressive processes that preserves sparsity to achieve O(1) variance proxies instead of O(N).
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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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Goldilocks RL: Tuning Task Difficulty to Escape Sparse Rewards for Reasoning
A teacher-driven sampling method selects appropriately difficult questions for student models in GRPO-based RL to improve reasoning performance under fixed compute on OpenMathReasoning.
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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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Depth-Breadth Synergy in RLVR: Unlocking LLM Reasoning Gains with Adaptive Exploration
DARS adaptively increases rollouts on hard problems in RLVR to improve Pass@K, and when paired with batch scaling for breadth, achieves gains in both Pass@K and Pass@1 by treating depth and breadth as complementary exploration dimensions.
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Kalman Filter Enhanced GRPO for Reinforcement Learning-Based Language Model Reasoning
KRPO uses a Kalman filter to estimate latent prompt-level reward baselines from per-group rewards in GRPO, yielding better reward curves and accuracy on math reasoning benchmarks.
- DualKV: Shared-Prompt Flash Attention for Efficient RL Training with Large Rollouts and Long Contexts