VA-OPD improves VLM performance over standard on-policy distillation by reweighting rollouts and separating KL terms according to token-level visual advantage on math and visual benchmarks.
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Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning
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abstract
Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a powerful approach to enhancing the reasoning capabilities of Large Language Models (LLMs), while its mechanisms are not yet well understood. In this work, we undertake a pioneering exploration of RLVR through the novel perspective of token entropy patterns, comprehensively analyzing how different tokens influence reasoning performance. By examining token entropy patterns in Chain-of-Thought (CoT) reasoning, we observe that only a small fraction of tokens exhibit high entropy, and these tokens act as critical forks that steer the model toward diverse reasoning pathways. Furthermore, studying how entropy patterns evolve during RLVR training reveals that RLVR largely adheres to the base model's entropy patterns, primarily adjusting the entropy of high-entropy tokens. These findings highlight the significance of high-entropy tokens (i.e., forking tokens) to RLVR. We ultimately improve RLVR by restricting policy gradient updates to forking tokens and uncover a finding even beyond the 80/20 rule: utilizing only 20% of the tokens while maintaining performance comparable to full-gradient updates on the Qwen3-8B base model and significantly surpassing full-gradient updates on the Qwen3-32B (+11.04 on AIME'25 and +7.71 on AIME'24) and Qwen3-14B (+4.79 on AIME'25 and +5.21 on AIME'24) base models, highlighting a strong scaling trend. In contrast, training exclusively on the 80% lowest-entropy tokens leads to a marked decline in performance. These findings indicate that the efficacy of RLVR primarily arises from optimizing the high-entropy tokens that decide reasoning directions. Collectively, our results highlight the potential to understand RLVR through a token-entropy perspective and optimize RLVR by leveraging high-entropy minority tokens to further improve LLM reasoning.
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representative citing papers
DISA decouples partition function estimation using offline importance sampling for distribution-matching LLM-RL, matching or exceeding online baselines like FlowRL on math and code benchmarks while retaining more strategy diversity.
PluRule is a new multimodal multilingual benchmark showing that state-of-the-art vision-language models perform only marginally better than a trivial baseline at detecting specific rule violations in pluralistic online communities.
PCM uses success-failure action variance to probabilistically select and mask chunks for gradient updates in GRPO, matching standard success rates with 2.38x wall-clock speedup and 60% lower memory on LIBERO benchmarks.
The cancellation hypothesis shows how rollout-level rewards produce token-level credit assignment in critic-free RL through cancellation of opposing signals on shared tokens, with empirical support and batching interventions that enhance performance.
Standard top-k routers in MoE language models often select suboptimal routes for difficult tokens, and updating only the final router layer raises pass@K on AIME and HMMT benchmarks across multiple models.
HORA adaptively allocates rollouts using hit utility to improve Pass@K over compute-matched GRPO on math reasoning benchmarks while preserving Pass@1.
The Stepwise Informativeness Assumption explains the correlation between LLM entropy dynamics and reasoning correctness by positing that correct traces accumulate answer-relevant information stepwise during generation.
SDRL trains LLMs via self-generated multi-path debates and joint optimization of standalone plus debate-conditioned responses to boost both single-model reasoning and multi-agent debate performance.
Looped language models with latent iterative computation and entropy-regularized depth allocation achieve performance matching up to 12B standard LLMs through superior knowledge manipulation.
Prefix-RFT blends SFT and RFT via prefix sampling from demonstrations to outperform standalone SFT, RFT, and mixed-policy baselines on math reasoning problems.
TOPD augments on-policy distillation by using near-future trajectory signals to suppress non-divergent high-loss tokens and distribute guidance, raising average accuracy from 47.8% to 52.2% on reasoning benchmarks.
High-Entropy Sum (HES) selects high-quality reasoning data for LLMs by summing entropy of the top highest-entropy tokens, matching full-dataset performance with top 20% in SFT and outperforming baselines in RFT and RL.
DelTA estimates token coefficients to amplify discriminative directions in token-gradient vectors, reweighting the RLVR surrogate to produce more contrastive side-wise centroids and yielding 3.26 and 2.62 point gains on math benchmarks for 8B and 14B Qwen3 models.
DMPO approximates forward KL minimization in on-policy RL by aligning the policy to a group-level reward-proportional target distribution, yielding 9-12% relative gains over GRPO on NP-Bench and smaller gains on math reasoning.
CES applies conditional bidirectional entropy control on top of DAPO to improve accuracy and shorten responses on mathematical benchmarks for 7B and 1.5B LLMs.
Mu-GRPO enables substantially more off-policy GRPO training for LLMs via relaxed clipping and negative-advantage veto in large staged batches, matching standard GRPO performance at ~2x training speed.
Reasoning gaps between base LLMs and LRMs concentrate on ~8% of early planning tokens; intervening with the reasoning model only at high-disagreement positions recovers performance.
Policy entropy remains constant in flow-matching models during RLHF due to fixed noise schedules while perceptual diversity collapses from mode-seeking policy gradients, so perceptual entropy constraints are introduced to preserve diversity and improve quality.
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.
SORT turns all-wrong prompts into selective learning signals by weighting tokens more predictable under plan guidance from reference solutions, improving over GRPO on reasoning benchmarks especially for weaker models.
OPEFO prevents entropy collapse in RLVR by rescaling token updates according to their entropy change contributions, yielding more stable optimization and better results on math benchmarks.
UG-TTT adds epistemic uncertainty measured by adapter disagreement as an exploration bonus in RL for LLMs, raising maximum reward and diversity on scientific discovery benchmarks.
AIPO adds active multi-agent consultation (Verify, Knowledge, Reasoning agents) plus custom importance sampling to RLVR training so LLMs expand their reasoning boundary and then operate without the agents.
citing papers explorer
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Visual-Advantage On-Policy Distillation for Vision-Language Models
VA-OPD improves VLM performance over standard on-policy distillation by reweighting rollouts and separating KL terms according to token-level visual advantage on math and visual benchmarks.
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DISA: Offline Importance Sampling for Distribution-Matching LLM-RL
DISA decouples partition function estimation using offline importance sampling for distribution-matching LLM-RL, matching or exceeding online baselines like FlowRL on math and code benchmarks while retaining more strategy diversity.
-
PluRule: A Benchmark for Moderating Pluralistic Communities on Social Media
PluRule is a new multimodal multilingual benchmark showing that state-of-the-art vision-language models perform only marginally better than a trivial baseline at detecting specific rule violations in pluralistic online communities.
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Learn Where Outcomes Diverge: Efficient VLA RL via Probabilistic Chunk Masking
PCM uses success-failure action variance to probabilistically select and mask chunks for gradient updates in GRPO, matching standard success rates with 2.38x wall-clock speedup and 60% lower memory on LIBERO benchmarks.
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The Cancellation Hypothesis in Critic-Free RL: From Outcome Rewards to Token Credits
The cancellation hypothesis shows how rollout-level rewards produce token-level credit assignment in critic-free RL through cancellation of opposing signals on shared tokens, with empirical support and batching interventions that enhance performance.
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When Are Experts Misrouted? Counterfactual Routing Analysis in Mixture-of-Experts Language Models
Standard top-k routers in MoE language models often select suboptimal routes for difficult tokens, and updating only the final router layer raises pass@K on AIME and HMMT benchmarks across multiple models.
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Where to Spend Rollouts: Hit-Utility Optimal Rollout Allocation for Group-Based RLVR
HORA adaptively allocates rollouts using hit utility to improve Pass@K over compute-matched GRPO on math reasoning benchmarks while preserving Pass@1.
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The Stepwise Informativeness Assumption: Why are Entropy Dynamics and Reasoning Correlated in LLMs?
The Stepwise Informativeness Assumption explains the correlation between LLM entropy dynamics and reasoning correctness by positing that correct traces accumulate answer-relevant information stepwise during generation.
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Learning from Self-Debate: Preparing Reasoning Models for Multi-Agent Debate
SDRL trains LLMs via self-generated multi-path debates and joint optimization of standalone plus debate-conditioned responses to boost both single-model reasoning and multi-agent debate performance.
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Scaling Latent Reasoning via Looped Language Models
Looped language models with latent iterative computation and entropy-regularized depth allocation achieve performance matching up to 12B standard LLMs through superior knowledge manipulation.
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Blending Supervised and Reinforcement Fine-Tuning with Prefix Sampling
Prefix-RFT blends SFT and RFT via prefix sampling from demonstrations to outperform standalone SFT, RFT, and mixed-policy baselines on math reasoning problems.
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Bridging Reasoning Trajectories in On-Policy Distillation via Near-Future Guidance
TOPD augments on-policy distillation by using near-future trajectory signals to suppress non-divergent high-loss tokens and distribute guidance, raising average accuracy from 47.8% to 52.2% on reasoning benchmarks.
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Unified Data Selection for LLM Reasoning
High-Entropy Sum (HES) selects high-quality reasoning data for LLMs by summing entropy of the top highest-entropy tokens, matching full-dataset performance with top 20% in SFT and outperforming baselines in RFT and RL.
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DelTA: Discriminative Token Credit Assignment for Reinforcement Learning from Verifiable Rewards
DelTA estimates token coefficients to amplify discriminative directions in token-gradient vectors, reweighting the RLVR surrogate to produce more contrastive side-wise centroids and yielding 3.26 and 2.62 point gains on math benchmarks for 8B and 14B Qwen3 models.
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Beyond Mode Collapse: Distribution Matching for Diverse Reasoning
DMPO approximates forward KL minimization in on-policy RL by aligning the policy to a group-level reward-proportional target distribution, yielding 9-12% relative gains over GRPO on NP-Bench and smaller gains on math reasoning.
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Taming the Thinker: Conditional Entropy Shaping for Adaptive LLM Reasoning
CES applies conditional bidirectional entropy control on top of DAPO to improve accuracy and shorten responses on mathematical benchmarks for 7B and 1.5B LLMs.
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How Off-Policy Can GRPO Be? Mu-GRPO for Efficient LLM Reinforcement Learning
Mu-GRPO enables substantially more off-policy GRPO training for LLMs via relaxed clipping and negative-advantage veto in large staged batches, matching standard GRPO performance at ~2x training speed.
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Reasoning Can Be Restored by Correcting a Few Decision Tokens
Reasoning gaps between base LLMs and LRMs concentrate on ~8% of early planning tokens; intervening with the reasoning model only at high-disagreement positions recovers performance.
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When Policy Entropy Constraint Fails: Preserving Diversity in Flow-based RLHF via Perceptual Entropy
Policy entropy remains constant in flow-matching models during RLHF due to fixed noise schedules while perceptual diversity collapses from mode-seeking policy gradients, so perceptual entropy constraints are introduced to preserve diversity and improve quality.
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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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Selective Off-Policy Reference Tuning with Plan Guidance
SORT turns all-wrong prompts into selective learning signals by weighting tokens more predictable under plan guidance from reference solutions, improving over GRPO on reasoning benchmarks especially for weaker models.
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Understanding and Preventing Entropy Collapse in RLVR with On-Policy Entropy Flow Optimization
OPEFO prevents entropy collapse in RLVR by rescaling token updates according to their entropy change contributions, yielding more stable optimization and better results on math benchmarks.
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Epistemic Uncertainty for Test-Time Discovery
UG-TTT adds epistemic uncertainty measured by adapter disagreement as an exploration bonus in RL for LLMs, raising maximum reward and diversity on scientific discovery benchmarks.
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AIPO: Learning to Reason from Active Interaction
AIPO adds active multi-agent consultation (Verify, Knowledge, Reasoning agents) plus custom importance sampling to RLVR training so LLMs expand their reasoning boundary and then operate without the agents.
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HTPO: Towards Exploration-Exploitation Balanced Policy Optimization via Hierarchical Token-level Objective Control
HTPO introduces hierarchical token-level objective control in RLVR to balance exploration and exploitation by grouping tokens according to difficulty, correctness, and entropy, yielding up to 8.6% gains on AIME benchmarks over DAPO.
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Rethinking RL for LLM Reasoning: It's Sparse Policy Selection, Not Capability Learning
RL for LLM reasoning acts as sparse policy selection at high-entropy tokens already present in the base model, enabling ReasonMaxxer—an efficient contrastive method that recovers most RL gains at three orders of magnitude lower cost.
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Estimating the Black-box LLM Uncertainty with Distribution-Aligned Adversarial Distillation
DisAAD trains a 1%-sized proxy model via adversarial distillation to quantify uncertainty in black-box LLMs by aligning with their output distributions.
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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.
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GRPO-VPS: Enhancing Group Relative Policy Optimization with Verifiable Process Supervision for Effective Reasoning
GRPO-VPS improves GRPO by using segment-wise conditional probabilities of the correct answer to supply process-level feedback, yielding up to 2.6-point accuracy gains and 13.7% shorter reasoning on math tasks.
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Too Correct to Learn: Reinforcement Learning on Saturated Reasoning Data
A parameter-free sampling strategy called CUTS combined with Mixed-CUTS training prevents mode collapse in RL for saturated LLM reasoning tasks and raises AIME25 Pass@1 accuracy by up to 15.1% over standard GRPO.
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HEALing Entropy Collapse: Enhancing Exploration in Few-Shot RLVR via Hybrid-Domain Entropy Dynamics Alignment
HEAL mitigates entropy collapse in few-shot RLVR by selectively adding general-domain data and aligning trajectory-level entropy dynamics, matching full-shot performance with 32 target samples.
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Characterizing Model-Native Skills
Recovering an orthogonal basis from model activations yields a model-native skill characterization that improves reasoning Pass@1 by up to 41% via targeted data selection and supports inference steering, outperforming human-characterized alternatives.
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HiRO-Nav: Hybrid ReasOning Enables Efficient Embodied Navigation
HiRO-Nav adaptively triggers reasoning only on high-entropy actions via a hybrid training pipeline and shows better success-token trade-offs than always-reason or never-reason baselines on the CHORES-S benchmark.
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The Master Key Hypothesis: Unlocking Cross-Model Capability Transfer via Linear Subspace Alignment
The Master Key Hypothesis states that capabilities are low-dimensional directions transferable across models through linear subspace alignment, with UNLOCK demonstrating gains such as 12.1% accuracy improvement on MATH when transferring CoT from 14B to 7B models.
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LLMs Should Express Uncertainty Explicitly
Training LLMs to verbalize uncertainty explicitly at the end or during reasoning reduces overconfident errors and improves answer quality on factual tasks while enabling RAG triggers.
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From Broad Exploration to Stable Synthesis: Entropy-Guided Optimization for Autoregressive Image Generation
EG-GRPO improves autoregressive text-to-image models by reallocating RL updates according to token entropy, excluding low-entropy tokens from reward signals while adding entropy bonuses to high-entropy ones, yielding state-of-the-art results on standard benchmarks.
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Training-Trajectory-Aware Token Selection
Training-Trajectory-Aware Token Selection (T3S) reconstructs the token-level training objective to overcome a performance bottleneck in continual distillation of reasoning capabilities from large to small language models.
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Boosting Reasoning in Large Multimodal Models via Activation Replay
Activation Replay boosts multimodal reasoning in post-trained LMMs by replaying low-entropy activations from base models to RLVR counterparts at test time via visual token manipulation.
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Unlocking Exploration in RLVR: Uncertainty-aware Advantage Shaping for Deeper Reasoning
UCAS refines RLVR advantage signals with a logit-space self-confidence proxy for response-level modulation and asymmetric token-level penalties based on raw logit certainty to boost exploration and reduce entropy collapse.
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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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GIFT: Guided Importance-Aware Fine-Tuning for Diffusion Language Models
GIFT weights tokens by entropy during fine-tuning of diffusion language models and reports better performance than standard SFT on reasoning benchmarks across multiple settings.
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The Landscape of Agentic Reinforcement Learning for LLMs: A Survey
Survey that defines agentic RL for LLMs via POMDPs, introduces a taxonomy of planning/tool-use/memory/reasoning capabilities and domains, and compiles open environments from over 500 papers.
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Stabilizing Knowledge, Promoting Reasoning: Dual-Token Constraints for RLVR
Archer introduces response-level entropy normalization and differentiated clipping/KL regularization in RLVR to encourage exploration on reasoning tokens while stabilizing knowledge tokens, yielding gains in pass@1 and pass@K on reasoning benchmarks.
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MiniMax-M1: Scaling Test-Time Compute Efficiently with Lightning Attention
MiniMax-M1 is a 456B parameter hybrid-attention MoE model trained with CISPO RL that achieves performance comparable or superior to DeepSeek-R1 and Qwen3-235B on reasoning and software engineering tasks while training in three weeks on 512 GPUs.
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How You Begin is How You Reason: Driving Exploration in RLVR via Prefix-Tuned Priors
IMAX trains soft prefixes with an InfoMax reward to drive diverse exploration in RLVR, yielding up to 11.60% gains in Pass@4 over standard RLVR across model scales.
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Mid-Training with Self-Generated Data Improves Reinforcement Learning in Language Models
Mid-training LLMs on self-generated diverse reasoning paths improves subsequent RL performance on mathematical benchmarks and OOD tasks.
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EGAD: Entropy-Guided Adaptive Distillation for Token-Level Knowledge Transfer
EGAD adaptively distills LLM knowledge at the token level by using entropy to create a curriculum from low- to high-entropy tokens, adjust temperature, and switch between logits-only and feature-based branches.
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MCPO: Mastery-Consolidated Policy Optimization for Large Reasoning Models
MCPO fixes vanishing training signals and shrinking weights in GRPO by using a hinge-KL regularizer on mastered prompts and prioritizing majority-correct prompts, yielding higher pass@1 and pass@k on math tasks.
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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.
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A Model Can Help Itself: Reward-Free Self-Training for LLM Reasoning
SePT alternates self-generation of responses at controlled temperatures with training on the latest model outputs, yielding gains over a strong no-training baseline on six math reasoning benchmarks.