Persistent 'Rock Tokens' in on-policy distillation resist teacher corrections, consume large gradient norms, yet add negligible value to reasoning, allowing targeted bypassing to streamline alignment.
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Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning
30 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
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
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.
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 aggregation in GRPO via the Hölder mean with dynamic p annealing, reporting 54.9% average math-benchmark accuracy and 93.8% ALFWorld success.
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 trains LLMs to expand their reasoning capability boundary via active multi-agent interaction with Verify, Knowledge, and Reasoning agents during RLVR, using importance sampling and clipping to handle feedback, then drops the agents at inference.
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.
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.
DisAAD trains a 1%-sized proxy model via adversarial distillation to quantify uncertainty in black-box LLMs by aligning with their output distributions.
Embedding-based defenses fail against attacks that align malicious message embeddings with benign ones in LLM multi-agent systems, but token-level confidence scores improve robustness by enabling better pruning of suspicious messages.
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.
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.
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.
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.
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.
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.
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.
Training LLMs to express uncertainty explicitly via global confidence or local markers enhances calibration and intervention triggers compared to post-hoc estimation.
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.
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.
Mid-training LLMs on self-generated diverse reasoning paths improves subsequent RL performance on mathematical benchmarks and OOD tasks.
citing papers explorer
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Cornerstones or Stumbling Blocks? Deciphering the Rock Tokens in On-Policy Distillation
Persistent 'Rock Tokens' in on-policy distillation resist teacher corrections, consume large gradient norms, yet add negligible value to reasoning, allowing targeted bypassing to streamline alignment.
-
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.
-
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.
-
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.
-
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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H\"older Policy Optimisation
HölderPO unifies token aggregation in GRPO via the Hölder mean with dynamic p annealing, reporting 54.9% average math-benchmark accuracy and 93.8% ALFWorld success.
-
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.
-
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.
-
AIPO: : Learning to Reason from Active Interaction
AIPO trains LLMs to expand their reasoning capability boundary via active multi-agent interaction with Verify, Knowledge, and Reasoning agents during RLVR, using importance sampling and clipping to handle feedback, then drops the agents at inference.
-
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.
-
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.
-
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.
-
When Embedding-Based Defenses Fail: Rethinking Safety in LLM-Based Multi-Agent Systems
Embedding-based defenses fail against attacks that align malicious message embeddings with benign ones in LLM multi-agent systems, but token-level confidence scores improve robustness by enabling better pruning of suspicious messages.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
LLMs Should Express Uncertainty Explicitly
Training LLMs to express uncertainty explicitly via global confidence or local markers enhances calibration and intervention triggers compared to post-hoc estimation.
-
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.
-
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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OGER: A Robust Offline-Guided Exploration Reward for Hybrid Reinforcement Learning
OGER adds an auxiliary exploration reward built from offline trajectories and model entropy to hybrid RL training, yielding gains on math reasoning benchmarks and out-of-domain generalization.
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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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Rethinking Token-Level Credit Assignment in RLVR: A Polarity-Entropy Analysis
Token credit in RLVR is upper-bounded by entropy, with reasoning gains concentrated in high-entropy tokens, motivating Entropy-Aware Policy Optimization that outperforms baselines.
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GLM-4.5: Agentic, Reasoning, and Coding (ARC) Foundation Models
GLM-4.5, a 355B-parameter MoE model with hybrid reasoning, scores 70.1% on TAU-Bench, 91.0% on AIME 24, and 64.2% on SWE-bench Verified while ranking 3rd overall and 2nd on agentic benchmarks.
- Selective Off-Policy Reference Tuning with Plan Guidance