SARL rewards reasoning topology to improve label-free RL, outperforming baselines with gains up to 44.7% on math and 34.6% on open-ended tasks while maintaining more stable training.
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The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoning
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abstract
Entropy minimization (EM) trains the model to concentrate even more probability mass on its most confident outputs. We show that this simple objective alone, without any labeled data, can substantially improve large language models' (LLMs) performance on challenging math, physics, and coding tasks. We explore three approaches: (1) EM-FT minimizes token-level entropy similarly to instruction finetuning, but on unlabeled outputs drawn from the model; (2) EM-RL: reinforcement learning with negative entropy as the only reward to maximize; (3) EM-INF: inference-time logit adjustment to reduce entropy without any training data or parameter updates. On Qwen-7B, EM-RL, without any labeled data, achieves comparable or better performance than strong RL baselines such as GRPO and RLOO that are trained on 60K labeled examples. Furthermore, EM-INF enables Qwen-32B to match or exceed the performance of proprietary models like GPT-4o, Claude 3 Opus, and Gemini 1.5 Pro on the challenging SciCode benchmark, while being 3x more efficient than self-consistency and sequential refinement. Our findings reveal that many pretrained LLMs possess previously underappreciated reasoning capabilities that can be effectively elicited through entropy minimization alone, without any labeled data or even any parameter updates.
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representative citing papers
GCPO uses team-level credit assignment via determinant volume over reward-weighted semantic embeddings to promote non-redundant correct reasoning paths, improving both accuracy and diversity in LLM training.
Derives a rigorous entropy minimization formulation for autoregressive test-time adaptation that decomposes into policy gradient and entropy terms, reinterpreting prior methods and improving Whisper ASR across 20+ domains.
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.
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.
Mutual Reinforcement Learning allows heterogeneous LLMs to exchange experience through mechanisms like Peer Rollout Pooling, Cross-Policy GRPO Advantage Sharing, and Success-Gated Transfer, with outcome-level sharing identified as favorable on the stability-support trade-off.
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.
TOFU loss mitigates the narrowing of generative diversity in LLMs after supervised fine-tuning by addressing neglect of low-frequency patterns and forgetting of prior knowledge.
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.
Online Label Refinement lets LLMs learn robust reasoning from noisy supervision by correcting labels when majority answers show rising rollout success and stable history, delivering 3-4% gains on math and reasoning benchmarks even at high noise levels.
Self-distillation turns pretrained autoregressive LMs into multi-token predictors that decode over 3x faster with under 5% accuracy drop on GSM8K.
Parallel inference rollouts aggregated into pseudo-references enable reference-free RL supervision that matches expert-annotated performance on health tasks while using 9x less test-time compute.
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.
D²Evo mines medium-difficulty anchors from the current model, trains a Questioner to generate matching questions, and jointly optimizes Solver and Questioner for progressive gains, outperforming baselines on math reasoning with under 2K real samples.
FREIA applies free energy principles and adaptive advantage shaping to unsupervised RL, outperforming baselines by 0.5-3.5 Pass@1 points on math reasoning with a 1.5B model.
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.
Derives SimPO from MaxEnt RL and reports that MaxEnt RL in online RLHF exhibits frequent overoptimization and unstable KL dynamics across scales, unlike stable KL-constrained baselines.
Self-aligned reward uses relative perplexity differences to encourage concise, query-specific reasoning in LLMs, yielding 4% accuracy gains and 30% lower inference cost when added to PPO or GRPO.
The paper unifies perspectives on Long CoT in reasoning LLMs by introducing a taxonomy, detailing characteristics of deep reasoning and reflection, and discussing emergence phenomena and future directions.
A survey compiling RL methods, challenges, data resources, and applications for enhancing reasoning in large language models and large reasoning models since DeepSeek-R1.
citing papers explorer
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SARL: Label-Free Reinforcement Learning by Rewarding Reasoning Topology
SARL rewards reasoning topology to improve label-free RL, outperforming baselines with gains up to 44.7% on math and 34.6% on open-ended tasks while maintaining more stable training.
-
Breaking $\textit{Winner-Takes-All}$: Cooperative Policy Optimization Improves Diverse LLM Reasoning
GCPO uses team-level credit assignment via determinant volume over reward-weighted semantic embeddings to promote non-redundant correct reasoning paths, improving both accuracy and diversity in LLM training.
-
Rethinking Entropy Minimization in Test-Time Adaptation for Autoregressive Models
Derives a rigorous entropy minimization formulation for autoregressive test-time adaptation that decomposes into policy gradient and entropy terms, reinterpreting prior methods and improving Whisper ASR across 20+ domains.
-
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.
-
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.
-
Experience Sharing in Mutual Reinforcement Learning for Heterogeneous Language Models
Mutual Reinforcement Learning allows heterogeneous LLMs to exchange experience through mechanisms like Peer Rollout Pooling, Cross-Policy GRPO Advantage Sharing, and Success-Gated Transfer, with outcome-level sharing identified as favorable on the stability-support trade-off.
-
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.
-
Diversity in Large Language Models under Supervised Fine-Tuning
TOFU loss mitigates the narrowing of generative diversity in LLMs after supervised fine-tuning by addressing neglect of low-frequency patterns and forgetting of prior knowledge.
-
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.
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Can LLMs Learn to Reason Robustly under Noisy Supervision?
Online Label Refinement lets LLMs learn robust reasoning from noisy supervision by correcting labels when majority answers show rising rollout success and stable history, delivering 3-4% gains on math and reasoning benchmarks even at high noise levels.
-
Multi-Token Prediction via Self-Distillation
Self-distillation turns pretrained autoregressive LMs into multi-token predictors that decode over 3x faster with under 5% accuracy drop on GSM8K.
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Compute as Teacher: Turning Inference Compute Into Reference-Free Supervision
Parallel inference rollouts aggregated into pseudo-references enable reference-free RL supervision that matches expert-annotated performance on health tasks while using 9x less test-time compute.
-
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.
-
D$^2$Evo: Dual Difficulty-Aware Self-Evolution for Data-Efficient Reinforcement Learning
D²Evo mines medium-difficulty anchors from the current model, trains a Questioner to generate matching questions, and jointly optimizes Solver and Questioner for progressive gains, outperforming baselines on math reasoning with under 2K real samples.
-
Free Energy-Driven Reinforcement Learning with Adaptive Advantage Shaping for Unsupervised Reasoning in LLMs
FREIA applies free energy principles and adaptive advantage shaping to unsupervised RL, outperforming baselines by 0.5-3.5 Pass@1 points on math reasoning with a 1.5B model.
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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.
-
Failure Modes of Maximum Entropy RLHF
Derives SimPO from MaxEnt RL and reports that MaxEnt RL in online RLHF exhibits frequent overoptimization and unstable KL dynamics across scales, unlike stable KL-constrained baselines.
-
Self-Aligned Reward: Towards Effective and Efficient Reasoners
Self-aligned reward uses relative perplexity differences to encourage concise, query-specific reasoning in LLMs, yielding 4% accuracy gains and 30% lower inference cost when added to PPO or GRPO.
-
Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models
The paper unifies perspectives on Long CoT in reasoning LLMs by introducing a taxonomy, detailing characteristics of deep reasoning and reflection, and discussing emergence phenomena and future directions.
-
A Survey of Reinforcement Learning for Large Reasoning Models
A survey compiling RL methods, challenges, data resources, and applications for enhancing reasoning in large language models and large reasoning models since DeepSeek-R1.
- Position: The Hidden Costs and Measurement Gaps of Reinforcement Learning with Verifiable Rewards