# No Free Lunch: Rethinking Internal Feedback for LLM Reasoning

arXiv: https://arxiv.org/abs/2506.17219 · HTML: https://mlsanity.com/paper/2506.17219/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 31 of its 42 references that are in the map.
- First posted on arXiv 20 Jun 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

## Builds on (most cited first, 30 of 31)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [ChatGLM: A Family of Large Language Models from GLM-130B to GLM-4 All Tools](https://mlsanity.com/paper/2406.12793/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity](https://mlsanity.com/paper/2506.06941/) (2025)
- [Towards Large Reasoning Models: A Survey of Reinforced Reasoning with Large Language Models](https://mlsanity.com/paper/2501.09686/) (2025)
- [VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks](https://mlsanity.com/paper/2504.05118/) (2025)
- [TTRL: Test-Time Reinforcement Learning](https://mlsanity.com/paper/2504.16084/) (2025)
- [Model Merging in LLMs, MLLMs, and Beyond: Methods, Theories, Applications and Opportunities](https://mlsanity.com/paper/2408.07666/) (2024)
- [REINFORCE++: Stabilizing Critic-Free Policy Optimization with Global Advantage Normalization](https://mlsanity.com/paper/2501.03262/) (2025)
- [Learning to Reason without External Rewards](https://mlsanity.com/paper/2505.19590/) (2025)
- [Right Question is Already Half the Answer: Fully Unsupervised LLM Reasoning Incentivization](https://mlsanity.com/paper/2504.05812/) (2025)
- [Proof or Bluff? Evaluating LLMs on 2025 USA Math Olympiad](https://mlsanity.com/paper/2503.21934/) (2025)
- [Confidence Is All You Need: Few-Shot RL Fine-Tuning of Language Models](https://mlsanity.com/paper/2506.06395/) (2025)
- [One-shot Entropy Minimization](https://mlsanity.com/paper/2505.20282/) (2025)
- [AM-Thinking-v1: Advancing the Frontier of Reasoning at 32B Scale](https://mlsanity.com/paper/2505.08311/) (2025)
- [Self-Reflection Makes Large Language Models Safer, Less Biased, and Ideologically Neutral](https://mlsanity.com/paper/2406.10400/) (2024)

## Built on by (most cited first, 30 of 37)

- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [Reasoning or Memorization? Unreliable Results of Reinforcement Learning Due to Data Contamination](https://mlsanity.com/paper/2507.10532/) (2025)
- [Embarrassingly Simple Self-Distillation Improves Code Generation](https://mlsanity.com/paper/2604.01193/) (2026)
- [Reinforcement Learning Meets Large Language Models: A Survey of Advancements and Applications Across the LLM Lifecycle](https://mlsanity.com/paper/2509.16679/) (2025)
- [Co-rewarding: Stable Self-supervised RL for Eliciting Reasoning in Large Language Models](https://mlsanity.com/paper/2508.00410/) (2025)
- [RESTRAIN: From Spurious Votes to Signals -- Self-Driven RL with Self-Penalization](https://mlsanity.com/paper/2510.02172/) (2025)
- [Towards Agents That Know When They Don't Know: Uncertainty as a Control Signal for Structured Reasoning](https://mlsanity.com/paper/2509.02401/) (2025)
- [VI-CuRL: Stabilizing Verifier-Independent RL Reasoning via Confidence-Guided Variance Reduction](https://mlsanity.com/paper/2602.12579/) (2026)
- [Self-Aligned Reward: Towards Effective and Efficient Reasoners](https://mlsanity.com/paper/2509.05489/) (2025)
- [Semantic Voting: A Self-Evaluation-Free Approach for Efficient LLM Self-Improvement on Unverifiable Open-ended Tasks](https://mlsanity.com/paper/2509.23067/) (2025)
- [Model Whisper: Steering Vectors Unlock Large Language Models' Potential in Test-time](https://mlsanity.com/paper/2512.04748/) (2025)
- [TraPO: A Semi-Supervised Reinforcement Learning Framework for Boosting LLM Reasoning](https://mlsanity.com/paper/2512.13106/) (2025)
- [PEAR: Phase Entropy Aware Reward for Efficient Reasoning](https://mlsanity.com/paper/2510.08026/) (2025)
- [When Models Judge Themselves: Unsupervised Self-Evolution for Multimodal Reasoning](https://mlsanity.com/paper/2603.21289/) (2026)
- [Scaling Large Reasoning Models beyond Human Supervision: A Path toward Superintelligence](https://mlsanity.com/paper/2608.31075/) (2026)
- [On the Generalization Gap in Self-Evolving Language Model Reasoning](https://mlsanity.com/paper/2606.01075/) (2026)
- [Reinforcement Learning with Metacognitive Feedback Elicits Faithful Uncertainty Expression in LLMs](https://mlsanity.com/paper/2606.32032/) (2026)
- [Breaking the Self-Confirming Loop: Diagnosing and Mitigating Systemic Reward Bias in Self-Rewarding RL](https://mlsanity.com/paper/2510.08977/) (2025)
- [ThinkPilot: Steering Reasoning Models via Automated Think-prefixes Optimization](https://mlsanity.com/paper/2510.12063/) (2025)
- [TrajSelector: Harnessing Latent Representations for Efficient and Effective Best-of-N in Large Reasoning Model](https://mlsanity.com/paper/2510.16449/) (2025)
- [When Does Multi-Agent Collaboration Help? An Entropy Perspective](https://mlsanity.com/paper/2602.04234/) (2026)
- [Round-trip Reinforcement Learning: Self-Consistent Training for Better Chemical LLMs](https://mlsanity.com/paper/2510.01527/) (2025)
- [PowerFlow: Unlocking the Dual Nature of LLMs via Principled Distribution Matching](https://mlsanity.com/paper/2603.18363/) (2026)
- [EmbedGrad: Gradient-Based Prompt Optimization in Embedding Space for Large Language Models](https://mlsanity.com/paper/2508.03533/) (2025)
- [Experience Sharing in Mutual Reinforcement Learning for Heterogeneous Language Models](https://mlsanity.com/paper/2605.07244/) (2026)
- [Smart Picks in the Dark: Towards Efficient RLVR for Reasoning via Tracing Metacognitive Pivots](https://mlsanity.com/paper/2606.04503/) (2026)
- [Continual Self-Improvement with Lightweight Experiential Latent Memories](https://mlsanity.com/paper/2606.17803/) (2026)
- [PaperGuide: Making Small Language-Model Paper-Reading Agents More Efficient](https://mlsanity.com/paper/2601.12988/) (2026)
- [Easy Samples Are All You Need: Self-Evolving LLMs via Data-Efficient Reinforcement Learning](https://mlsanity.com/paper/2604.18639/) (2026)
- [TEMPO: Scaling Test-time Training for Large Reasoning Models](https://mlsanity.com/paper/2604.19295/) (2026)

## Abstract (arXiv)

Reinforcement learning has emerged as a powerful paradigm for post-training large language models (LLMs) to improve reasoning. Approaches like Reinforcement Learning from Human Feedback (RLHF) and Reinforcement Learning with Verifiable Rewards (RLVR) have shown strong results, but they require extensive external supervision. We investigate an alternative class of methods, Reinforcement Learning from Internal Feedback (RLIF), which relies solely on intrinsic model-derived signals instead of external rewards. In particular, we leverage unsupervised reward proxies such as token-level entropy, trajectory-level entropy, and self-certainty. Our theoretical analysis shows these internal objectives are partially equivalent, and we empirically evaluate various RLIF strategies on challenging math reasoning benchmarks. Experimental results demonstrate that RLIF can boost the reasoning performance of base LLMs at the beginning phase of the training, matching or surpassing RLVR techniques on these tasks. However, when training progresses, performance degrades even below the model before training. Moreover, we find that RLIF yields little improvement for instruction-tuned models, indicating diminishing returns of intrinsic feedback once an LLM is already instruction-tuned. We further analyze this limitation by mixing model weights and explain the reason of RLIF's training behaviors, providing practical guidelines for integrating internal feedback signals into LLM training. We hope our analysis of internal feedback will inform more principled and effective strategies for LLM post-training.