# Label-Free Reinforcement Learning via Cross-Model Entropy

arXiv: https://arxiv.org/abs/2605.29009 · HTML: https://mlsanity.com/paper/2605.29009/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 16 of its 30 references that are in the map.
- First posted on arXiv 27 May 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 16 of 16)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Length-Controlled AlpacaEval: A Simple Way to Debias Automatic Evaluators](https://mlsanity.com/paper/2404.04475/) (2024)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [UltraFeedback: Boosting Language Models with Scaled AI Feedback](https://mlsanity.com/paper/2310.01377/) (2023)
- [The Effects of Reward Misspecification: Mapping and Mitigating Misaligned Models](https://mlsanity.com/paper/2201.03544/) (2022)
- [Spurious Rewards: Rethinking Training Signals in RLVR](https://mlsanity.com/paper/2506.10947/) (2025)
- [The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoning](https://mlsanity.com/paper/2505.15134/) (2025)
- [Evolving Language Models without Labels: Majority Drives Selection, Novelty Promotes Variation](https://mlsanity.com/paper/2509.15194/) (2025)
- [Surrogate Signals from Format and Length: Reinforcement Learning for Solving Mathematical Problems without Ground Truth Answers](https://mlsanity.com/paper/2505.19439/) (2025)
- [Cross-Model Disagreement as a Label-Free Correctness Signal](https://mlsanity.com/paper/2603.25450/) (2026)

## Abstract (arXiv)

Post-training large language models with reinforcement learning is bottlenecked by the reward signal. Existing approaches require either ground-truth verifiable rewards, restricting training to domains with automatic correctness checks (e.g., mathematics, code execution), or human preference labels, which are expensive to collect and prone to reward hacking. Recent label-free methods replace ground-truth verifiers with self-referential signals like majority voting or token entropy over a model's own outputs, but risk reinforcing a model's own errors. In this work we propose Cross-Model Entropy (CME), the mean log-likelihood of a generator's response under a separate verifier model, as a label-free reward signal for RL post-training. CME is continuous, training-free, and grounded in the principle that responses a verifier finds unsurprising are likely correct or high quality. Because the verifier is independent of the generator, the signal cannot be gamed through self-consistency. We integrate CME into GRPO with no other changes to the training loop, extending label-free RL to open-ended instruction following -- a regime where self-referential signals are inapplicable or poorly suited. On open-ended instruction following (UltraFeedback prompts, evaluated on AlpacaEval 2.0), CME rewards beat the untrained base in head-to-head LLM-as-Judge comparisons across four model families (Qwen, Llama, Gemma, OLMo) and three training regimes (pretrained, SFT, and instruction-tuned), with tie-adjusted win rates ranging from 52.5% to 71.4%. Code will be released upon publication.