# Beyond Entropy: Correctness-Aware Advantage Shaping via Contrastive Policy Optimization

arXiv: https://arxiv.org/abs/2607.14614 · HTML: https://mlsanity.com/paper/2607.14614/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 47 references that are in the map.
- First posted on arXiv 16 Jul 2026.

## Builds on (most cited first, 30 of 42)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [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)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Kimi K2: Open Agentic Intelligence](https://mlsanity.com/paper/2507.20534/) (2025)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Policy Distillation](https://mlsanity.com/paper/1511.06295/) (2015)
- [Fine-Grained Human Feedback Gives Better Rewards for Language Model Training](https://mlsanity.com/paper/2306.01693/) (2023)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoning](https://mlsanity.com/paper/2505.15134/) (2025)
- [Act Only When It Pays: Efficient Reinforcement Learning for LLM Reasoning via Selective Rollouts](https://mlsanity.com/paper/2506.02177/) (2025)
- [Self-Distillation Bridges Distribution Gap in Language Model Fine-Tuning](https://mlsanity.com/paper/2402.13669/) (2024)
- [Pass@K Policy Optimization: Solving Harder Reinforcement Learning Problems](https://mlsanity.com/paper/2505.15201/) (2025)
- [Rethinking Entropy Interventions in RLVR: An Entropy Change Perspective](https://mlsanity.com/paper/2510.10150/) (2025)

## Built on by (most cited first, 1 of 1)

- [Video-OPSD: Exploiting Privileged Visual Evidence for On-Policy Self-Distillation in Video Large Language Models](https://mlsanity.com/paper/2608.27065/) (2026)

## Abstract (arXiv)

Reinforcement learning with verifiable rewards (RLVR) commonly uses entropy for advantage shaping. However, entropy cannot distinguish useful uncertainty from detrimental confusion, limiting its effectiveness as a correctness signal. We propose Contrastive Policy Optimization (CPO), which uses token-level contrastive disagreement between reference-guided and vanilla generation distributions for correctness-aware advantage shaping. Both theoretical and empirical results show that this disagreement reliably indicates token-level correctness. We further show that On-policy Distillation is a special case of CPO, where the posterior distribution is instantiated by an external teacher model. CPO also resolves the zero-advantage problem. Experiments on in-domain and out-of-domain benchmarks demonstrate that CPO substantially outperforms entropy-based RLVR methods while maintaining strong generalization. Further analysis shows that correct and incorrect responses naturally support exploration and exploitation respectively, and balancing both leads to the best performance.