# CEPO: RLVR Self-Distillation using Contrastive Evidence Policy Optimization

arXiv: https://arxiv.org/abs/2605.19436 · HTML: https://mlsanity.com/paper/2605.19436/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 24 of its 29 references that are in the map.
- First posted on arXiv 19 May 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Builds on (most cited first, 24 of 24)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Qwen3-VL Technical Report](https://mlsanity.com/paper/2511.21631/) (2025)
- [MMMU: A Massive Multi-discipline Multimodal Understanding and Reasoning Benchmark for Expert AGI](https://mlsanity.com/paper/2311.16502/) (2023)
- [PyTorch FSDP: Experiences on Scaling Fully Sharded Data Parallel](https://mlsanity.com/paper/2304.11277/) (2023)
- [Measuring Multimodal Mathematical Reasoning with MATH-Vision Dataset](https://mlsanity.com/paper/2402.14804/) (2024)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [LMMs-Eval: Reality Check on the Evaluation of Large Multimodal Models](https://mlsanity.com/paper/2407.12772/) (2024)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [We-Math: Does Your Large Multimodal Model Achieve Human-like Mathematical Reasoning?](https://mlsanity.com/paper/2407.01284/) (2024)
- [Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning](https://mlsanity.com/paper/2410.08146/) (2024)
- [LogicVista: Multimodal LLM Logical Reasoning Benchmark in Visual Contexts](https://mlsanity.com/paper/2407.04973/) (2024)
- [DynaMath: A Dynamic Visual Benchmark for Evaluating Mathematical Reasoning Robustness of Vision Language Models](https://mlsanity.com/paper/2411.00836/) (2024)
- [Self-Distilled RLVR](https://mlsanity.com/paper/2604.03128/) (2026)
- [Privileged Information Distillation for Language Models](https://mlsanity.com/paper/2602.04942/) (2026)
- [Segment Policy Optimization: Effective Segment-Level Credit Assignment in RL for Large Language Models](https://mlsanity.com/paper/2505.23564/) (2025)
- [HDPO: Hybrid Distillation Policy Optimization via Privileged Self-Distillation](https://mlsanity.com/paper/2603.23871/) (2026)
- [From Reasoning to Agentic: Credit Assignment in Reinforcement Learning for Large Language Models](https://mlsanity.com/paper/2604.09459/) (2026)

## Built on by (most cited first, 8 of 8)

- [RLCSD: Reinforcement Learning with Contrastive On-Policy Self-Distillation](https://mlsanity.com/paper/2606.11709/) (2026)
- [H2SD: Hybrid Hindsight Self-Distillation](https://mlsanity.com/paper/2607.18955/) (2026)
- [Perception Before Supervision: Self-Contained Visual Distillation from Counterfactual Blind Spots](https://mlsanity.com/paper/2608.09931/) (2026)
- [On Repulsive and Attractive Teachers: Separating Correctness from Behavior in Self-Distillation](https://mlsanity.com/paper/2609.21561/) (2026)
- [VERPO: Verified Evidence Regularized Policy Optimization](https://mlsanity.com/paper/2609.06100/) (2026)
- [Look Where It Counts: A Free, Label-Free Visual Evidence Signal for Fine-Grained Vision-Language Reasoning](https://mlsanity.com/paper/2609.24244/) (2026)
- [SIPO: Unifying Reinforcement Learning with On-Policy Self-Distillation](https://mlsanity.com/paper/2609.36742/) (2026)
- [ReTeach: Building a Self-Teacher through Multi-Round Reflection and Retry](https://mlsanity.com/paper/2610.11529/) (2026)

## Abstract (arXiv)

When a model produces a correct solution under reinforcement learning with verifiable rewards (RLVR), every token receives the same reward signal regardless of whether it was a decisive reasoning step or a grammatical filler. A natural fix is to condition the model on the correct answer as a teacher, identifying tokens it would have generated differently had it known the answer. Prior work shows this either corrupts training by leaking the answer into the gradient, or produces a weak signal that cannot distinguish decisive steps from filler, since both look equally surprising relative to the model's baseline. We propose Contrastive Evidence Policy Optimization (CEPO), which asks a sharper question at every token: not just "does the correct answer favor this token?" but "does the correct answer favor it while the wrong answer disfavors it?" A token satisfying both is a genuine reasoning step; one satisfying neither is filler. The wrong-answer teacher is constructed from rejected rollouts already in the training batch, incurring no additional sampling cost. We prove CEPO inherits all structural safety guarantees of the prior state of the art while strictly sharpening credit at decisive tokens, with the improvement vanishing exactly at filler positions. Empirically, CEPO achieves 43.43% and 60.56% average accuracy across five multimodal mathematical reasoning benchmarks at 2B and 4B scale, respectively, versus 41.17% and 57.43% for GRPO under identical training budgets. Distribution-matching self-distillation methods (OPSD, SDPO) fall below the untrained baseline, empirically confirming the information leakage our theory predicts. Our code is available at https://github.com/ahmedheakl/CEPO.