---
title: "Rewarding the Unlikely — paper by He et al. (2025)"
description: "As a fix, they propose an unlikeliness reward that gives extra weight to correct but low-probability… 35 references, cited by 13 papers here."
authors: ["Andre Wang He", "Daniel Fried", "Sean Welleck"]
year: 2025
venue: "Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing"
source: "https://aclanthology.org/2025.emnlp-main.1298/"
doi: "10.18653/v1/2025.emnlp-main.1298"
licence: "CC BY 4.0 (ACL Anthology)"
licence_url: "https://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/he-2025-rewarding-unlikely-lifting-grpo-beyond/"
---
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# Rewarding the Unlikely: Lifting GRPO Beyond Distribution Sharpening

**Authors:** Andre Wang He, [Daniel Fried](https://md.research.elamur.ai/free/en/authors/daniel-fried/) and [Sean Welleck](https://md.research.elamur.ai/free/en/authors/sean-welleck/) · **Year:** 2025 · **Venue:** [Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing](https://md.research.elamur.ai/free/en/venues/emnlp/) ([EMNLP 2025](https://md.research.elamur.ai/free/en/venues/emnlp/2025/)) · **Publisher:** [Association for Computational Linguistics](https://md.research.elamur.ai/free/en/publishers/association-for-computational-linguistics/) · **Licence:** [CC BY 4.0 (ACL Anthology)](https://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://aclanthology.org/2025.emnlp-main.1298/) · [PDF](https://aclanthology.org/2025.emnlp-main.1298.pdf) · [DOI 10.18653/v1/2025.emnlp-main.1298](https://doi.org/10.18653/v1/2025.emnlp-main.1298) · [OpenAlex](https://openalex.org/W4416035674)

**Citations:** 2 citations (OpenAlex, 2026-10-14) · [13](https://md.research.elamur.ai/free/en/papers/he-2025-rewarding-unlikely-lifting-grpo-beyond/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
The authors ask whether GRPO, the standard reinforcement learning algorithm for improving LLM reasoning, teaches models to solve new problems or only concentrates probability on solutions the base model already finds. They study this in Lean 4 theorem proving, where a verifier gives exact binary rewards. Starting from DeepSeek-Prover-V1.5-SFT and a training set built from Lean Workbook and miniF2F-valid, they find that standard GRPO raises pass@N for small N. For large N, however, it falls behind simply sampling more from the base model.

They trace this to a "rank bias": GRPO updates mostly strengthen proofs that are already probable and largely ignore rare correct ones. As a fix, they propose an unlikeliness reward that gives extra weight to correct but low-probability samples. They also show that using more PPO epochs per batch helps for a related reason. Combining both changes yields a fully open training pipeline that roughly matches DeepSeek-Prover-V1.5-RL on miniF2F-test. This matters because verifier-backed domains depend on drawing many samples at test time.

## Key points
- **Data:** About 10K solvable theorems were taken from the ~140K-statement Lean Workbook and combined with the 244 miniF2F-valid problems. From this pool, 200 theorems were held out as an i.i.d. validation set (D_val), leaving 9.6K for training. miniF2F-test was used only for the final evaluation because results on it were noisy.
- **Setup:** GRPO was implemented on the verl framework with the Lean REPL providing rewards. Settings were 32 samples per problem, KL coefficient 0.02, learning rate lowered to 1e-6, responses capped at 512 tokens, and one pass over the training data.
- **Diagnosis:** Default GRPO improves pass@1 through pass@16 but underperforms the base model at large N (evaluated up to pass@512). This is consistent with Yue et al. (2025).
- **Fixes:** The unlikeliness reward up-weights rare correct proofs and increases sample diversity. Raising the number of PPO epochs per batch adds gradient steps on low-likelihood sequences once the likely ones saturate.
- **Results (pass@32 / pass@128):**
  - miniF2F-test: the new model scores 48.8% / 50.6%, versus 49.2% / 51.2% for DeepSeek-Prover-V1.5-RL and 47.1% / 49.2% for SFT.
  - D_val: the new model scores 84.3% / 88.8%, versus 84.8% / 87.5% for V1.5-RL.
  - Code is released at github.com/AndreHe02/rewarding-unlikely-release.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

## Institutions

- [Carnegie Mellon University](https://md.research.elamur.ai/free/en/universities/carnegie-mellon-university/) — University, Pittsburgh, United States · 539 works · 179,533 citations

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## Cite

Cite as: Andre Wang He, Daniel Fried and Sean Welleck. 2025. Rewarding the Unlikely: Lifting GRPO Beyond Distribution Sharpening. Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@inproceedings{he2025rewarding,
  title = {{Rewarding the Unlikely: Lifting GRPO Beyond Distribution Sharpening}},
  author = {Andre Wang He, Daniel Fried and Sean Welleck},
  booktitle = {Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing},
  year = {2025},
  doi = {10.18653/v1/2025.emnlp-main.1298},
  url = {https://doi.org/10.18653/v1/2025.emnlp-main.1298}
}
```

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*Updated 30 October 2026*