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ImProver 2: Iteratively Self-Improving LMs for Neurosymbolic Proof Optimization

Summary

ImProver 2 is a neurosymbolic framework for automated proof optimization in Lean 4. It combines a data-efficient expert-iteration pipeline with a scaffold that exposes formal structure alongside informal abstractions. A 7B-parameter model trained with this framework outperforms much larger models and competes with mid-tier frontier models, showing that small models can restructure research-level proofs effectively.

SourcearXiv AIAuthor: Riyaz Ahuja, Tate Rowney, Jeremy Avigad, Sean Welleck
ImProver 2: Iteratively Self-Improving LMs for Neurosymbolic Proof Optimization
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[2605.22885] ImProver 2: Iteratively Self-Improving LMs for Neurosymbolic Proof Optimization

[Submitted on 21 May 2026]

Title:ImProver 2: Iteratively Self-Improving LMs for Neurosymbolic Proof Optimization

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Abstract:Formal mathematics libraries are rapidly expanding, creating a growing need to refactor verified proofs for maintainability and to improve training data quality for neural provers. However, scalable proof optimization is hindered by heterogeneous and heuristically specified objectives, scarce data, and high training and inference costs. To overcome these challenges, we introduce ImProver 2, a neurosymbolic framework for automated proof optimization in Lean 4. ImProver 2 combines a data-efficient expert-iteration pipeline with a scaffold that exposes formal structure alongside lightweight informal abstractions. We further introduce a suite of metrics capturing structural proof properties. Using ImProver 2, we train a 7B-parameter model that outperforms orders-of-magnitude larger models within the same model family, and is competitive with mid-tier frontier models across metrics. We additionally demonstrate that our neurosymbolic scaffold significantly improves performance across both small and frontier models. We show that with proper scaffolding and training, small models can effectively restructure research-level proofs over complex and varied metrics, matching substantially larger systems and establishing proof optimization as a scalable, learnable task.

Subjects:

Artificial Intelligence (cs.AI); Computation and Language (cs.CL); Machine Learning (cs.LG); Logic in Computer Science (cs.LO)

Cite as: arXiv:2605.22885 [cs.AI]

(or arXiv:2605.22885v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2605.22885

arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Riyaz Ahuja [view email] [v1] Thu, 21 May 2026 02:20:26 UTC (8,321 KB)

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Key points and analysis

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Key points

  • ImProver 2 uses expert iteration and a neurosymbolic scaffold to efficiently optimize formal proofs.
  • A 7B-parameter model outperforms larger models in its family and competes with mid-tier frontier models.
  • The scaffold significantly improves performance for both small and frontier models.
  • Proof optimization is established as a scalable, learnable task.

Highlights and analysis are generated automatically and may contain errors. Check the original source.

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