ImProver 2: Iteratively Self-Improving LMs for Neurosymbolic Proof Optimization
Quick Answer
This paper shows that ImProver 2 is a neurosymbolic framework for proof optimization in Lean 4, achieving superior performance with a 7B-parameter model that outperforms larger models and matches mid-tier frontier models.
Quick Take
It effectively restructures complex proofs, demonstrating proof optimization as a scalable, learnable task.
Key Points
- ImProver 2 combines expert-iteration with a formal structure for proof optimization.
- The 7B-parameter model outperforms significantly larger models in the same family.
- New metrics capture structural proof properties, enhancing evaluation.
- Neurosymbolic scaffolding improves performance for both small and large models.
- Small models can restructure research-level proofs effectively.
Paper Resources
Article Content
From source RSS / original summaryarXiv:2605. 22885v1 Announce Type: new 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.
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