Learning to Reason with Insight for Informal Theorem Proving

• URL: http://arxiv.org/abs/2604.16278v1
• Date: Fri, 17 Apr 2026 17:36:21 GMT
• Title: Learning to Reason with Insight for Informal Theorem Proving
• Abstract summary: In this work, we identify a primary bottleneck in informal theorem proving as a lack of insight.<n>We propose a novel framework designed to cultivate this essential reasoning skill and enable LLMs to perform insightful reasoning.<n>Our experiments on challenging mathematical benchmarks demonstrate that this insight-aware generation strategy significantly outperforms baselines.
• Score: 50.054221663394195
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a primary bottleneck in informal theorem proving as a lack of insight, namely the difficulty of recognizing the core techniques required to solve complex problems. To address this, we propose a novel framework designed to cultivate this essential reasoning skill and enable LLMs to perform insightful reasoning. We propose $\mathtt{DeepInsightTheorem}$, a hierarchical dataset that structures informal proofs by explicitly extracting core techniques and proof sketches alongside the final proof. To fully exploit this dataset, we design a Progressive Multi-Stage SFT strategy that mimics the human learning process, guiding the model from basic proof writing to insightful thinking. Our experiments on challenging mathematical benchmarks demonstrate that this insight-aware generation strategy significantly outperforms baselines. These results demonstrate that teaching models to identify and apply core techniques can substantially improve their mathematical reasoning.

Related papers

• INSPIRE: An Internalize-Then-Improve Approach for Example-Driven Mathematical Reasoning [61.60016491769943]
  In human mathematics education, example-based reasoning such as constructing counterexamples to test theorem boundaries reflects deep conceptual understanding.<n>We propose INSPIRE, an Internalize-Then-Improve approach combining Reference-Guided Student Internalization (RGSI) with a stage-wise preference training strategy.<n>Experiments across multiple model scales and families demonstrate consistent improvements, even surpassing larger open-source models.
  arXiv  Detail & Related papers  (2026-08-27T03:24:03Z)
• On Multi-Step Theorem Prediction via Non-Parametric Structural Priors [50.16583672681106]
  In this work, we explore training-free theorem prediction through the lens of in-context learning (ICL)<n>We propose Theorem Precedence Graphs, which encode temporal dependencies from historical solution traces as directed graphs, and impose explicit topological constraints that effectively prune the search space during inference.<n>Experiments on the FormalGeo7k benchmark show that our method achieves 89.29% accuracy, substantially outperforming ICL baselines and matching state-of-the-art supervised models.
  arXiv  Detail & Related papers  (2026-03-05T06:08:50Z)
• Step-Aware Policy Optimization for Reasoning in Diffusion Large Language Models [57.42778606399764]
  Diffusion language models (dLLMs) offer a promising, non-autoregressive paradigm for text generation.<n>Current reinforcement learning approaches often rely on sparse, outcome-based rewards.<n>We argue that this stems from a fundamental mismatch with the natural structure of reasoning.
  arXiv  Detail & Related papers  (2025-10-02T00:34:15Z)
• Learning Temporal Abstractions via Variational Homomorphisms in Option-Induced Abstract MDPs [17.335266921332092]
  Large Language Models (LLMs) have shown remarkable reasoning ability through explicit Chain-of-Thought prompting.<n>We develop a framework for efficient, implicit reasoning, where the model "thinks" in a latent space without generating explicit text for every step.
  arXiv  Detail & Related papers  (2025-07-22T11:22:58Z)
• DeepTheorem: Advancing LLM Reasoning for Theorem Proving Through Natural Language and Reinforcement Learning [67.93945726549289]
  DeepTheorem is a comprehensive informal theorem-proving framework exploiting natural language to enhance mathematical reasoning.<n>DeepTheorem includes a large-scale benchmark dataset consisting of 121K high-quality IMO-level informal theorems and proofs.<n>We devise a novel reinforcement learning strategy (RL-Zero) explicitly tailored to informal theorem proving, leveraging the verified theorem variants to incentivize robust mathematical inference.
  arXiv  Detail & Related papers  (2025-05-29T17:59:39Z)
• Lean-STaR: Learning to Interleave Thinking and Proving [53.923617816215774]
  We present Lean-STaR, a framework for training language models to produce informal thoughts prior to each step of a proof.<n>Lean-STaR achieves state-of-the-art results on the miniF2F-test benchmark within the Lean theorem proving environment.
  arXiv  Detail & Related papers  (2024-07-14T01:43:07Z)
• Proof Artifact Co-training for Theorem Proving with Language Models [4.934817254755007]
  PACT (bf Proof bf Artifact bf Co-bf Training) is a general methodology for extracting self-supervised data from kernel-level proof terms for co-training. We instrument Lean with a neural theorem prover driven by a Transformer language model and show that PACT improves theorem proving success rate on a held-out suite of test theorems from 32% to 48%.
  arXiv  Detail & Related papers  (2021-02-11T18:59:24Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.