# ReForm: Reflective Autoformalization with Prospective Bounded Sequence Optimization

arXiv: https://arxiv.org/abs/2510.24592 · HTML: https://mlsanity.com/paper/2510.24592/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 36 of its 51 references that are in the map.
- First posted on arXiv 28 Oct 2025.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 30 of 36)

- [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)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics](https://mlsanity.com/paper/2109.00110/) (2021)
- [Generative Language Modeling for Automated Theorem Proving](https://mlsanity.com/paper/2009.03393/) (2020)
- [DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition](https://mlsanity.com/paper/2504.21801/) (2025)
- [VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks](https://mlsanity.com/paper/2504.05118/) (2025)
- [Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models](https://mlsanity.com/paper/2410.07985/) (2024)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [Autoformalization with Large Language Models](https://mlsanity.com/paper/2205.12615/) (2022)
- [DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data](https://mlsanity.com/paper/2405.14333/) (2024)
- [DeepSeek-Prover-V1.5: Harnessing Proof Assistant Feedback for Reinforcement Learning and Monte-Carlo Tree Search](https://mlsanity.com/paper/2408.08152/) (2024)
- [ProRL: Prolonged Reinforcement Learning Expands Reasoning Boundaries in Large Language Models](https://mlsanity.com/paper/2505.24864/) (2025)
- [ProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematics](https://mlsanity.com/paper/2302.12433/) (2023)
- [Kimina-Prover Preview: Towards Large Formal Reasoning Models with Reinforcement Learning](https://mlsanity.com/paper/2504.11354/) (2025)
- [PutnamBench: Evaluating Neural Theorem-Provers on the Putnam Mathematical Competition](https://mlsanity.com/paper/2407.11214/) (2024)
- [AlphaMath Almost Zero: Process Supervision without Process](https://mlsanity.com/paper/2405.03553/) (2024)
- [Goedel-Prover-V2: Scaling Formal Theorem Proving with Scaffolded Data Synthesis and Self-Correction](https://mlsanity.com/paper/2508.03613/) (2025)
- [Goedel-Prover: A Frontier Model for Open-Source Automated Theorem Proving](https://mlsanity.com/paper/2502.07640/) (2025)
- [Lean Workbook: A large-scale Lean problem set formalized from natural language math problems](https://mlsanity.com/paper/2406.03847/) (2024)
- [Big-Math: A Large-Scale, High-Quality Math Dataset for Reinforcement Learning in Language Models](https://mlsanity.com/paper/2502.17387/) (2025)
- [Reinforcement Learning Optimization for Large-Scale Learning: An Efficient and User-Friendly Scaling Library](https://mlsanity.com/paper/2506.06122/) (2025)
- [Seed-Prover: Deep and Broad Reasoning for Automated Theorem Proving](https://mlsanity.com/paper/2507.23726/) (2025)
- [Step-level Value Preference Optimization for Mathematical Reasoning](https://mlsanity.com/paper/2406.10858/) (2024)
- [WebResearcher: Unleashing unbounded reasoning capability in Long-Horizon Agents](https://mlsanity.com/paper/2509.13309/) (2025)
- [A Survey on Deep Learning for Theorem Proving](https://mlsanity.com/paper/2404.09939/) (2024)
- [FormalMATH: Benchmarking Formal Mathematical Reasoning of Large Language Models](https://mlsanity.com/paper/2505.02735/) (2025)
- [Multilingual Mathematical Autoformalization](https://mlsanity.com/paper/2311.03755/) (2023)

## Built on by (most cited first, 20 of 20)

- [IterResearch: Rethinking Long-Horizon Agents with Interaction Scaling](https://mlsanity.com/paper/2511.07327/) (2025)
- [Faithful Autoformalization via Roundtrip Verification and Repair](https://mlsanity.com/paper/2604.25031/) (2026)
- [Formalizing Numerical Analysis: An Agent Pipeline and Quality Audit Beyond Kernel Acceptance](https://mlsanity.com/paper/2606.14000/) (2026)
- [MathAtlas: A Benchmark for Autoformalization in the Wild](https://mlsanity.com/paper/2605.14061/) (2026)
- [FormalRx: Rectify and eXamine Semantic Failures in Autoformalization](https://mlsanity.com/paper/2607.04655/) (2026)
- [SHADOWBENCH: Toward Reliable Automatic Evaluation of Semantic Alignment in Autoformalization](https://mlsanity.com/paper/2608.29270/) (2026)
- [Efficient Test-Time Optimization for Multi-Agent Proof Autoformalization](https://mlsanity.com/paper/2607.11307/) (2026)
- [TheoremForge: Scaling up Formal Data Synthesis with Low-Budget Agentic Workflow](https://mlsanity.com/paper/2601.17332/) (2026)
- [FormalEvolve: Neuro-Symbolic Evolutionary Search for Diverse Autoformalization](https://mlsanity.com/paper/2603.19828/) (2026)
- [JURY-RL: Votes Propose, Proofs Dispose for Label-Free RLVR](https://mlsanity.com/paper/2604.25419/) (2026)
- [Automating Formal Verification with Reinforcement Learning and Recursive Inference](https://mlsanity.com/paper/2605.30914/) (2026)
- [From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier](https://mlsanity.com/paper/2607.07779/) (2026)
- [Just Type It in Isabelle! AI Agents Drafting, Mechanizing, and Generalizing from Human Hints](https://mlsanity.com/paper/2604.15713/) (2026)
- [Rethinking Supervision Granularity: Segment-Level Learning for LLM-Based Theorem Proving](https://mlsanity.com/paper/2605.11905/) (2026)
- [Neurosymbolic Auditing of Natural-Language Software Requirements](https://mlsanity.com/paper/2605.13817/) (2026)
- [Mask-Proof: An LLM-based Automated Data Curation Pipeline on Mathematical Proofs](https://mlsanity.com/paper/2606.15258/) (2026)
- [MathForm: Scaling Mathematical Autoformalization with Knowledge Retrieval and Verification-Guided Refinement](https://mlsanity.com/paper/2608.14221/) (2026)
- [ProofLoom: Proof-Obligation-Driven Theory Construction for Autoformalizing Research-Level Stochastic Optimization](https://mlsanity.com/paper/2609.34960/) (2026)
- [Sage: Formalization with Semantic Correction](https://mlsanity.com/paper/2609.35790/) (2026)
- [Aligning Faithfulness for Theory-Scale Autoformalization](https://mlsanity.com/paper/2610.18498/) (2026)

## Abstract (arXiv)

Autoformalization, which translates natural language mathematics into machine-verifiable formal statements, is critical for using formal mathematical reasoning to solve math problems stated in natural language. While Large Language Models can generate syntactically correct formal statements, they often fail to preserve the original problem's semantic intent. This limitation arises from the LLM approaches' treating autoformalization as a simplistic translation task which lacks mechanisms for self-reflection and iterative refinement that human experts naturally employ. To address these issues, we propose ReForm, a Reflective Autoformalization method that tightly integrates semantic consistency evaluation into the autoformalization process. This enables the model to iteratively generate formal statements, assess its semantic fidelity, and self-correct identified errors through progressive refinement. To effectively train this reflective model, we introduce Prospective Bounded Sequence Optimization (PBSO), which employs different rewards at different sequence positions to ensure that the model develops both accurate autoformalization and correct semantic validations, preventing superficial critiques that would undermine the purpose of reflection. Extensive experiments across four autoformalization benchmarks demonstrate that ReForm achieves an average improvement of 22.6 percentage points over the strongest baselines. To further ensure evaluation reliability, we introduce ConsistencyCheck, a benchmark of 859 expert-annotated items that not only validates LLMs as judges but also reveals that autoformalization is inherently difficult: even human experts produce semantic errors in up to 38.5% of cases.