Large Language Models (LLMs) have recently emerged as powerful tools for autoformalization. Despite their impressive performance, these models can still struggle to produce grounded and verifiable formalizations. Recent work in text-to-SQL, has revealed that LLMs can be sensitive to paraphrased natural language (NL) inputs, even when high degrees of semantic fidelity are preserved (Safarzadeh, Oroo-jlooyjadid, and Roth 2025). In this paper, we investigate this claim in the autoformalization domain. Specifically, we evaluate the robustness of LLMs generating formal proofs with semantically similar paraphrased NL statements by measuring semantic and compilation validity. Using the formal benchmarks MiniF2F (Zheng, Han, and Polu 2021) and Lean 4 version of ProofNet (Xin et al. 2024), and two modern LLMs, we generate paraphrased natural language statements and cross-evaluate these statements across both models. The results of this paper reveal performance variability across paraphrased inputs, demonstrating that minor shifts in NL statements can significantly impact model outputs.

Nowadays, formal theorem provers have made monumental progress on high-school and competition-level mathematics, but few of them generalize to more advanced mathematics. In this paper, we present REAL-Prover, a new open-source stepwise theorem prover for Lean 4 to push this boundary. This prover, based on our fine-tuned large language model (REAL-Prover-v1) and integrated with a retrieval system (Leansearch-PS), notably boosts performance on solving college-level mathematics problems. To train REAL-Prover-v1, we developed HERALD-AF, a data extraction pipeline that converts natural language math problems into formal statements, and a new open-source Lean 4 interactive environment (Jixia-interactive) to facilitate synthesis data collection. In our experiments, our prover using only supervised fine-tune achieves competitive results with a 23.7% success rate (Pass@64) on the ProofNet dataset-comparable to state-of-the-art (SOTA) models. To further evaluate our approach, we introduce FATE-M, a new benchmark focused on algebraic problems, where our prover achieves a SOTA success rate of 56.7% (Pass@64).

We determine the minimax optimal expected regret in the classic non-stochastic multi-armed bandit with expert advice problem, by proving a lower bound that matches the upper bound of Kale (2014). The two bounds determine the minimax optimal expected regret to be $Θ\left( \sqrt{T K \log (N/K) } \right)$, where $K$ is the number of arms, $N$ is the number of experts, and $T$ is the time horizon.

First, we would like to thank the reviewers for their helpful feedback. It is difficult/impossible to generate a worst case environment model in many scenarios. MDP, as opposed to the entirety of the agent's dynamics. Writing such worst-case constraints by hand is often feasible. How efficient is our algorithm?

This paper proposes a natural language translation method for machine-verifiable formal proofs that leverages the informalization (verbalization of formal language proof steps) and summarization capabilities of LLMs. For evaluation, it was applied to formal proof data created in accordance with natural language proofs taken from an undergraduate-level textbook, and the quality of the generated natural language proofs was analyzed in comparison with the original natural language proofs. Furthermore, we will demonstrate that this method can output highly readable and accurate natural language proofs by applying it to existing formal proof library of the Lean proof assistant.

We introduce DeepSeek-Prover-V2, an open-source large language model designed for formal theorem proving in Lean 4, with initialization data collected through a recursive theorem proving pipeline powered by DeepSeek-V3. The cold-start training procedure begins by prompting DeepSeek-V3 to decompose complex problems into a series of subgoals. The proofs of resolved subgoals are synthesized into a chain-of-thought process, combined with DeepSeek-V3's step-by-step reasoning, to create an initial cold start for reinforcement learning. This process enables us to integrate both informal and formal mathematical reasoning into a unified model. The resulting model, DeepSeek-Prover-V2-671B, achieves state-of-the-art performance in neural theorem proving, reaching 88.9% pass ratio on the MiniF2F-test and solving 49 out of 658 problems from PutnamBench. In addition to standard benchmarks, we introduce ProverBench, a collection of 325 formalized problems, to enrich our evaluation, including 15 selected problems from the recent AIME competitions (years 24-25). Further evaluation on these 15 AIME problems shows that the model successfully solves 6 of them. In comparison, DeepSeek-V3 solves 8 of these problems using majority voting, highlighting that the gap between formal and informal mathematical reasoning in large language models is substantially narrowing.

This position paper provides a critical but constructive discussion of current practices in benchmarking and evaluative practices in the field of formal reasoning and automated theorem proving. We take the position that open code, open data, and benchmarks that are complete and error-free will accelerate progress in this field. We identify practices that create barriers to contributing to this field and suggest ways to remove them. We also discuss some of the practices that might produce misleading evaluative information. We aim to create discussions that bring together people from various groups contributing to automated theorem proving, autoformalization, and informal reasoning.

The research in AI-based formal mathematical reasoning has shown an unstop- pable growth trend. These studies have excelled in mathematical competitions like IMO and have made significant progress. This paper focuses on formal verification, an immediate application scenario of formal reasoning, and breaks it down into sub-tasks. We constructed 18k high-quality instruction-response pairs across five formal specification languages (Coq, Lean4, Dafny, ACSL, and TLA+) by distilling gpt-4o and evaluated against ten open-sourced LLMs, including recent popular DeepSeek-R1. We also fine-tuned several 7~8B small models to achieve comparable performance with Deepseek-R1-671B. Interestingly, we observed that fine-tuning with formal data also enhances mathematics, reasoning, and coding capabilities. Fine-tuned models are released at https: //huggingface.co/fm-universe.

Using AI to write formal proofs for mathematical problems is a challenging task that has seen some advancements in recent years. Automated systems such as Lean can verify the correctness of proofs written in formal language, yet writing the proofs in formal language can be challenging for humans and machines. The miniF2F benchmark has 20 IMO problems in its testing set, yet formal proofs are available only for 7 of these problems (3 of which are written only by mathematicians). The model with best accuracy can only prove 4 of these 20 IMO problems, from 1950s and 60s, while its training set is a secret. In this work, we write complete, original formal proofs for the remaining 13 IMO problems in Lean along with 3 extra problems from IMO 2022 and 2023. This effort expands the availability of proof currently in the public domain by creating 5,150 lines of Lean proof. The goal of the paper is to pave the way for developing AI models that can automatically write the formal proofs for all the IMO problems in miniF2F and beyond. In this pursuit, we devise a method to decompose the proof of these problems into their building blocks, constructing a dataset of about 900 lemmas with 25,500 lines of Lean code. These lemmas are not trivial, yet they are approachable, providing the opportunity to evaluate and diagnose the failures and successes of AI models. We then evaluate the ability of GPT-4 in writing formal proofs for these lemmas with zero shot prompting, CoT reasoning and lemma retrieval. In evaluating the responses, we also analyze the confounding factor of LLM's ability to write the proofs in natural language vs Lean language.