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Verifiable formal languages like Lean have profoundly impacted mathematical reasoning, particularly through the use of large language models (LLMs) for automated reasoning. A significant challenge in training LLMs for these formal languages…
Large Language Models (LLMs) demonstrate impressive mathematical reasoning abilities, but their solutions frequently contain errors that cannot be automatically checked. Formal theorem proving systems such as Lean 4 offer automated…
We present an end-to-end approach that takes unstructured textual input and generates structured output compliant with a given vocabulary. Inspired by recent successes in neural machine translation, we treat the triples within a given…
The goal of this project is to (i) accumulate annotated informal/formal mathematical corpora suitable for training semi-automated translation between informal and formal mathematics by statistical machine-translation methods, (ii) to…
We introduce our Leanabell-Prover-V2, a 7B large language models (LLMs) that can produce formal theorem proofs in Lean 4, with verifier-integrated Long Chain-of-Thoughts (CoT). Following our previous work Leanabell-Prover-V1, we continual…
Linear Temporal Logic (LTL) is a widely used task specification language for autonomous systems. To mitigate the significant manual effort and expertise required to define LTL-encoded tasks, several methods have been proposed for…
Recent advancements in large language models (LLMs) have sparked considerable interest in automated theorem proving and a prominent line of research integrates stepwise LLM-based provers into tree search. In this paper, we introduce a novel…
In mathematics, it is common practice to have several constructions for the same objects. Mathematicians will identify them modulo isomorphism and will not worry later on which construction they use, as theorems proved for one construction…
The Lax Logical Framework, LLFP, was introduced, by a team including the last two authors, to provide a conceptual framework for integrating different proof development tools, thus allowing for external evidence and for postponing,…
Neural theorem proving has advanced rapidly in the past year, reaching IMO gold-medalist capabilities and producing formal proofs that span thousands of lines. Although such proofs are mechanically verified by formal systems like Lean,…
The challenge of formal proof generation has a rich history, but with modern techniques, we may finally be at the stage of making actual progress in real-life mathematical problems. This paper explores the integration of ChatGPT and basic…
The demand for synthetic data in mathematical reasoning has increased due to its potential to enhance the mathematical capabilities of large language models (LLMs). However, ensuring the validity of intermediate reasoning steps remains a…
We propose RoCoFT, a parameter-efficient fine-tuning method for large-scale language models (LMs) based on updating only a few rows and columns of the weight matrices in transformers. Through extensive experiments with medium-size LMs like…
Formal reasoning and automated theorem proving constitute a challenging subfield of machine learning, in which machines are tasked with proving mathematical theorems using formal languages like Lean. A formal verification system can check…
Formalizing mathematical proofs using computerized verification languages like Lean 4 has the potential to significantly impact the field of mathematics, it offers prominent capabilities for advancing mathematical reasoning. However,…
Autoformalization aims to convert informal mathematical proofs into machine-verifiable formats, bridging the gap between natural and formal languages. However, ensuring semantic alignment between the informal and formalized statements…
Literary translation has recently gained attention as a distinct and complex task in machine translation research. However, the translation by small open models remains an open problem. We contribute to this ongoing research by introducing…
This paper investigates the logical reasoning capabilities of large language models (LLMs). For a precisely defined yet tractable formulation, we choose the conceptually simple but technically complex task of constructing proofs in Boolean…
There is growing excitement about the potential of Language Models (LMs) to accelerate scientific discovery. Falsifying hypotheses is key to scientific progress, as it allows claims to be iteratively refined over time. This process requires…
Practical guidance on training Large Language Models (LLMs) to leverage Code Interpreter across diverse tasks remains lacking. We present R1-Code-Interpreter, an extension of a text-only LLM trained via multi-turn supervised fine-tuning…