Related papers: Proving Theorems Recursively
Automating the formalization of mathematical statements for theorem proving remains a major challenge for Large Language Models (LLMs). LLMs struggle to identify and utilize the prerequisite mathematical knowledge and its corresponding…
We propose a minimal agentic baseline that enables systematic comparison across different AI-based theorem prover architectures. This design implements the core features shared among state-of-the-art systems: iterative proof refinement,…
Formal theorem proving, a field at the intersection of mathematics and computer science, has seen renewed interest with advancements in large language models (LLMs). This paper introduces SubgoalXL, a novel approach that synergizes…
The famous Policy Iteration algorithm alternates between policy improvement and policy evaluation. Implementations of this algorithm with several variants of the latter evaluation stage, e.g, $n$-step and trace-based returns, have been…
Reinforcement Learning with Verifiable Rewards (RLVR) elicits long chain-of-thought reasoning in large language models (LLMs), but outcome-based rewards lead to coarse-grained advantage estimation. While existing approaches improve RLVR via…
A synonym of a polysemous word is usually only the paraphrase of one sense among many. When lexicons are used to improve vector-space word representations, such paraphrases are unreliable and bring noise to the vector-space. The prior works…
We propose an incremental approach for safety proofs that decomposes a proof with a complex inductive invariant into a sequence of simpler proof steps. Our proof system combines rules for (i) forward reasoning using inductive invariants,…
Recent advances in Automated Theorem Proving have shown the effectiveness of leveraging a (large) language model that generates tactics (i.e. proof steps) to search through proof states. The current model, while trained solely on successful…
We describe Verse by Verse, our experiment in augmenting the creative process of writing poetry with an AI. We have created a group of AI poets, styled after various American classic poets, that are able to offer as suggestions generated…
Reasoning has emerged as the next major frontier for language models (LMs), with rapid advances from both academic and industrial labs. However, this progress often outpaces methodological rigor, with many evaluations relying on…
Current approaches for training Process Reward Models (PRMs) often involve breaking down responses into multiple reasoning steps using rule-based techniques, such as using predefined placeholder tokens or setting the reasoning step's length…
This paper presents a novel framework for enhancing reasoning capabilities in large language models (LLMs) by leveraging iterative reasoning and feedback-driven methodologies. Building on the limitations identified in the SimpleBench…
Large language models (LLMs) have achieved strong performance on complex reasoning tasks using techniques such as chain-of-thought and self-consistency. However, ensemble-based approaches, especially self-consistency which relies on…
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…
Test-time scaling has emerged as an effective way to improve language models on challenging reasoning tasks. However, most existing methods treat each problem in isolation and do not systematically reuse knowledge from prior reasoning…
We perform a thorough analysis of the formal and informal statements in the miniF2F benchmark from the perspective of an AI system that is tasked to participate in a math Olympiad consisting of the problems in miniF2F. In such setting, the…
We introduce an approach aimed at enhancing the reasoning capabilities of Large Language Models (LLMs) through an iterative preference learning process inspired by the successful strategy employed by AlphaZero. Our work leverages Monte…
We present IBR, an Iterative Backward Reasoning model to solve the proof generation tasks on rule-based Question Answering (QA), where models are required to reason over a series of textual rules and facts to find out the related proof path…
Large language models are increasingly capable at closed-world mathematical reasoning, but research assistance also requires source-grounded use of the literature. When a proof reaches a non-trivial step, a useful assistant should determine…
We explore a method for improving the performance of large language models through self-reflection and reinforcement learning. By incentivizing the model to generate better self-reflections when it answers incorrectly, we demonstrate that a…