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This paper introduces a novel method, referred to as "hashing", which involves masking potentially bias-inducing words in large language models (LLMs) with hash-like meaningless identifiers to reduce cognitive biases and reliance on…
A theorem prover without an extensive library is much less useful to its potential users. Algebra, the study of algebraic structures, is a core component of such libraries. Algebraic theories also are themselves structured, the study of…
Proof assistants, such as Isabelle/HOL, offer tools to facilitate inductive theorem proving. Isabelle experts know how to use these tools effectively; however, there is a little tool support for transferring this expert knowledge to a wider…
Combining different forms of prompts with pre-trained large language models has yielded remarkable results on reasoning tasks (e.g. Chain-of-Thought prompting). However, along with testing on more complex reasoning, these methods also…
Recently, tool learning with large language models (LLMs) has emerged as a promising paradigm for augmenting the capabilities of LLMs to tackle highly complex problems. Despite growing attention and rapid advancements in this field, the…
Theorem provers are tools that help users to write machine readable proofs. Some of this tools are also interactive. The need of such softwares is increasing since they provide proofs that are more certified than the hand written ones. Agda…
Recent progress in large language models has made them increasingly capable research assistants in mathematics. Yet, as their reasoning abilities improve, evaluating their mathematical competence becomes increasingly challenging. The…
We introduce ToRL (Tool-Integrated Reinforcement Learning), a framework for training large language models (LLMs) to autonomously use computational tools via reinforcement learning. Unlike supervised fine-tuning, ToRL allows models to…
Large language models (LLMs) have shown exceptional performance as general-purpose assistants, excelling across a variety of reasoning tasks. This achievement represents a significant step toward achieving artificial general intelligence…
We introduce DreamProver, an agentic framework that leverages a "wake-sleep" program induction paradigm to discover reusable lemmas for formal theorem proving. Existing approaches either rely on fixed lemma libraries, which limit…
We introduce CSAR, an algorithm for inducing morphemes from emergent language corpora of parallel utterances and meanings. It is a greedy algorithm that (1) weights morphemes based on mutual information between forms and meanings, (2)…
Solving mathematical problems using computer-verifiable languages like Lean has significantly impacted the mathematical and computer science communities. State-of-the-art methods utilize a single Large Language Model (LLM) to generate…
Mella is a minimalistic dependently typed programming language and interactive theorem prover implemented in Haskell. Its main purpose is to investigate the effective integration of automated theorem provers in a pure and simple setting.…
Tool-Integrated Reasoning (TIR) has emerged as a promising direction by extending Large Language Models' (LLMs) capabilities with external tools during reasoning. Existing TIR methods typically rely on external tool documentation during…
In this paper, we propose an effective THresholding method based on ORder Statistic, called THORS, to convert an arbitrary scoring-type classifier, which can induce a continuous cumulative distribution function of the score, into a…
The present dissertation introduces the research project on HOLMS (\textbf{HOL} Light Library for \textbf{M}odal \textbf{S}ystems), a growing modular framework for modal reasoning within the HOL Light proof assistant. To provide an…
Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…
Hallucination, the generation of factually incorrect content, is a growing challenge in Large Language Models (LLMs). Existing detection and mitigation methods are often isolated and insufficient for domain-specific needs, lacking a…
A central notion in practical and theoretical machine learning is that of a $\textit{weak learner}$, classifiers that achieve better-than-random performance (on any given distribution over data), even by a small margin. Such weak learners…
Automated theorem proving is fundamental to formal methods, and the recent trend is to integrate large language models (LLMs) and proof assistants to form effective proof agents. While existing proof agents show promising performance, they…