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This monograph offers a toolbox of mathematical techniques, which have been effective and widely applicable in information-theoretic analysis. The first tool is a generalization of the method of types to Gaussian settings, and then to…

Generative AI, particularly Large Language Models, increasingly integrates graph-based representations to enhance reasoning, retrieval, and structured decision-making. Despite rapid advances, there remains limited clarity regarding when,…

Large language models (LLMs) have emerged as powerful tools for natural language table reasoning, where there are two main categories of methods. Prompt-based approaches rely on language-only inference or one-pass program generation without…

The search for linguistic patterns, stylometry and forensic linguistics have in the theory of complex networks, their structures and associated mathematical tools, allies with which to model and analyze texts. In this paper we present a new…

Recent advancements in large language models (LLMs) have spurred growing interest in automatic theorem proving using Lean4, where effective tree search methods are crucial for navigating the underlying large proof search spaces. While the…

Verifying mathematical proofs is difficult, but can be automated with the assistance of a computer. Autoformalization is the task of automatically translating natural language mathematics into a formal language that can be verified by a…

Complex Table Question Answering involves providing accurate answers to specific questions based on intricate tables that exhibit complex layouts and flexible header locations. Despite considerable progress having been made in the LLM era,…

Although automated reasoning with diagrams has been possible for some years, tools for diagrammatic reasoning are generally much less sophisticated than their sentential cousins. The tasks of exploring levels of automation and abstraction…

Large language models (LLMs) have achieved remarkable multi-step reasoning capabilities across various domains. However, LLMs still face distinct challenges in complex logical reasoning, as (1) proof-finding requires systematic exploration…

To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary…

Sequent calculus is widely used for formalizing proofs. However, due to the proliferation of data, understanding the proofs of even simple mathematical arguments soon becomes impossible. Graphical user interfaces help in this matter, but…

This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…

Geometry problems are a crucial testbed for AI reasoning capabilities. Most existing geometry solving systems cannot express problems within a unified framework, thus are difficult to integrate with other mathematical fields. Besides, since…

Traditional Retrieval-Augmented Generation (RAG) effectively supports single-hop question answering with large language models but faces significant limitations in multi-hop question answering tasks, which require combining evidence from…

With the advent of large language models (LLMs), in both the open source and proprietary domains, attention is turning to how to exploit such artificial intelligence (AI) systems in assisting complex scientific tasks, such as material…

Mathematical reasoning and optimization are fundamental to artificial intelligence and computational problem-solving. Recent advancements in Large Language Models (LLMs) have significantly improved AI-driven mathematical reasoning, theorem…

Large Language Models (LLMs) are increasingly excelling and outpacing human performance on many tasks. However, to improve LLM reasoning, researchers either rely on ad-hoc generated datasets or formal mathematical proof systems such as the…

Theorem proving serves as a major testbed for evaluating complex reasoning abilities in large language models (LLMs). However, traditional automated theorem proving (ATP) approaches rely heavily on formal proof systems that poorly align…

We present ML4PG - a machine learning extension for Proof General. It allows users to gather proof statistics related to shapes of goals, sequences of applied tactics, and proof tree structures from the libraries of interactive higher-order…

Large Language Models (LLMs) have achieved remarkable success across various domains. However, they still face significant challenges, including high computational costs for training and limitations in solving complex reasoning problems.…