Document Understanding, Measurement, and Manipulation Using Category Theory

TL;DR

This paper introduces a category theory-based framework for document understanding, enabling new methods for information measurement, summarization, extension, and self-supervised model improvement, applicable to multimodal documents.

Contribution

It develops a mathematical representation of documents as categories of question-answer pairs and introduces orthogonalization and rate distortion analysis for advanced document processing.

Findings

Effective multimodal document structure extraction

Novel summarization and extension techniques

Self-supervised model enhancement using RLVR

Abstract

We apply category theory to extract multimodal document structure which leads us to develop information theoretic measures, content summarization and extension, and self-supervised improvement of large pretrained models. We first develop a mathematical representation of a document as a category of question-answer pairs. Second, we develop an orthogonalization procedure to divide the information contained in one or more documents into non-overlapping pieces. The structures extracted in the first and second steps lead us to develop methods to measure and enumerate the information contained in a document. We also build on those steps to develop new summarization techniques, as well as to develop a solution to a new problem viz. exegesis resulting in an extension of the original document. Our question-answer pair methodology enables a novel rate distortion analysis of summarization techniques. We implement our techniques using large pretrained models, and we propose a multimodal extension of our overall mathematical framework. Finally, we develop a novel self-supervised method using RLVR to improve large pretrained models using consistency constraints such as composability and closure under certain operations that stem naturally from our category theoretic framework.