Document Understanding, Measurement, and Manipulation Using Category Theory
This work addresses document understanding and manipulation for AI and NLP researchers, offering incremental advancements through a novel mathematical framework.
The authors tackled the problem of understanding and manipulating documents by applying category theory to extract multimodal structure, which enabled them to develop information-theoretic measures, summarization techniques, and a self-supervised method to improve large pretrained models, resulting in new capabilities like document extension and rate distortion analysis.
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.