Document Understanding, Measurement, and Manipulation Using Category
  Theory
Authors: name: Jared Claypoole, name: Yunye Gong, name: Noson S. Yanofsky, name: Ajay Divakaran
Organization: SRI International

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.