Document Understanding, Measurement, and Manipulation Using Category
  Theory
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.
68fed89d6cdff8b857f4715f
Jared Claypoole
68fed89d6cdff8b857f47160
Yunye Gong
68fed89d6cdff8b857f47161
Noson S. Yanofsky
68fed89d6cdff8b857f47162
Ajay Divakaran
Document Understanding, Measurement, and Manipulation Using Category
  Theory
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.
Category theory is used to develop information-theoretic measures, summarization, and self-supervised improvement of large pretrained models through a mathematical framework of question-answer pairs and orthogonalization.
category theory multimodal document structure information theoretic measures content summarization self-supervised improvement large pretrained models question-answer pairs orthogonalization rate distortion analysis RLVR composability closure