Document Understanding, Measurement, and Manipulation Using Category Theory

2025-10-24

AI Summary

Multimodal document structural understanding lacks formal theoretical foundations. Method: This paper proposes a novel categorical modeling paradigm grounded in category theory: documents are formalized as categories whose objects are document elements and morphisms are question-answer pairs; information orthogonal decomposition and composability constraints are introduced to enable mathematical representation and rate-distortion analysis of document content. Building upon this, we develop a measurable, enumerable information-theoretic evaluation framework—enabling unsupervised text exegesis expansion and consistency-aware abstractive summarization—and optimize large language models via RLVR (Reconstruction-Labeling-Verification-Refinement) self-supervision. Contribution/Results: This work is the first to systematically integrate category theory into document structure modeling; it establishes the principle of information orthogonality and unifies structural, semantic, and generative aspects under a quantitative framework. Empirical results demonstrate significant improvements in summary quality and generation consistency, enabling theory-driven, self-supervised enhancement of multimodal foundation models.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Natural Language Processing: Summarization
• Computer Vision: Multi-modal Vision

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Extracting multimodal document structure using category theory
• Developing information measurement and summarization techniques
• Improving pretrained models through self-supervised learning methods

Innovation

• Applying category theory to document structure extraction
• Developing orthogonalization for non-overlapping information division
• Creating self-supervised RLVR method for model improvement