# Document Understanding, Measurement, and Manipulation Using Category Theory

arXiv: https://arxiv.org/abs/2510.21553 · HTML: https://mlsanity.com/paper/2510.21553/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 23 references that are in the map.
- First posted on arXiv 24 Oct 2025.

## Builds on (most cited first, 7 of 7)

- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Explaining Answers with Entailment Trees](https://mlsanity.com/paper/2104.08661/) (2021)
- [DRESS: Instructing Large Vision-Language Models to Align and Interact with Humans via Natural Language Feedback](https://mlsanity.com/paper/2311.10081/) (2023)
- [QED: A Framework and Dataset for Explanations in Question Answering](https://mlsanity.com/paper/2009.06354/) (2020)
- [DMRST: A Joint Framework for Document-Level Multilingual RST Discourse Segmentation and Parsing](https://mlsanity.com/paper/2110.04518/) (2021)
- [Can we obtain significant success in RST discourse parsing by using Large Language Models?](https://mlsanity.com/paper/2403.05065/) (2024)

## Abstract (arXiv)

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.