# Succinct Representations for Concepts

arXiv: https://arxiv.org/abs/2303.00446 · HTML: https://mlsanity.com/paper/2303.00446/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 8 references that are in the map.
- First posted on arXiv 1 Mar 2023.

## Builds on (most cited first, 2 of 2)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [On the Power of Foundation Models](https://mlsanity.com/paper/2211.16327/) (2022)

## Built on by (most cited first, 2 of 2)

- [A Categorical Framework of General Intelligence](https://mlsanity.com/paper/2303.04571/) (2023)
- [Clarifying Before Reasoning: A Coq Prover with Structural Context](https://mlsanity.com/paper/2507.02541/) (2025)

## Abstract (arXiv)

Foundation models like chatGPT have demonstrated remarkable performance on various tasks. However, for many questions, they may produce false answers that look accurate. How do we train the model to precisely understand the concepts? In this paper, we introduce succinct representations of concepts based on category theory. Such representation yields concept-wise invariance properties under various tasks, resulting a new learning algorithm that can provably and accurately learn complex concepts or fix misconceptions. Moreover, by recursively expanding the succinct representations, one can generate a hierarchical decomposition, and manually verify the concept by individually examining each part inside the decomposition.