Summary of Category-theoretical and Topos-theoretical Frameworks in Machine Learning: a Survey, by Yiyang Jia et al.
Category-Theoretical and Topos-Theoretical Frameworks in Machine Learning: A Survey
by Yiyang Jia, Guohong Peng, Zheng Yang, Tianhao Chen
First submitted to arxiv on: 26 Aug 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: None
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary A category theory-derived machine learning survey spans four perspectives: gradient-based learning, probability-based learning, invariance and equivalence-based learning, and topos-based learning. The first three topics focus on recent research (five years) with updates and expansions from Shiebler et al.’s previous survey. To the contrary, the fourth topic delves into higher category theory, specifically topos theory, which is surveyed for the first time in this paper. Functors’ compositionality plays a crucial role in certain machine learning methods, prompting categorical frameworks. However, when considering global properties reflecting local structures and geometric properties expressed with logic, the topos structure becomes profound. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Machine learning uses category theory to improve how it works. The paper looks at four ways this is done: using gradients, probabilities, invariance, and topos (higher-level) categories. It reviews what’s happened in the past five years and adds new ideas from Shiebler et al.’s previous work. Topos categories are especially important for understanding how global patterns affect local parts of a network. |
Keywords
* Artificial intelligence * Machine learning * Probability * Prompting
