# Computing with Categories in Machine Learning

arXiv: https://arxiv.org/abs/2303.04156 · HTML: https://mlsanity.com/paper/2303.04156/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 24 references that are in the map.
- First posted on arXiv 7 Mar 2023.

## Builds on (most cited first, 15 of 15)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Routing Networks: Adaptive Selection of Non-linear Functions for Multi-Task Learning](https://mlsanity.com/paper/1711.01239/) (2017)
- [Building machines that adapt and compute like brains](https://mlsanity.com/paper/1711.04203/) (2017)
- [Modular Networks: Learning to Decompose Neural Computation](https://mlsanity.com/paper/1811.05249/) (2018)
- [A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics](https://mlsanity.com/paper/1908.07021/) (2019)
- [The Omniglot challenge: a 3-year progress report](https://mlsanity.com/paper/1902.03477/) (2019)
- [One-Shot Generalization in Deep Generative Models](https://mlsanity.com/paper/1603.05106/) (2016)
- [Category Theory in Machine Learning](https://mlsanity.com/paper/2106.07032/) (2021)
- [Faithful Inversion of Generative Models for Effective Amortized Inference](https://mlsanity.com/paper/1712.00287/) (2017)
- [Learning Hierarchical Features from Generative Models](https://mlsanity.com/paper/1702.08396/) (2017)
- [The Variational Homoencoder: Learning to learn high capacity generative models from few examples](https://mlsanity.com/paper/1807.08919/) (2018)
- [Automatic structured variational inference](https://mlsanity.com/paper/2002.00643/) (2020)
- [Learning Task-General Representations with Generative Neuro-Symbolic Modeling](https://mlsanity.com/paper/2006.14448/) (2020)
- [The operad of wiring diagrams: formalizing a graphical language for databases, recursion, and plug-and-play circuits](https://mlsanity.com/paper/1305.0297/) (2013)

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

- [Working Paper: Towards a Category-theoretic Comparative Framework for Artificial General Intelligence](https://mlsanity.com/paper/2603.28906/) (2026)
- [Transport of Algebraic Structure to Latent Embeddings](https://mlsanity.com/paper/2405.16763/) (2024)

## Abstract (arXiv)

Category theory has been successfully applied in various domains of science, shedding light on universal principles unifying diverse phenomena and thereby enabling knowledge transfer between them. Applications to machine learning have been pursued recently, and yet there is still a gap between abstract mathematical foundations and concrete applications to machine learning tasks. In this paper we introduce DisCoPyro as a categorical structure learning framework, which combines categorical structures (such as symmetric monoidal categories and operads) with amortized variational inference, and can be applied, e.g., in program learning for variational autoencoders. We provide both mathematical foundations and concrete applications together with comparison of experimental performance with other models (e.g., neuro-symbolic models). We speculate that DisCoPyro could ultimately contribute to the development of artificial general intelligence.