---
title: "Category Theory in Machine Learning"
authors:
  - "Dan Shiebler"
  - "Bruno Gavranović"
  - "Paul Wilson"
year: 2021
venue: "arXiv:cs.LG"
arxiv: "2106.07032"
doi: null
source: "https://arxiv.org/abs/2106.07032"
topics:
  - "category-theory"
  - "machine-learning"
  - "survey"
seed_rank: 955
seed_batch: "user-add-2026-08-13"
reviewed: "2026-08-13"
pool: "maths-foundations"
relevance_score: 8
lineage: categorical-deep-learning
cites:
  - title: "Backprop as Functor: A compositional perspective on supervised learning"
    url: "https://arxiv.org/abs/1711.10455"
    year: 2019
    arxiv: "1711.10455"
see:
  - "943-backprop-as-functor-compositional-supervised-learning"
---

# Category Theory in Machine Learning

## One-sentence takeaway

Shiebler, Gavranović, and Wilson survey the 2010s–2021 wave of category theory applied to machine learning, organizing it around gradient-based learning, probability, and equivariance rather than proving a new theorem.

## Why it matters here

This is the map of the categorical-deep-learning neighbourhood before Gavranović 2024 and Weaves 2026: a reading order for lenses, string diagrams, and supervised-learning-as-functor, written by the same circle Broadside already cites.

## Key ideas

- Motivation: category theory as a shared language across disciplines, now leaking into ML architectures and training stories.
- Three clusters: (1) gradient-based learning as a compositional process (lenses / backprop-as-functor), (2) categorical probability and generative models, (3) equivariance and geometric deep learning.
- Documents common themes — compositionality, parameter-update as a morphism, symmetry as a group action — instead of a single formalism.
- Snapshot dated June 2021; later NCD/Weaves work is outside its horizon.

## Caveats

## Links

- arXiv: [2106.07032](https://arxiv.org/abs/2106.07032)