---
title: "Position: Categorical Deep Learning is an Algebraic Theory of All Architectures"
authors:
  - "Bruno Gavranović"
  - "Paul Lessard"
  - "Andrew Dudzik"
year: 2024
venue: "ICML"
arxiv: "2402.15332"
doi: null
source: "https://arxiv.org/abs/2402.15332"
topics:
  - "categorical-deep-learning"
  - "position"
  - "architectures"
seed_rank: 945
seed_batch: "user-add-2026-08-13"
reviewed: "2026-08-13"
pool: "maths-foundations"
relevance_score: 9
lineage: categorical-deep-learning
cites:
  - title: "Category Theory in Machine Learning"
    url: "https://arxiv.org/abs/2106.07032"
    year: 2021
    arxiv: "2106.07032"
  - title: "Categorical Foundations of Gradient-Based Learning"
    url: "https://arxiv.org/abs/2103.01931"
    year: 2022
    arxiv: "2103.01931"
see:
  - "955-category-theory-in-machine-learning"
  - "940-categorical-foundations-of-gradient-based-learning"
---

# Position: Categorical Deep Learning is an Algebraic Theory of All Architectures

## One-sentence takeaway

Position paper: categorical deep learning is not a niche — it is an algebraic theory meant to cover all architectures.

## Why it matters here

The manifesto Weaves quietly implements. If you only read one CDL position piece, this is it: algebra of architectures, not just string diagrams of one net.

## Key ideas

- ICML 2024 position; arXiv:2402.15332.
- Claims an algebraic (not merely diagrammatic) theory of architectures.
- Sits with Cruttwell/Gavranović lenses (cards 940/941) and the Shiebler et al. 2021 survey (card 955).
- Position, not a complete calculus; Weaves 2026 is the broadcasting-and-implementation follow-through.

## Caveats

## Links

- arXiv: [2402.15332](https://arxiv.org/abs/2402.15332)
- PDF: https://arxiv.org/pdf/2402.15332