---
title: "Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges"
authors:
  - "Michael M. Bronstein"
  - "Joan Bruna"
  - "Taco Cohen"
  - "Petar Veličković"
year: 2021
venue: "arXiv:cs.LG"
arxiv: "2104.13478"
doi: null
source: "https://arxiv.org/abs/2104.13478"
topics:
  - "geometric-deep-learning"
  - "equivariance"
  - "graphs"
seed_rank: 938
seed_batch: "user-add-2026-08-13"
reviewed: "2026-08-13"
pool: "languages"
relevance_score: 9
lineage: categorical-deep-learning
cites:
  - title: "Attention Is All You Need"
    url: "https://arxiv.org/abs/1706.03762"
    year: 2017
    arxiv: "1706.03762"
  - title: "Graph Attention Networks"
    url: "https://arxiv.org/abs/1710.10903"
    year: 2018
    arxiv: "1710.10903"
see:
  - "013-attention-is-all-you-need"
  - "956-graph-attention-networks"
---

# Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges

## One-sentence takeaway

An Erlangen-style unification of CNNs, GNNs, RNNs, and Transformers as architectures that respect geometric priors — grids, groups, graphs, geodesics, and gauges.

## Why it matters here

The 'why these architectures' counterpart to Weaves' 'how to write them as terms'. Equivariance is the geometric twin of broadcasting: both are about which axes a map is allowed to see.

## Key ideas

- arXiv:2104.13478, 156-page proto-book.
- Two principles do most of the work: representation/feature learning, and local gradient methods; the rest is the geometry of the domain.
- Constructive programme: start from a physical symmetry and derive the architecture, rather than taxonomizing existing nets after the fact.
- Transformers and GAT sit inside the same picture as convnets once the domain (set, graph, group) is named.

## Caveats

## Links

- arXiv: [2104.13478](https://arxiv.org/abs/2104.13478)
- PDF: https://arxiv.org/pdf/2104.13478