## TL;DR
Geometric Deep Learning reveals that CNNs, GNNs, and Transformers share a common mathematical blueprint — equivariance to symmetry groups. Group-equivariant networks exploit this insight to achieve better sample efficiency and generalization on structured data.

## Core Explanation
Symmetry principle: if a transformation (translation, rotation, permutation) applied to the input should produce a corresponding transformation in the output, the network should respect this equivariance. Traditional CNNs are translation-equivariant by design (shared weights). GDL extends this to arbitrary groups: rotation-equivariant CNNs for medical imaging, permutation-equivariant GNNs for molecular graphs, gauge-equivariant networks for spherical data.

## Detailed Analysis
Group convolution generalizes standard convolution: instead of shifting a filter across spatial positions, transform the filter by all group elements. SE(3)-equivariant networks respect 3D rotation and translation — critical for protein structure prediction and molecular dynamics. Steerable CNNs learn filters expressed as linear combinations of basis functions, guaranteeing equivariance by construction. AlphaFold 2 and 3 leverage SE(3)-equivariant message passing.

## Further Reading
- Geometric Deep Learning Course (AMMI)
- e3nn PyTorch Library
- Equivariant Self-Attention (SE3-Transformer)