Chapters

1. 01 Introduction Why Euclidean deep learning hits a wall on graphs, manifolds and groups — and how geometric priors invert the data–architecture relationship.
2. 02 Artificial Neural Networks The perceptron, layers as measurable maps, and a full proof of Cybenko's universal approximation theorem — with the parametric limits of Euclidean architectures.
3. 03 Geometric Deep Learning The unifying framework — the 5 Gs, equivariance and invariance, and equivariant message passing that recovers CNNs, GNNs and Transformers as special cases.
4. 04 Convolutional Models From classical CNNs to group, steerable, spherical, E(3)/SE(3), gauge and Clifford convolutions — culminating in an equivariant universality theorem.
5. 05 Attention Models Transformers as adaptive message passing, then equivariant, hyperbolic and topological attention — GATr, Hodge Laplacians and persistent homology.
6. 06 Conclusions Geometry as an organizing principle — how domain, symmetry group and connectivity separate ANNs, CNNs, GNNs and Transformers, and where the open problems lie.