Topic 06 — Geometry, Topology, and Equivariance

Data often lies on low-dimensional manifolds, and successful architectures must respect the intrinsic symmetries (rotations, translations, permutations) of the domain. This module explores Geometric Deep Learning, Group Representation Theory, and Topological Data Analysis (TDA).

Prerequisite Tier: Tier 2-3 — Intermediate / Advanced (Linear Algebra, Abstract Algebra, Topology)

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📚 Course Modules

• Lecture: Unified Mathematical Foundations Erlangen Program, Equivariance, GDL Blueprint, and Persistent Homology.

• Practice: Exercises and Solutions Theoretical proofs on circulant matrices, Euler characteristics, and coding tasks for TDA.

• Project: Equivariant GNNs and TDA Modeling molecular systems with EGNNs and shape classification using topological features.

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📄 Key Research Literature

• Bronstein, M. M., et al. (2021): Geometric Deep Learning - The foundational "blueprint" paper.
• Cohen, T. S., & Welling, M. (2016): Group Equivariant Convolutional Networks - Introduction of G-CNNs.
• Satorras, V. G., et al. (2021): E(n) Equivariant Graph Neural Networks - Standard architecture for molecular modeling.
• Carlsson, G. (2009): Topology and Data - Foundational paper for TDA.