Geometric Deep Learning

Begin with symmetry and graph representation learning, then move through geometric neural networks, flow matching, and applications in proteins, genomes, and materials. Every chapter also stands on its own.

20 of 20 chapters published

Geometry and graphs

  1. Symmetry and Equivariance for Geometric Data
    A concrete account of group actions, invariance, equivariance, and feature types for geometric machine learning.
    GDL Lectures 1–2; ML4Mol Lecture 5
  2. Graph Neural Networks as Learnable Message Passing
    Why permutation symmetry leads to message passing, how familiar GNNs instantiate it, and why graph Transformers still need structure.
    GDL Lecture 3; ML4Mol Lecture 4
  3. Two Routes to Graph Convolution
    Two derivations of graph convolution—from Laplacian spectral filters and permutation-equivariant linear maps—and what each reveals and hides.
    GDL Lecture 4
  4. What Graph Neural Networks Can and Cannot Distinguish
    Graph neural network expressivity through multiset aggregation, the Weisfeiler--Leman test, its blind spots, and the cost of stronger models.
    GDL Lecture 5; ML4Mol Lecture 4
  5. Depth, Over-Smoothing, and Over-Squashing in Graph Networks
    Why deeper graph networks face under-reaching, over-smoothing, and over-squashing—and how topology determines which remedy helps.
    GDL Lecture 6; ML4Mol Lecture 4

Geometric neural networks

  1. Scalar and Vector Geometric Graph Networks
    How geometric graph networks move from invariant distances and angles to equivariant coordinates and vector channels—and what directionality buys.
    GDL Lecture 7; ML4Mol Lecture 5
  2. Frames, Canonicalization, and Symmetrization
    How canonicalization, local frames, frame averaging, and probabilistic symmetrization create geometric models—and why continuity is difficult.
    GDL Lecture 8
  3. Steerable Features and Tensor Products
    How irreducible rotation types, spherical harmonics, and Clebsch–Gordan tensor products create expressive equivariant neural-network layers.
    GDL Lectures 9–10; ML4Mol Lecture 5
  4. Equivariant Transformers and Machine-Learned Potentials
    How invariant attention scores, equivariant values, and energy-based force prediction turn geometric Transformers into practical interatomic potentials.
    GDL Lectures 11–12; ML4Mol Lecture 7

Geometric generative models

  1. ODEs, SDEs, and Probability Flow
    How ODEs and SDEs transport probability, why scores appear in reverse-time diffusion, and how probability-flow ODEs match SDE marginals.
    GDL Lecture 13; ML4Mol Lecture 6
  2. Diffusion Models and Flow Matching
    A unified derivation of diffusion and flow matching through conditional probability paths, marginalization identities, and simulation-free regression.
    GDL Lecture 14; ML4Mol Lecture 6
  3. Geometric Flow Matching on Manifolds
    Flow matching beyond Euclidean space, from tangent velocity fields and geodesic conditional paths to product manifolds for molecular geometry.
    GDL Lectures 15–16; ML4Mol Lecture 6
  4. Discrete Flow and Generator Matching
    How continuous-time Markov chains transport categorical probability, how their rates become learnable, and how generator matching extends across modalities.
    GDL Lectures 16–17; ML4Mol Lecture 6

Applications

  1. Protein Structure Prediction from AlphaFold 1 to 3
    How coevolutionary constraints, pairwise geometric reasoning, residue frames, and all-atom diffusion shaped AlphaFold—and where structure prediction stops.
    GDL Lecture 18; ML4Mol Lecture 12
  2. Protein Representation Learning Across Sequence and Structure
    How sequence, alignments, residue graphs, backbone frames, surfaces, and multimodal objectives shape what protein embeddings can support.
    GDL Lecture 18; ML4Mol Lecture 13
  3. Protein Ensembles and Learned Molecular Dynamics
    How metastable protein conformations become equilibrium ensembles and kinetic models, and what learned samplers must preserve beyond structural plausibility.
    GDL Lecture 19
  4. Generative Models for Protein Design
    Protein design as sequence–structure–function inference, from inverse folding and backbone diffusion to computational filters and experimental evidence.
    GDL Lecture 19; ML4Mol Lecture 13
  5. Genomic Foundation Models and Virtual Cells
    From genomic sequence models and noisy single-cell measurements to perturbation prediction and the stronger requirements of a virtual cell.
    GDL Lecture 20; ML4Mol Lecture 14
  6. Materials Discovery Connects Structure, Properties, and Synthesis
    A material is more than a formula: discovery must connect periodic structure, competing phases, target properties, processing, and experimental formation.
    GDL Lecture 21; ML4Mol Lecture 3
  7. Crystal Property Prediction and Generative Design
    How periodic representations support crystal prediction and generation—and why relaxation, first-principles validation, and synthesis remain decisive.
    GDL Lecture 21; ML4Mol Lecture 10