Shih-Hsin Wang 王士欣
中文

Geometric Deep Learning

Designing machine learning models around the geometric and symmetry structure in data: graph neural networks, invariance and equivariance, and applications to molecules, proteins and other structured data.

5 units + 5 planned 7 notes Read 0 / 7 Jun 2026
  1. G1 Symmetry and Translation 0 / 2 Output actions, groups, convolutional sharing, composition, boundaries, and translation tests.
    1. G1.0 The Same Taipei Map, Seen Through Two Phone Views
    2. G1.2 Why CNNs Naturally Fit Maps and Images
  2. G2 Rotations and Feature Types 0 / 1 Orientation channels, group convolution, feature types, readouts, and C4 tests.
    1. G2.0 When the Phone Rotates, Should the Model Rotate Too?
  3. G3 Sets and Permutations 0 / 1 Deep Sets, per-point sharing, and PointNet; where a shared summary falls short.
    1. G3.0 What If a Map Is a Set of Points?
  4. G5 Graphs and Message Passing 0 / 1 Relabeling, message passing, GCN, GIN, and expressivity limits.
    1. G5.0 A Map Is Also a Graph
  5. G6 Euclidean Geometry 0 / 2 Relative geometry, EGNN, energy-gradient forces, and chirality.
    1. G6.0 Point Clouds Need Two Kinds of Symmetry
    2. G6.3 Symmetry Is Not a Free Lunch
  6. G7 Tensor Features Planned Planned expansion.

    Articles are being planned.

    1. G7.0 What do scalars and vectors leave out?
    2. G7.1 How can we encode directions on a sphere?
    3. G7.2 How do angular features transform together?
    4. G7.3 What types result from combining features?
    5. G7.4 What must a tensor field layer respect?
    6. G7.5 How should we choose parity and a feature budget?
    7. G7.6 Lab: rotation tests for typed tensor features
  7. G8 Graph Structure and Spectral Methods Planned Planned expansion.

    Articles are being planned.

    1. G8.0 What information is missing from local messages?
    2. G8.1 Smoothing and the graph Laplacian
    3. G8.2 What is frequency without a regular grid?
    4. G8.3 How can graph frequencies define a filter?
    5. G8.4 Why do messages become too similar?
    6. G8.5 What happens when distant information meets a bottleneck?
    7. G8.6 Can connections and structure provide distant information?
    8. G8.7 Lab: depth, bottlenecks, and structural encoding
  8. G9 Surfaces and Local Frames Planned Planned expansion.

    Articles are being planned.

    1. G9.0 Is a straight line still shortest on a surface?
    2. G9.1 A tangent plane at each position
    3. G9.2 How can we compare arrows at different positions?
    4. G9.3 How does an answer change with its local frame?
    5. G9.4 How should a surface kernel respect local frames?
    6. G9.5 Which geometric relations survive a full surface network?
    7. G9.6 Lab: testing changes of local frames
  9. G10 Approximate Symmetry and Canonicalization Planned Planned expansion.

    Articles are being planned.

    1. G10.0 Is approximate symmetry a task or a model mismatch?
    2. G10.1 Multiple views or a canonical view?
    3. G10.2 What happens when a canonical orientation jumps?
    4. G10.3 What should remain when symmetry is relaxed?
    5. G10.4 Lab: performance and consistency with approximate symmetry
  10. G11 Geometric Generative Models Planned Planned expansion.

    Articles are being planned.

    1. G11.0 Is a generated molecule a coordinate set or a distribution?
    2. G11.1 Translation and centered probability models
    3. G11.2 How should scores and velocities transform?
    4. G11.3 Does an equivariant ODE preserve distributional symmetry?
    5. G11.4 How should we test symmetry in a stochastic sampler?
    6. G11.5 Does geometric consistency imply chemical validity?
    7. G11.6 Lab: geometric generation and validity evaluation

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