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Tensor field networks---- Rotation- and translation-equivariant neural networks for

huyi / August 2022

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0. Abstract

• tensor field neural networks: locally equivariant to 3D rotations, translations, and permutations of points at every layer

  1. Motivation

• CNN的平移不变性：识别目标放在图的哪里都可以识别得到

  2. Related work

3. Group representations and equivariance in 3D

3.1 Permutation equivariance

3.2 Translation equivariance

3.3 Rotation equivariance

4. Tensor field network layers

4.1 Point convolution

4.1.1 Spherical harmonics and filters

4.1.2 Combining representations using tensor products

4.1.3 Layer definition

4.2 Self-interaction

4.3 Nonlinearity

5. Demonstrations

5.1 Geometry: shape classification

5.2 Physics: vectors and tensors in classical mechanics

5.3 Chemistry: toward geometrically generating molecular structures

6. Future work