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10. Equivariant Neural Networks — deep learning for molecules & materials

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The previous chapter Input Data & Equivariances discussed data transformation and network architecture decisions that can be made to make a neural network equivariant with respect to translation, rotation, and permutations. However, those ideas limit the expressibility of our networks and are constructed ad-hoc. Now we will take a more systematic approach to defining equivariances and prove that there is only one layer type that can preserve a given equivariance. The result of this section will be layers that can be equivariant with respect to any transform, even for more esoteric cases like points on a sphere or mirror operations. To achieve this, we will need tools from group theory, representation theory, harmonic analysis, and deep learning. Equivariant neural networks are part of a broader topic of geometric deep learning, which is learning with data that has some underlying geometric relationships. Geometric deep learning is thus a broad-topic and includes the “5Gs”: grids, group

10. Equivariant Neural Networks # The previous chapter Input Data & Equivariances discussed data transformation and network architecture decisions that can be made to make a neural network equivariant with respect to translation, rotation, and permutations. However, those ideas limit the expressibility of our networks and are constructed ad-hoc. Now we will take a more systematic approach to defining equivariances and prove that there is only one layer type that can preserve a given equivariance. The result of this section will be layers that can be equivariant with respect to any transform, e

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