Title: Tensor Field Networks: rotation-, translation-, and permutation-equivariant convolutional neural networks for 3D points
Abstract: Atomic systems (molecules, crystals, proteins, nanoclusters, etc.) are naturally represented by a set of coordinates in 3D space labeled by atom type. This is a challenging representation to use for neural networks because the coordinates are sensitive to 3D rotations and translations and there is no canonical orientation or position for these systems. We present a general neural network architecture that naturally handles 3D geometry and operates on the scalar, vector, and tensor fields that characterize physical systems. Our networks are locally equivariant to 3D rotations and translations at every layer. In this talk, we describe how the network achieves these equivariances and demonstrate the capabilities of our network using simple tasks: for example, given a small organic molecule with an atom removed, it can replace the correct element at the correct location in space. We also discuss applications of these networks to molecular dynamics, structure optimization, and basis set optimization.