UNiTE: Unitary N-body Tensor Equivariant Network with Applications to Quantum Chemistry

Equivariant neural networks have been successful in incorporating various types of symmetries, but are mostly limited to vector representations of geometric objects. Despite the prevalence of higher-order tensors in various application domains, e.g. in quantum chemistry, equivariant neural networks for general tensors remain unexplored. Previous strategies for learning equivariant functions on tensors mostly rely on expensive tensor factorization which is not scalable when the dimensionality of the problem becomes large. In this work, we propose unitary $N$-body tensor equivariant neural network (UNiTE), an architecture for a general class of symmetric tensors called $N$-body tensors. The proposed neural network is equivariant with respect to the actions of a unitary group, such as the group of 3D rotations. Furthermore, it has a linear time complexity with respect to the number of non-zero elements in the tensor. We also introduce a normalization method, viz., Equivariant Normalization, to improve generalization of the neural network while preserving symmetry. When applied to quantum chemistry, UNiTE outperforms all state-of-the-art machine learning methods of that domain with over 110% average improvements on multiple benchmarks. Finally, we show that UNiTE achieves a robust zero-shot generalization performance on diverse down stream chemistry tasks, while being three orders of magnitude faster than conventional numerical methods with competitive accuracy.