Spatial Attention Kinetic Networks with E(n)-Equivariance

• URL: http://arxiv.org/abs/2301.08893v2
• Date: Tue, 24 Jan 2023 18:01:05 GMT
• Title: Spatial Attention Kinetic Networks with E(n)-Equivariance
• Authors: Yuanqing Wang and John D. Chodera
• Abstract summary: Neural networks that are equivariant to rotations, translations, reflections, and permutations on n-dimensional geometric space have shown promise in physical modeling. We propose a simple alternative functional form that uses neurally parametrized linear combinations of edge vectors to achieve equivariance. We design spatial attention kinetic networks with E(n)-equivariance, or SAKE, which are competitive in many-body system modeling tasks while being significantly faster.
• Score: 0.951828574518325
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural networks that are equivariant to rotations, translations, reflections, and permutations on n-dimensional geometric space have shown promise in physical modeling for tasks such as accurately but inexpensively modeling complex potential energy surfaces to guiding the sampling of complex dynamical systems or forecasting their time evolution. Current state-of-the-art methods employ spherical harmonics to encode higher-order interactions among particles, which are computationally expensive. In this paper, we propose a simple alternative functional form that uses neurally parametrized linear combinations of edge vectors to achieve equivariance while still universally approximating node environments. Incorporating this insight, we design spatial attention kinetic networks with E(n)-equivariance, or SAKE, which are competitive in many-body system modeling tasks while being significantly faster.

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