Geometric and Physical Quantities Improve E(3) Equivariant Message Passing | Johannes Brandstetter

Join the Learning on Graphs and Geometry Reading Group: https://hannes-stark.com/logag-reading-group Paper “Geometric and Physical Quantities Improve E(3) Equivariant Message Passing”https://arxiv.org/abs/2110.02905 Abstract: Including covariant information, such as position, force, velocity or spin is important in many tasks in computational physics and chemistry. We introduce Steerable E(3) Equivariant Graph Neural Networks (SEGNNs) that generalize equivariant graph networks, such that node and edge attributes are not restricted to invariant scalars, but can contain covariant information, such as vectors or tensors. This model, composed of steerable MLPs, is able to incorporate geometric and physical information in both the message and update functions. Through the definition of steerable node attributes, the MLPs provide a new class of activation functions for general use with steerable feature fields. We discuss ours and related work through the lens of equivariant non-linear convolutions, which further allows us to pin-point the successful components of SEGNNs: non-linear message aggregation improves upon classic linear (steerable) point convolutions; steerable messages improve upon recent equivariant graph networks that send invariant messages. We demonstrate the effectiveness of our method on several tasks in computational physics and chemistry and provide extensive ablation studies. Authors: Johannes Brandstetter, Rob Hesselink, Elise van der Pol, Erik J Bekkers, Max Welling Twitter Hannes: https://twitter.com/HannesStaerk Twitter Dominique: https://twitter.com/dom_beaini Twitter Valence Discovery: https://twitter.com/valence_ai Reading Group Slack: https://join.slack.com/t/logag/shared_invite/zt-u0mbo1ec-zElmvd1oSCXGjXvxLSokvg Chapters ~ 00:00 Intro 00:16 Background 02:23 Overview and Findings 11:15 Discussion/Q&A 15:43 The Core of SEGNN’s 19:54 Non-linear vs Linear Convolution 31:22 New Steerable Activation Functions 47:36 Performance and Applicability 59:04 Q+A