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Poster
A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups
Marc Finzi · Max Welling · Andrew Wilson

Tue Jul 20 09:00 PM -- 11:00 PM (PDT) @
Symmetries and equivariance are fundamental to the generalization of neural networks on domains such as images, graphs, and point clouds. Existing work has primarily focused on a small number of groups, such as the translation, rotation, and permutation groups. In this work we provide a completely general algorithm for solving for the equivariant layers of matrix groups. In addition to recovering solutions from other works as special cases, we construct multilayer perceptrons equivariant to multiple groups that have never been tackled before, including $\mathrm{O}(1,3)$, $\mathrm{O}(5)$, $\mathrm{Sp}(n)$, and the Rubik's cube group. Our approach outperforms non-equivariant baselines, with applications to particle physics and modeling dynamical systems. We release our software library to enable researchers to construct equivariant layers for arbitrary

#### Author Information

##### Max Welling (University of Amsterdam)

Prof. Dr. Max Welling is a research chair in Machine Learning at the University of Amsterdam and a VP Technologies at Qualcomm. He has a secondary appointment as a senior fellow at the Canadian Institute for Advanced Research (CIFAR). He is co-founder of “Scyfer BV” a university spin-off in deep learning which got acquired by Qualcomm in summer 2017. In the past he held postdoctoral positions at Caltech (’98-’00), UCL (’00-’01) and the U. Toronto (’01-’03). He received his PhD in ’98 under supervision of Nobel laureate Prof. G. 't Hooft. Max Welling has served as associate editor in chief of IEEE TPAMI from 2011-2015 (impact factor 4.8). He serves on the board of the NIPS foundation since 2015 (the largest conference in machine learning) and has been program chair and general chair of NIPS in 2013 and 2014 respectively. He was also program chair of AISTATS in 2009 and ECCV in 2016 and general chair of MIDL 2018. He has served on the editorial boards of JMLR and JML and was an associate editor for Neurocomputing, JCGS and TPAMI. He received multiple grants from Google, Facebook, Yahoo, NSF, NIH, NWO and ONR-MURI among which an NSF career grant in 2005. He is recipient of the ECCV Koenderink Prize in 2010. Welling is in the board of the Data Science Research Center in Amsterdam, he directs the Amsterdam Machine Learning Lab (AMLAB), and co-directs the Qualcomm-UvA deep learning lab (QUVA) and the Bosch-UvA Deep Learning lab (DELTA). Max Welling has over 200 scientific publications in machine learning, computer vision, statistics and physics.

##### Andrew Wilson (New York University)

Andrew Gordon Wilson is faculty in the Courant Institute and Center for Data Science at NYU. His interests include probabilistic modelling, Gaussian processes, Bayesian statistics, physics inspired machine learning, and loss surfaces and generalization in deep learning. His webpage is https://cims.nyu.edu/~andrewgw.