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Poster
Universal Equivariant Multilayer Perceptrons
Siamak Ravanbakhsh

Thu Jul 16 06:00 AM -- 06:45 AM & Thu Jul 16 05:00 PM -- 05:45 PM (PDT) @
in Poster Session 41 »

Group invariant and equivariant Multilayer Perceptrons (MLP), also known as Equivariant Networks, have achieved remarkable success in learning on a variety of data structures, such as sequences, images, sets, and graphs. Using tools from group theory, this paper proves the universality of a broad class of equivariant MLPs with a single hidden layer. In particular, it is shown that having a hidden layer on which the group acts regularly is sufficient for universal equivariance (invariance). A corollary is unconditional universality of equivariant MLPs for Abelian groups, such as CNNs with a single hidden layer. A second corollary is the universality of equivariant MLPs with a high-order hidden layer, where we give both group-agnostic bounds and means for calculating group-specific bounds on the order of hidden layer that guarantees universal equivariance (invariance).

Keywords: Deep Learning Theory · Representation Learning · Other · Deep Learning - General

Author Information

Siamak Ravanbakhsh (McGill - Mila)

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