Symmetry Breaking and Equivariant Neural Networks
Submission Track: Extended Abstract
Keywords: deep learning, invariance, equivariance, symmetry breaking, graph representation learning, physics
TL;DR: We discuss limitations of equivariant neural networks in dealing with symmetry breaking and propose solution.
Abstract: Using symmetry as an inductive bias in deep learning has been proven to be a principled approach for sample-efficient model design. However, the relationship between symmetry and the imperative for equivariance in neural networks is not always obvious. Here, we analyze a key limitation that arises in equivariant functions: their incapacity to break symmetry at the level of individual data samples. In response, we introduce a novel notion of 'relaxed equivariance' that circumvents this limitation. We further demonstrate how to incorporate this relaxation into equivariant multilayer perceptrons (E-MLPs), offering an alternative to the noise-injection method. The relevance of symmetry breaking is then discussed in various application domains: physics, graph representation learning, combinatorial optimization and equivariant decoding.
Submission Number: 43
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