Symmetry Breaking and Equivariant Neural Networks

• URL: http://arxiv.org/abs/2312.09016v2
• Date: Fri, 22 Mar 2024 04:12:08 GMT
• Title: Symmetry Breaking and Equivariant Neural Networks
• Authors: Sékou-Oumar Kaba, Siamak Ravanbakhsh,
• Abstract summary: We introduce a novel notion of'relaxed equiinjection' We show how to incorporate this relaxation into equivariant multilayer perceptronrons (E-MLPs) The relevance of symmetry breaking is then discussed in various application domains.
• Score: 17.740760773905986
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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.

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