Symmetry Breaking and Equivariant Neural Networks
This addresses a fundamental limitation in symmetry-based neural networks for applications in physics, graph learning, optimization, and decoding, though it appears incremental as an extension of existing equivariant methods.
The paper identifies a limitation in equivariant neural networks where they cannot break symmetry at the individual sample level, and introduces a 'relaxed equivariance' concept to address this, demonstrating its application in E-MLPs as an alternative to noise-injection methods.
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.