Approximate Equivariance via Projection-based Regularisation
arXiv:2601.05028v2 Announce Type: replace Abstract: Equivariance is a powerful inductive bias in neural networks, improving generalisation and physical consistency. Recently, however, non-equivariant models have regained attention, due to their better runtime performance and imperfect symmetries that might arise in real-world applications. This has motivated the development of approximately equivariant models that strike a middle ground between respecting symmetries and fitting the data distribution. Existing approaches in this field usually apply sample-based regularisers which depend on data augmentation at training time, incurring a high sample complexity, in particular for continuous groups such as $SO(3)$. This work instead approaches approximate equivariance via a projection-based regulariser which leverages the orthogonal decomposition of linear layers into equivariant and non-equivariant components. In contrast to existing methods, this penalises non-equivariance at an operator