Parameter-free approximate equivariance for tasks with finite group symmetry
This provides a more efficient solution for tasks requiring finite group symmetry, though it is incremental as it builds on existing equivariance concepts.
The paper tackles the computational intensity and high parameter counts of existing equivariant neural networks by proposing a zero-parameter method that imposes approximate equivariance through a loss penalty, achieving similar or better performance on three datasets with fewer parameters.
Equivariant neural networks incorporate symmetries through group actions, embedding them as an inductive bias to improve performance on a wide variety of tasks. However, existing equivariant methods can be computationally intensive, with high parameter counts, and are often tied to a specific architecture. We propose a simple zero-parameter approach that imposes approximate equivariance for a finite group in the latent representation, as an additional term in the loss function. We conduct experiments which allow the network to learn a group representation on the latent space, and show in every case it prefers to learn the regular representation. Fixing this action on the latent space, this yields a simple method to impose approximate equivariance as an additional loss penalty. We benchmark our approach on three datasets and compare it against several existing equivariant methods, showing that in many cases it achieves similar or better performance for a fraction of the parameters.