Improved Canonicalization for Model Agnostic Equivariance

This work introduces a novel approach to achieving architecture-agnostic equivariance in deep learning, particularly addressing the limitations of traditional layerwise equivariant architectures and the inefficiencies of the existing architecture-agnostic methods. Building equivariant models using traditional methods requires designing equivariant versions of existing models and training them from scratch, a process that is both impractical and resource-intensive. Canonicalization has emerged as a promising alternative for inducing equivariance without altering model architecture, but it suffers from the need for highly expressive and expensive equivariant networks to learn canonical orientations accurately. We propose a new optimization-based method that employs any non-equivariant network for canonicalization. Our method uses contrastive learning to efficiently learn a canonical orientation and offers more flexibility for the choice of canonicalization network. We empirically demonstrate that this approach outperforms existing methods in achieving equivariance for large pretrained models and significantly speeds up the canonicalization process, making it up to 2 times faster.