Emergent Equivariance in Deep Ensembles
This addresses the problem of achieving equivariance in deep learning models for researchers, offering a method that is incremental but provides theoretical guarantees.
The paper demonstrates that deep ensembles achieve equivariance for all inputs and training times through data augmentation, with the effect holding off-manifold and for any architecture in the infinite width limit, as verified by neural tangent kernel theory and numerical experiments.
We show that deep ensembles become equivariant for all inputs and at all training times by simply using data augmentation. Crucially, equivariance holds off-manifold and for any architecture in the infinite width limit. The equivariance is emergent in the sense that predictions of individual ensemble members are not equivariant but their collective prediction is. Neural tangent kernel theory is used to derive this result and we verify our theoretical insights using detailed numerical experiments.