Scale equivariance in CNNs with vector fields

TL;DR

This paper introduces a method to embed local scale equivariance into CNNs by applying filters at multiple scales, resulting in improved performance on scale-related tasks and enhanced scale invariance.

Contribution

The paper proposes a novel approach to incorporate local scale equivariance in CNNs using multi-scale filters and vector field outputs, enhancing scale-related task performance.

Findings

Over 20% improvement in scale regression accuracy on scaled MNIST.

Effective for scale-invariant classification tasks.

Internal scale relationships are better captured with the proposed method.

Abstract

We study the effect of injecting local scale equivariance into Convolutional Neural Networks. This is done by applying each convolutional filter at multiple scales. The output is a vector field encoding for the maximally activating scale and the scale itself, which is further processed by the following convolutional layers. This allows all the intermediate representations to be locally scale equivariant. We show that this improves the performance of the model by over $20\%$ in the scale equivariant task of regressing the scaling factor applied to randomly scaled MNIST digits. Furthermore, we find it also useful for scale invariant tasks, such as the actual classification of randomly scaled digits. This highlights the usefulness of allowing for a compact representation that can also learn relationships between different local scales by keeping internal scale equivariance.