Neural Fourier Transform: A General Approach to Equivariant Representation Learning
This work addresses a general challenge in symmetry learning for machine learning, offering a novel framework that could be broadly applicable, though it appears incremental in advancing equivariance methods.
The paper tackles the problem of learning equivariant representations without prior knowledge of group actions on data by proposing Neural Fourier Transform (NFT), achieving results that demonstrate its application in scenarios with varying levels of group knowledge.
Symmetry learning has proven to be an effective approach for extracting the hidden structure of data, with the concept of equivariance relation playing the central role. However, most of the current studies are built on architectural theory and corresponding assumptions on the form of data. We propose Neural Fourier Transform (NFT), a general framework of learning the latent linear action of the group without assuming explicit knowledge of how the group acts on data. We present the theoretical foundations of NFT and show that the existence of a linear equivariant feature, which has been assumed ubiquitously in equivariance learning, is equivalent to the existence of a group invariant kernel on the dataspace. We also provide experimental results to demonstrate the application of NFT in typical scenarios with varying levels of knowledge about the acting group.