Neural Fourier Transform: A General Approach to Equivariant Representation Learning

Masanori Koyama, Kenji Fukumizu, Kohei Hayashi, Takeru Miyato

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Keywords: Fourier transform, equivariance, harmonic analysis, representation learning

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TL;DR: We present Neural Fourier Transform, a general framework of equivariance learning that does not assume any explicit knowledge of how the group acts on data.

Abstract:

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.

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Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

Submission Number: 5155