  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.
