  Learning neural fields has been an active topic in deep learning research,
focusing, among other issues, on finding more compact and easy-to-fit
representations. In this paper, we introduce a novel low-rank representation
termed Tensor Train Neural Fields (TT-NF) for learning neural fields on dense
regular grids and efficient methods for sampling from them. Our representation
is a TT parameterization of the neural field, trained with backpropagation to
minimize a non-convex objective. We analyze the effect of low-rank compression
on the downstream task quality metrics in two settings. First, we demonstrate
the efficiency of our method in a sandbox task of tensor denoising, which
admits comparison with SVD-based schemes designed to minimize reconstruction
error. Furthermore, we apply the proposed approach to Neural Radiance Fields,
where the low-rank structure of the field corresponding to the best quality can
be discovered only through learning.
