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.

@article{obukhov2022ttnf,
  author = {Obukhov, Anton and Usvyatsov, Mikhail and Sakaridis, Christos and Schindler, Konrad and Van Gool, Luc},
  journal = {IEEE Journal of Selected Topics in Signal Processing},
  title = {TT-NF: Tensor Train Neural Fields},
  year = {2024},
  pages = {1-13},
  doi = {10.1109/JSTSP.2024.3454980}
}