TT-NF: Tensor Train Neural Fields
This work addresses the need for more compact and easy-to-fit neural field representations in deep learning, presenting an incremental improvement through a novel low-rank method.
The paper tackles the problem of learning compact neural field representations by introducing Tensor Train Neural Fields (TT-NF), a low-rank parameterization trained with backpropagation, which achieves efficiency in tensor denoising and Neural Radiance Fields, though specific numerical results are not provided.
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.