TT-NF: Tensor Train Neural Fields

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.Comment: Preprint, under revie

T4DT: Tensorizing Time for Learning Temporal 3D Visual Data

Unlike 2D raster images, there is no single dominant representation for 3D visual data processing. Different formats like point clouds, meshes, or implicit functions each have their strengths and weaknesses. Still, grid representations such as signed distance functions have attractive properties also in 3D. In particular, they offer constant-time random access and are eminently suitable for modern machine learning. Unfortunately, the storage size of a grid grows exponentially with its dimension. Hence they often exceed memory limits even at moderate resolution. This work explores various low-rank tensor formats, including the Tucker, tensor train, and quantics tensor train decompositions, to compress time-varying 3D data. Our method iteratively computes, voxelizes, and compresses each frame's truncated signed distance function and applies tensor rank truncation to condense all frames into a single, compressed tensor that represents the entire 4D scene. We show that low-rank tensor compression is extremely compact to store and query time-varying signed distance functions. It significantly reduces the memory footprint of 4D scenes while surprisingly preserving their geometric quality. Unlike existing iterative learning-based approaches like DeepSDF and NeRF, our method uses a closed-form algorithm with theoretical guarantees

tntorch: Tensor Network Learning with PyTorch

We present tntorch, a tensor learning framework that supports multiple decompositions (including Candecomp/Parafac, Tucker, and Tensor Train) under a unified interface. With our library, the user can learn and handle low-rank tensors with automatic differentiation, seamless GPU support, and the convenience of PyTorch's API. Besides decomposition algorithms, tntorch implements differentiable tensor algebra, rank truncation, cross-approximation, batch processing, comprehensive tensor arithmetics, and more.ISSN:1532-4435ISSN:1533-792

Cherry-Picking Gradients: Learning Low-Rank Embeddings of Visual Data via Differentiable Cross-Approximation

We propose an end-to-end trainable framework that processes large-scale visual data tensors by looking at a fraction of their entries only. Our method combines a neural network encoder with a tensor train decomposition to learn a low-rank latent encoding, coupled with cross-approximation (CA) to learn the representation through a subset of the original samples. CA is an adaptive sampling algorithm that is native to tensor decompositions and avoids working with the full high-resolution data explicitly. Instead, it actively selects local representative samples that we fetch out-of-core and on-demand. The required number of samples grows only logarithmically with the size of the input. Our implicit representation of the tensor in the network enables processing large grids that could not be otherwise tractable in their uncompressed form. The proposed approach is particularly useful for large-scale multidimensional grid data (e.g., 3D tomography), and for tasks that require context over a large receptive field (e.g., predicting the medical condition of entire organs). The code is available at https://github.com/aelphy/c-pic