# TT-NF: Tensor Train Neural Fields

arXiv: https://arxiv.org/abs/2209.15529 · HTML: https://mlsanity.com/paper/2209.15529/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 72 references that are in the map.
- First posted on arXiv 30 Sep 2022.

## Builds on (most cited first, 30 of 33)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [Direct Voxel Grid Optimization: Super-fast Convergence for Radiance Fields Reconstruction](https://mlsanity.com/paper/2111.11215/) (2021)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Baking Neural Radiance Fields for Real-Time View Synthesis](https://mlsanity.com/paper/2103.14645/) (2021)
- [Speeding up Convolutional Neural Networks with Low Rank Expansions](https://mlsanity.com/paper/1405.3866/) (2014)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [Speeding-up Convolutional Neural Networks Using Fine-tuned CP-Decomposition](https://mlsanity.com/paper/1412.6553/) (2014)
- [Implicit Neural Representations for Image Compression](https://mlsanity.com/paper/2112.04267/) (2021)
- [NeRS: Neural Reflectance Surfaces for Sparse-view 3D Reconstruction in the Wild](https://mlsanity.com/paper/2110.07604/) (2021)
- [TensorLy: Tensor Learning in Python](https://mlsanity.com/paper/1610.09555/) (2016)
- [AI Benchmark: All About Deep Learning on Smartphones in 2019](https://mlsanity.com/paper/1910.06663/) (2019)
- [Learning Signed Distance Field for Multi-view Surface Reconstruction](https://mlsanity.com/paper/2108.09964/) (2021)
- [Pix2NeRF: Unsupervised Conditional π-GAN for Single Image to Neural Radiance Fields Translation](https://mlsanity.com/paper/2202.13162/) (2022)
- [Learning Filter Basis for Convolutional Neural Network Compression](https://mlsanity.com/paper/1908.08932/) (2019)
- [Ultimate tensorization: compressing convolutional and FC layers alike](https://mlsanity.com/paper/1611.03214/) (2016)
- [Tensor Methods in Computer Vision and Deep Learning](https://mlsanity.com/paper/2107.03436/) (2021)
- [Wide Compression: Tensor Ring Nets](https://mlsanity.com/paper/1802.09052/) (2018)
- [Reparameterizing Convolutions for Incremental Multi-Task Learning without Task Interference](https://mlsanity.com/paper/2007.12540/) (2020)
- [TTHRESH: Tensor Compression for Multidimensional Visual Data](https://mlsanity.com/paper/1806.05952/) (2018)
- [T-Net: Parametrizing Fully Convolutional Nets with a Single High-Order Tensor](https://mlsanity.com/paper/1904.02698/) (2019)
- [T-Basis: a Compact Representation for Neural Networks](https://mlsanity.com/paper/2007.06631/) (2020)
- [Optimal High-order Tensor SVD via Tensor-Train Orthogonal Iteration](https://mlsanity.com/paper/2010.02482/) (2020)
- [tntorch: Tensor Network Learning with PyTorch](https://mlsanity.com/paper/2206.11128/) (2022)

## Built on by (most cited first, 7 of 7)

- [DiffDreamer: Towards Consistent Unsupervised Single-view Scene Extrapolation with Conditional Diffusion Models](https://mlsanity.com/paper/2211.12131/) (2022)
- [Strivec: Sparse Tri-Vector Radiance Fields](https://mlsanity.com/paper/2307.13226/) (2023)
- [Breathing New Life into 3D Assets with Generative Repainting](https://mlsanity.com/paper/2309.08523/) (2023)
- [Towards Practical Control of Singular Values of Convolutional Layers](https://mlsanity.com/paper/2211.13771/) (2022)
- [Canonical Factors for Hybrid Neural Fields](https://mlsanity.com/paper/2308.15461/) (2023)
- [Decomposition Ascribed Synergistic Learning for Unified Image Restoration](https://mlsanity.com/paper/2308.00759/) (2023)
- [Squeeze3D: Extreme Neural Compression with Latent Space Bridging](https://mlsanity.com/paper/2506.07932/) (2025)

## Abstract (arXiv)

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.