# tntorch: Tensor Network Learning with PyTorch

arXiv: https://arxiv.org/abs/2206.11128 · HTML: https://mlsanity.com/paper/2206.11128/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 29 references that are in the map.
- First posted on arXiv 22 Jun 2022.

## Builds on (most cited first, 15 of 15)

- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [TensorLy: Tensor Learning in Python](https://mlsanity.com/paper/1610.09555/) (2016)
- [A Tensorized Transformer for Language Modeling](https://mlsanity.com/paper/1906.09777/) (2019)
- [Tensor Methods in Computer Vision and Deep Learning](https://mlsanity.com/paper/2107.03436/) (2021)
- [Factorized Higher-Order CNNs with an Application to Spatio-Temporal Emotion Estimation](https://mlsanity.com/paper/1906.06196/) (2019)
- [Scalable Gaussian Processes with Billions of Inducing Inputs via Tensor Train Decomposition](https://mlsanity.com/paper/1710.07324/) (2017)
- [Tensorized Embedding Layers for Efficient Model Compression](https://mlsanity.com/paper/1901.10787/) (2019)
- [TensorNetwork: A Library for Physics and Machine Learning](https://mlsanity.com/paper/1905.01330/) (2019)
- [TTOpt: A Maximum Volume Quantized Tensor Train-based Optimization and its Application to Reinforcement Learning](https://mlsanity.com/paper/2205.00293/) (2022)
- [Hyperspectral Super-Resolution via Coupled Tensor Ring Factorization](https://mlsanity.com/paper/2001.01547/) (2020)
- [Kronecker CP Decomposition with Fast Multiplication for Compressing RNNs](https://mlsanity.com/paper/2008.09342/) (2020)
- [A Prior of a Googol Gaussians: a Tensor Ring Induced Prior for Generative Models](https://mlsanity.com/paper/1910.13148/) (2019)
- [TedNet: A Pytorch Toolkit for Tensor Decomposition Networks](https://mlsanity.com/paper/2104.05018/) (2021)
- [MUSCO: Multi-Stage Compression of neural networks](https://mlsanity.com/paper/1903.09973/) (2019)
- [Cherry-Picking Gradients: Learning Low-Rank Embeddings of Visual Data via Differentiable Cross-Approximation](https://mlsanity.com/paper/2105.14250/) (2021)

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

- [Tensor Networks Meet Neural Networks: A Survey and Future Perspectives](https://mlsanity.com/paper/2302.09019/) (2023)
- [TT-NF: Tensor Train Neural Fields](https://mlsanity.com/paper/2209.15529/) (2022)
- [tn4ml: Tensor Network Training and Customization for Machine Learning](https://mlsanity.com/paper/2502.13090/) (2025)
- [Tensorization of neural networks for improved privacy and interpretability](https://mlsanity.com/paper/2501.06300/) (2025)
- [T4DT: Tensorizing Time for Learning Temporal 3D Visual Data](https://mlsanity.com/paper/2208.01421/) (2022)
- [Leveraging Digital Perceptual Technologies for Remote Perception and Analysis of Human Biomechanical Processes: A Contactless Approach for Workload and Joint Force Assessment](https://mlsanity.com/paper/2404.01576/) (2024)
- [Quantum-inspired tensor networks in machine learning models](https://mlsanity.com/paper/2604.14287/) (2026)

## Abstract (arXiv)

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.