# TensorLy: Tensor Learning in Python

arXiv: https://arxiv.org/abs/1610.09555 · HTML: https://mlsanity.com/paper/1610.09555/

## Key facts

- Cited by 104 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2016.

## Built on by (most cited first, 30 of 104)

- [Multi-Grid Tensorized Fourier Neural Operator for High-Resolution PDEs](https://mlsanity.com/paper/2310.00120/) (2023)
- [Tensor Methods in Computer Vision and Deep Learning](https://mlsanity.com/paper/2107.03436/) (2021)
- [A Library for Learning Neural Operators](https://mlsanity.com/paper/2412.10354/) (2024)
- [Tensor Networks Meet Neural Networks: A Survey and Future Perspectives](https://mlsanity.com/paper/2302.09019/) (2023)
- [Data-driven emergence of convolutional structure in neural networks](https://mlsanity.com/paper/2202.00565/) (2022)
- [PandA: Unsupervised Learning of Parts and Appearances in the Feature Maps of GANs](https://mlsanity.com/paper/2206.00048/) (2022)
- [Tensor and Matrix Low-Rank Value-Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/2201.09736/) (2022)
- [GaLore 2: Large-Scale LLM Pre-Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2504.20437/) (2025)
- [Tensor Component Analysis for Interpreting the Latent Space of GANs](https://mlsanity.com/paper/2111.11736/) (2021)
- [Concept-Based Techniques for "Musicologist-friendly" Explanations in a Deep Music Classifier](https://mlsanity.com/paper/2208.12485/) (2022)
- [Quantum-Inspired Machine Learning: a Survey](https://mlsanity.com/paper/2308.11269/) (2023)
- [TensorLLM: Tensorising Multi-Head Attention for Enhanced Reasoning and Compression in LLMs](https://mlsanity.com/paper/2501.15674/) (2025)
- [TedNet: A Pytorch Toolkit for Tensor Decomposition Networks](https://mlsanity.com/paper/2104.05018/) (2021)
- [HEAT: Hardware-Efficient Automatic Tensor Decomposition for Transformer Compression](https://mlsanity.com/paper/2211.16749/) (2022)
- [Guaranteed Approximation Bounds for Mixed-Precision Neural Operators](https://mlsanity.com/paper/2307.15034/) (2023)
- [Uncovering audio patterns in music with Nonnegative Tucker Decomposition for structural segmentation](https://mlsanity.com/paper/2104.08580/) (2021)
- [Beyond Smoothness: Incorporating Low-Rank Analysis into Nonparametric Density Estimation](https://mlsanity.com/paper/2204.00930/) (2022)
- [tntorch: Tensor Network Learning with PyTorch](https://mlsanity.com/paper/2206.11128/) (2022)
- [TT-NF: Tensor Train Neural Fields](https://mlsanity.com/paper/2209.15529/) (2022)
- [Laplacian Change Point Detection for Single and Multi-view Dynamic Graphs](https://mlsanity.com/paper/2302.01204/) (2023)
- [Automatic differentiation for Riemannian optimization on low-rank matrix and tensor-train manifolds](https://mlsanity.com/paper/2103.14974/) (2021)
- [Subquadratic Kronecker Regression with Applications to Tensor Decomposition](https://mlsanity.com/paper/2209.04876/) (2022)
- [TensorGRaD: Tensor Gradient Robust Decomposition for Memory-Efficient Neural Operator Training](https://mlsanity.com/paper/2501.02379/) (2025)
- [Identifying Misinformation from Website Screenshots](https://mlsanity.com/paper/2102.07849/) (2021)
- [Implicit Regularization in Deep Tensor Factorization](https://mlsanity.com/paper/2105.01346/) (2021)
- [Fast Low-Rank Tensor Decomposition by Ridge Leverage Score Sampling](https://mlsanity.com/paper/2107.10654/) (2021)
- [Cost-efficient Gaussian Tensor Network Embeddings for Tensor-structured Inputs](https://mlsanity.com/paper/2205.13163/) (2022)
- [SiBBlInGS: Similarity-driven Building-Block Inference using Graphs across States](https://mlsanity.com/paper/2306.04817/) (2023)
- [A Joint Matrix Factorization Analysis of Multilingual Representations](https://mlsanity.com/paper/2310.15513/) (2023)
- [TRAWL: Tensor Reduced and Approximated Weights for Large Language Models](https://mlsanity.com/paper/2406.17261/) (2024)

## Abstract (arXiv)

Tensors are higher-order extensions of matrices. While matrix methods form the cornerstone of machine learning and data analysis, tensor methods have been gaining increasing traction. However, software support for tensor operations is not on the same footing. In order to bridge this gap, we have developed TensorLy, a high-level API for tensor methods and deep tensorized neural networks in Python. TensorLy aims to follow the same standards adopted by the main projects of the Python scientific community, and seamlessly integrates with them. Its BSD license makes it suitable for both academic and commercial applications. TensorLy's backend system allows users to perform computations with NumPy, MXNet, PyTorch, TensorFlow and CuPy. They can be scaled on multiple CPU or GPU machines. In addition, using the deep-learning frameworks as backend allows users to easily design and train deep tensorized neural networks. TensorLy is available at https://github.com/tensorly/tensorly