# Learning Relevant Features of Data with Multi-scale Tensor Networks

arXiv: https://arxiv.org/abs/1801.00315 · HTML: https://mlsanity.com/paper/1801.00315/

## Key facts

- Cited by 51 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Dec 2017.

## Built on by (most cited first, 30 of 51)

- [Variational Quantum Reinforcement Learning via Evolutionary Optimization](https://mlsanity.com/paper/2109.00540/) (2021)
- [Enhancing Generative Models via Quantum Correlations](https://mlsanity.com/paper/2101.08354/) (2021)
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- [Implicit Regularization in Hierarchical Tensor Factorization and Deep Convolutional Neural Networks](https://mlsanity.com/paper/2201.11729/) (2022)
- [Tensor networks for unsupervised machine learning](https://mlsanity.com/paper/2106.12974/) (2021)
- [Tensor networks for quantum machine learning](https://mlsanity.com/paper/2303.11735/) (2023)
- [Tensor networks for interpretable and efficient quantum-inspired machine learning](https://mlsanity.com/paper/2311.11258/) (2023)
- [Generative modeling with projected entangled-pair states](https://mlsanity.com/paper/2202.08177/) (2022)
- [Machine learning with tree tensor networks, CP rank constraints, and tensor dropout](https://mlsanity.com/paper/2305.19440/) (2023)
- [Tensor networks and efficient descriptions of classical data](https://mlsanity.com/paper/2103.06872/) (2021)
- [On the Ability of Graph Neural Networks to Model Interactions Between Vertices](https://mlsanity.com/paper/2211.16494/) (2022)
- [Privacy-preserving machine learning with tensor networks](https://mlsanity.com/paper/2202.12319/) (2022)
- [Quantum-Inspired Tensor Neural Networks for Partial Differential Equations](https://mlsanity.com/paper/2208.02235/) (2022)
- [Explainable Natural Language Processing with Matrix Product States](https://mlsanity.com/paper/2112.08628/) (2021)
- [Probabilistic Graphical Models and Tensor Networks: A Hybrid Framework](https://mlsanity.com/paper/2106.15666/) (2021)
- [Entangled q-Convolutional Neural Nets](https://mlsanity.com/paper/2103.11785/) (2021)
- [Interaction Decompositions for Tensor Network Regression](https://mlsanity.com/paper/2208.06029/) (2022)
- [Combining Reinforcement Learning and Tensor Networks, with an Application to Dynamical Large Deviations](https://mlsanity.com/paper/2209.14089/) (2022)
- [What Makes Data Suitable for a Locally Connected Neural Network? A Necessary and Sufficient Condition Based on Quantum Entanglement](https://mlsanity.com/paper/2303.11249/) (2023)
- [Ultra-low latency quantum-inspired machine learning predictors implemented on FPGA](https://mlsanity.com/paper/2409.16075/) (2024)
- [Positive unlabeled learning with tensor networks](https://mlsanity.com/paper/2211.14085/) (2022)
- [Tensor-Networks-based Learning of Probabilistic Cellular Automata Dynamics](https://mlsanity.com/paper/2404.11768/) (2024)
- [Riemannian Optimization on Tree Tensor Networks with Application in Machine Learning](https://mlsanity.com/paper/2507.21726/) (2025)
- [DisCoCLIP: A Distributional Compositional Tensor Network Encoder for Vision-Language Understanding](https://mlsanity.com/paper/2509.21287/) (2025)
- [Infinitely Wide Tensor Networks as Gaussian Process](https://mlsanity.com/paper/2101.02333/) (2021)
- [Neural Tangent Kernel of Matrix Product States: Convergence and Applications](https://mlsanity.com/paper/2111.14046/) (2021)
- [Deep tensor networks with matrix product operators](https://mlsanity.com/paper/2209.09098/) (2022)
- [Quantum-inspired tensor network for Earth science](https://mlsanity.com/paper/2301.07528/) (2023)
- [Boosting Defect Detection in Manufacturing using Tensor Convolutional Neural Networks](https://mlsanity.com/paper/2401.01373/) (2023)
- [Towards Tensor Network Models for Low-Latency Jet Tagging on FPGAs](https://mlsanity.com/paper/2601.10801/) (2026)

## Abstract (arXiv)

Inspired by coarse-graining approaches used in physics, we show how similar algorithms can be adapted for data. The resulting algorithms are based on layered tree tensor networks and scale linearly with both the dimension of the input and the training set size. Computing most of the layers with an unsupervised algorithm, then optimizing just the top layer for supervised classification of the MNIST and fashion-MNIST data sets gives very good results. We also discuss mixing a prior guess for supervised weights together with an unsupervised representation of the data, yielding a smaller number of features nevertheless able to give good performance.