# A Multi-Scale Tensor Network Architecture for Classification and Regression

arXiv: https://arxiv.org/abs/2001.08286 · HTML: https://mlsanity.com/paper/2001.08286/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jan 2020.

## Built on by (most cited first, 14 of 14)

- [Tensor networks for quantum machine learning](https://mlsanity.com/paper/2303.11735/) (2023)
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- [Quantum-inspired event reconstruction with Tensor Networks: Matrix Product States](https://mlsanity.com/paper/2106.08334/) (2021)
- [Generative Learning of Continuous Data by Tensor Networks](https://mlsanity.com/paper/2310.20498/) (2023)
- [Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC data](https://mlsanity.com/paper/2202.10471/) (2022)
- [Improvements to Gradient Descent Methods for Quantum Tensor Network Machine Learning](https://mlsanity.com/paper/2203.03366/) (2022)
- [Deep Tree Tensor Networks](https://mlsanity.com/paper/2502.09928/) (2025)
- [Segmenting two-dimensional structures with strided tensor networks](https://mlsanity.com/paper/2102.06900/) (2021)
- [Quantum-inspired Techniques in Tensor Networks for Industrial Contexts](https://mlsanity.com/paper/2404.11277/) (2024)
- [Using matrix-product states for time-series machine learning](https://mlsanity.com/paper/2412.15826/) (2024)
- [T'ecnicas Quantum-Inspired en Tensor Networks para Contextos Industriales](https://mlsanity.com/paper/2404.17645/) (2024)
- [Trainable Quantum Neural Network for Multiclass Image Classification with the Power of Pre-trained Tree Tensor Networks](https://mlsanity.com/paper/2504.14995/) (2025)
- [Hybrid quantum tensor networks for aeroelastic applications](https://mlsanity.com/paper/2508.05169/) (2025)
- [When AI meets quantum information: A comprehensive review](https://mlsanity.com/paper/2607.00365/) (2026)

## Abstract (arXiv)

We present an algorithm for supervised learning using tensor networks, employing a step of preprocessing the data by coarse-graining through a sequence of wavelet transformations. We represent these transformations as a set of tensor network layers identical to those in a multi-scale entanglement renormalization ansatz (MERA) tensor network, and perform supervised learning and regression tasks through a model based on a matrix product state (MPS) tensor network acting on the coarse-grained data. Because the entire model consists of tensor contractions (apart from the initial non-linear feature map), we can adaptively fine-grain the optimized MPS model backwards through the layers with essentially no loss in performance. The MPS itself is trained using an adaptive algorithm based on the density matrix renormalization group (DMRG) algorithm. We test our methods by performing a classification task on audio data and a regression task on temperature time-series data, studying the dependence of training accuracy on the number of coarse-graining layers and showing how fine-graining through the network may be used to initialize models with access to finer-scale features.