# Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

arXiv: https://arxiv.org/abs/1708.09165 · HTML: https://mlsanity.com/paper/1708.09165/

## Key facts

- Cited by 54 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Aug 2017.

## Built on by (most cited first, 30 of 54)

- [Tensor Methods in Computer Vision and Deep Learning](https://mlsanity.com/paper/2107.03436/) (2021)
- [Understanding DDPM Latent Codes Through Optimal Transport](https://mlsanity.com/paper/2202.07477/) (2022)
- [Tensor Networks Meet Neural Networks: A Survey and Future Perspectives](https://mlsanity.com/paper/2302.09019/) (2023)
- [Tesseract: Tensorised Actors for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2106.00136/) (2021)
- [Tensor networks for quantum machine learning](https://mlsanity.com/paper/2303.11735/) (2023)
- [Alternating Local Enumeration (TnALE): Solving Tensor Network Structure Search with Fewer Evaluations](https://mlsanity.com/paper/2304.12875/) (2023)
- [Graph Tensor Networks: An Intuitive Framework for Designing Large-Scale Neural Learning Systems on Multiple Domains](https://mlsanity.com/paper/2303.13565/) (2023)
- [Generative Learning of Continuous Data by Tensor Networks](https://mlsanity.com/paper/2310.20498/) (2023)
- [More Efficient Sampling for Tensor Decomposition With Worst-Case Guarantees](https://mlsanity.com/paper/2110.07631/) (2021)
- [Model based Multi-agent Reinforcement Learning with Tensor Decompositions](https://mlsanity.com/paper/2110.14524/) (2021)
- [Tensor networks in machine learning](https://mlsanity.com/paper/2207.02851/) (2022)
- [Rank-R FNN: A Tensor-Based Learning Model for High-Order Data Classification](https://mlsanity.com/paper/2104.05048/) (2021)
- [Tensor-Train Recurrent Neural Networks for Interpretable Multi-Way Financial Forecasting](https://mlsanity.com/paper/2105.04983/) (2021)
- [Reinforcement Learning in Factored Action Spaces using Tensor Decompositions](https://mlsanity.com/paper/2110.14538/) (2021)
- [Quantized Fourier and Polynomial Features for more Expressive Tensor Network Models](https://mlsanity.com/paper/2309.05436/) (2023)
- [tnGPS: Discovering Unknown Tensor Network Structure Search Algorithms via Large Language Models (LLMs)](https://mlsanity.com/paper/2402.02456/) (2024)
- [Entangled q-Convolutional Neural Nets](https://mlsanity.com/paper/2103.11785/) (2021)
- [Marginalizable Density Models](https://mlsanity.com/paper/2106.04741/) (2021)
- [Are Quantum Computers Practical Yet? A Case for Feature Selection in Recommender Systems using Tensor Networks](https://mlsanity.com/paper/2205.04490/) (2022)
- [Position: Tensor Networks are a Valuable Asset for Green AI](https://mlsanity.com/paper/2205.12961/) (2022)
- [Positive unlabeled learning with tensor networks](https://mlsanity.com/paper/2211.14085/) (2022)
- [To Fold or Not to Fold: Graph Regularized Tensor Train for Visual Data Completion](https://mlsanity.com/paper/2306.11123/) (2023)
- [Tensor Network-Constrained Kernel Machines as Gaussian Processes](https://mlsanity.com/paper/2403.19500/) (2024)
- [Protecting Big Data Privacy Using Randomized Tensor Network Decomposition and Dispersed Tensor Computation](https://mlsanity.com/paper/2101.04194/) (2021)
- [Tensor-Train Networks for Learning Predictive Modeling of Multidimensional Data](https://mlsanity.com/paper/2101.09184/) (2021)
- [A Dimensionality Reduction Approach for Convolutional Neural Networks](https://mlsanity.com/paper/2110.09163/) (2021)
- [A rank-adaptive higher-order orthogonal iteration algorithm for truncated Tucker decomposition](https://mlsanity.com/paper/2110.12564/) (2021)
- [TTML: tensor trains for general supervised machine learning](https://mlsanity.com/paper/2203.04352/) (2022)
- [Sampling-Based Decomposition Algorithms for Arbitrary Tensor Networks](https://mlsanity.com/paper/2210.03828/) (2022)
- [Translate your gibberish: black-box adversarial attack on machine translation systems](https://mlsanity.com/paper/2303.10974/) (2023)

## Abstract (arXiv)

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.