Deep tensor networks with matrix product operators
Not on the map. Why?
Abstract (arXiv)
We introduce deep tensor networks, which are exponentially wide neural networks based on the tensor network representation of the weight matrices. We evaluate the proposed method on the image classification (MNIST, FashionMNIST) and sequence prediction (cellular automata) tasks. In the image classification case, deep tensor networks improve our matrix product state baselines and achieve 0.49% error rate on MNIST and 8.3% error rate on FashionMNIST. In the sequence prediction case, we demonstrate an exponential improvement in the number of parameters compared to the one-layer tensor network methods. In both cases, we discuss the non-uniform and the uniform tensor network models and show that the latter generalizes well to different input sizes.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 34 of its 48 references that are in the map. First posted on arXiv 16 Sep 2022.
Builds on
34 of 48 references.
References · 34
- 2017Attention Is All You Needcited by 59,932
- 2014Going Deeper with Convolutionscited by 4,231
- 2020The effect of data encoding on the expressive power of variational quantum machine learning modelscited by 328
- 2015Tensorizing Neural Networkscited by 246
- 2015On the Expressive Power of Deep Learning: A Tensor Analysiscited by 97
- 2019Tree Tensor Networks for Generative Modelingcited by 63
- 2016Ultimate tensorization: compressing convolutional and FC layers alikecited by 55
- 2019Expressive power of tensor-network factorizations for probabilistic modeling, with applications from hidden Markov models to quantum machine learningcited by 55
- 2017Learning Relevant Features of Data with Multi-scale Tensor Networkscited by 50
- 2017Machine Learning by Unitary Tensor Network of Hierarchical Tree Structurecited by 39
- 2016Supervised Learning with Quantum-Inspired Tensor Networkscited by 35
- 2017Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machinescited by 33
22 more
- 2020Quantum-inspired Machine Learning on high-energy physics datacited by 30
- 2020Supervised Learning with Projected Entangled Pair Statescited by 30
- 2019TensorNetwork for Machine Learningcited by 29
- 2019Tensorized Embedding Layers for Efficient Model Compressioncited by 27
- 2017Equivalence of restricted Boltzmann machines and tensor network statescited by 26
- 2020Anomaly Detection with Tensor Networkscited by 26
- 2017Deep Learning and Quantum Entanglement: Fundamental Connections with Implications to Network Designcited by 22
- 2019Generative Tensor Network Classification Model for Supervised Machine Learningcited by 22
- 2021Tensor networks for unsupervised machine learningcited by 20
- 2019Modeling Sequences with Quantum States: A Look Under the Hoodcited by 19
- 2020Entanglement and Tensor Networks for Supervised Image Classificationcited by 18
- 2021Tensor networks and efficient descriptions of classical datacited by 13
- 2019Probabilistic Modeling with Matrix Product Statescited by 11
- 2017Tensor network language modelcited by 9
- 2020Quantum Tensor Networks, Stochastic Processes, and Weighted Automatacited by 9
- 2020Residual Matrix Product State for Machine Learningcited by 9
- 2021Quantum Tensor Network in Machine Learning: An Application to Tiny Object Classificationcited by 9
- 2020Language Modeling with Reduced Densitiescited by 5
- 2021Tensor network to learn the wavefunction of datacited by 4
- 2020Network Anomaly Detection based on Tensor Decompositioncited by 3
- 2015Enhanced Image Classification With a Fast-Learning Shallow Convolutional Neural Networkcited by 1
- 2017Provably efficient neural network representation for image classificationcited by 1
Built on by
Citing papers per year: 2022: 2.
2 papers.
- 2022Positive unlabeled learning with tensor networks25 Nov 2022
- 2022Grokking phase transitions in learning local rules with gradient descent26 Oct 2022