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Tensor networks provide an efficient approximation of operations involving high dimensional tensors and have been extensively used in modelling quantum many-body systems. More recently, supervised learning has been attempted with tensor…
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…
Gaussian state space models have been used for decades as generative models of sequential data. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption. We introduce a unified…
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…
Tensor networks are efficient factorisations of high-dimensional tensors into a network of lower-order tensors. They have been most commonly used to model entanglement in quantum many-body systems and more recently are witnessing increased…
This work introduces a tensor-based method to perform supervised classification on spatiotemporal data processed in an echo state network. Typically when performing supervised classification tasks on data processed in an echo state network,…
Generative Adversarial Network (GAN) and its variants exhibit state-of-the-art performance in the class of generative models. To capture higher-dimensional distributions, the common learning procedure requires high computational complexity…
State-of-the-art training algorithms for deep learning models are based on stochastic gradient descent (SGD). Recently, many variations have been explored: perturbing parameters for better accuracy (such as in Extragradient), limiting SGD…
Deep learning's success has led to larger and larger models to handle more and more complex tasks; trained models can contain millions of parameters. These large models are compute- and memory-intensive, which makes it a challenge to deploy…
In this study, we introduce a novel family of tensor networks, termed constrained matrix product states (MPS), designed to incorporate exactly arbitrary discrete linear constraints, including inequalities, into sparse block structures.…
We propose a restricted class of tensor network state, built from number-state preserving tensors, for supervised learning tasks. This class of tensor network is argued to be a natural choice for classifiers as (i) they map classical data…
Classification can be performed using either a discriminative or a generative learning approach. Discriminative learning consists of constructing the conditional probability of the outputs given the inputs, while generative learning…
Modeling probability distributions via the wave function of a quantum state is central to quantum-inspired generative modeling and quantum state tomography (QST). We investigate a common failure mode in training randomly initialized matrix…
Principal component analysis, dictionary learning, and auto-encoders are all unsupervised methods for learning representations from a large amount of training data. In all these methods, the higher the dimensions of the input data, the…
This article considers the generative modeling of the (mixed) states of quantum systems, and an approach based on denoising diffusion model is proposed. The key contribution is an algorithmic innovation that respects the physical nature of…
In this paper we present an end-to-end meta-learned system for image compression. Traditional machine learning based approaches to image compression train one or more neural network for generalization performance. However, at inference…
Generative models aim to learn the probability distributions underlying data, enabling the generation of new, realistic samples. Quantum inspired generative models, such as Born machines based on the matrix product state framework, have…
Tensor-network Born machines (TNBMs) are quantum-inspired generative models for learning data distributions. Using tensor-network contraction and optimization techniques, the model learns an efficient representation of the target…
Training neural networks is a challenging non-convex optimization problem, and backpropagation or gradient descent can get stuck in spurious local optima. We propose a novel algorithm based on tensor decomposition for guaranteed training of…
Tensor decomposition is an effective approach to compress over-parameterized neural networks and to enable their deployment on resource-constrained hardware platforms. However, directly applying tensor compression in the training process is…