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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…
With the increasing adoption of machine learning tools like neural networks across several domains, interesting connections and comparisons to concepts from other domains are coming to light. In this work, we focus on the class of Tensor…
Tensor networks are factorisations of high rank tensors into networks of lower rank tensors and have primarily been used to analyse quantum many-body problems. Tensor networks have seen a recent surge of interest in relation to supervised…
The recently introduced locally orderless tensor network (LoTeNet) for supervised image classification uses matrix product state (MPS) operations on grids of transformed image patches. The resulting patch representations are combined back…
Matrix product states (MPS), a tensor network designed for one-dimensional quantum systems, has been recently proposed for generative modeling of natural data (such as images) in terms of `Born machine'. However, the exponential decay of…
Modern approaches to generative modeling of continuous data using tensor networks incorporate compression layers to capture the most meaningful features of high-dimensional inputs. These methods, however, rely on traditional Matrix Product…
Tensor networks, a model that originated from quantum physics, has been gradually generalized as efficient models in machine learning in recent years. However, in order to achieve exact contraction, only tree-like tensor networks such as…
Tensor networks, which are originally developed for characterizing complex quantum many-body systems, have recently emerged as a powerful framework for capturing high-dimensional probability distributions with strong physical…
Quantum machine learning (QML) is a rapidly expanding field that merges the principles of quantum computing with the techniques of machine learning. One of the powerful mathematical frameworks in this domain is tensor networks. These…
Tensor networks are efficient representations of high-dimensional tensors which have been very successful for physics and mathematics applications. We demonstrate how algorithms for optimizing such networks can be adapted to supervised…
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.…
This paper introduces matrix product state (MPS) decomposition as a computational tool for extracting features of multidimensional data represented by higher-order tensors. Regardless of tensor order, MPS extracts its relevant features to…
Tensor networks are a powerful modeling framework developed for computational many-body physics, which have only recently been applied within machine learning. In this work we utilize a uniform matrix product state (u-MPS) model for…
Tensor networks establish an adaptable framework for the emulation of quantum circuits. By partitioning exponentially large registers and gates into smaller tensors, this unlocks fast transformations through tensor algebra, and grants fine…
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,…
This paper introduces matrix product state (MPS) decomposition as a new and systematic method to compress multidimensional data represented by higher-order tensors. It solves two major bottlenecks in tensor compression: computation and…
Deep learning based models, generally, require a large number of samples for appropriate training, a requirement that is difficult to satisfy in the medical field. This issue can usually be avoided with a proper initialization of the…
Tensor network, which originates from quantum physics, is emerging as an efficient tool for classical and quantum machine learning. Nevertheless, there still exists a considerable accuracy gap between tensor network and the sophisticated…
Tensor networks, originally designed to address computational problems in quantum many-body physics, have recently been applied to machine learning tasks. However, compared to quantum physics, where the reasons for the success of 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…