Related papers: Cons-training Tensor Networks: Embedding and Optim…

Efficient methods to access the entanglement of a quantum many-body state, where the complexity generally scales exponentially with the system size $N$, have long a concern. Here we propose the Schmidt tensor network state (Schmidt TNS)…

In this era of big data, data analytics and machine learning, it is imperative to find ways to compress large data sets such that intrinsic features necessary for subsequent analysis are not lost. The traditional workhorse for data…

A central primitive in quantum tensor network simulations is the problem of approximating a matrix product state with one of a lower bond dimension. This problem forms the central bottleneck in algorithms for time evolution and for…

Recent work by Wu {\em et al.} [arXiv:1910.11011] proposed a numerical method, so-called matrix product operator-matrix product state (MPO-MPS) method, by which several types of quantum many-body wave functions, in particular, the projected…

Tensor networks (TNs) have become one of the most essential building blocks for various fields of theoretical physics such as condensed matter theory, statistical mechanics, quantum information, and quantum gravity. This review provides a…

Real-world systems are often formulated as constrained optimization problems. Techniques to incorporate constraints into Neural Networks (NN), such as Neural Ordinary Differential Equations (Neural ODEs), have been used. However, these…

Tensor network (TN) techniques - often used in the context of quantum many-body physics - have shown promise as a tool for tackling machine learning (ML) problems. The application of TNs to ML, however, has mostly focused on supervised and…

Tensor network methods have progressed from variational techniques based on matrix-product states able to compute properties of one-dimensional condensed-matter lattice models into methods rooted in more elaborate states such as projected…

Tensor parallelism is an essential technique for distributed training of large neural networks. However, automatically determining an optimal tensor parallel strategy is challenging due to the gigantic search space, which grows…

Tensor network states constitute an important variational set of quantum states for numerical studies of strongly correlated systems in condensed-matter physics, as well as in mathematical physics. This is specifically true for finitely…

We study the conditions under which Matrix Product States (MPS) or Matrix Product Operators are exact eigenvectors of an extensive local operator, such as a Hamiltonian. By suitably choosing the local operator, this covers a wide range of…

Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient…

Training a classifier under non-convex constraints has gotten increasing attention in the machine learning community thanks to its wide range of applications such as algorithmic fairness and class-imbalanced classification. However, several…

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

Numerical simulations are a powerful tool to study quantum systems beyond exactly solvable systems lacking an analytic expression. For one-dimensional entangled quantum systems, tensor network methods, amongst them Matrix Product States…

Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular case of TNS and are used for the simulation of 1+1 dimensional…

A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The…

Deep Neural Networks (DNNs) are increasingly deployed in highly energy-constrained environments such as autonomous drones and wearable devices while at the same time must operate in real-time. Therefore, reducing the energy consumption has…

Deep neural networks have achieved great success in many data processing applications. However, the high computational complexity and storage cost makes deep learning hard to be used on resource-constrained devices, and it is not…

Constrained counting is a fundamental problem in artificial intelligence. A promising new algebraic approach to constrained counting makes use of tensor networks, following a reduction from constrained counting to the problem of…