Related papers: Stochastically Projecting Tensor Networks
Tensor-network techniques have enjoyed outstanding success in physics, and have recently attracted attention in machine learning, both as a tool for the formulation of new learning algorithms and for enhancing the mathematical understanding…
There has been considerable recent interest in Bayesian modeling of high-dimensional networks via latent space approaches. When the number of nodes increases, estimation based on Markov Chain Monte Carlo can be extremely slow and show poor…
Progress in the application of machine learning techniques to the prediction of solid-state and molecular materials properties has been greatly facilitated by the development state-of-the-art feature representations and novel deep learning…
Low-fidelity analytical models of turbine wakes have traditionally been used for wind farm planning, performance evaluation, and demonstrating the utility of advanced control algorithms in increasing the annual energy production. In…
Tensor regression has shown to be advantageous in learning tasks with multi-directional relatedness. Given massive multiway data, traditional methods are often too slow to operate on or suffer from memory bottleneck. In this paper, we…
Neural-network quantum states (NQS) offer a versatile and expressive alternative to traditional variational ans\"atze for simulating physical systems. Energy-based frameworks, like Hopfield networks and Restricted Boltzmann Machines,…
We first propose the regular sketch-and-project method for solving tensor equations with respect to the popular t-product. Then, three adaptive sampling strategies and three corresponding adaptive sketch-and-project methods are derived. We…
We present a general graph-based Projected Entangled-Pair State (gPEPS) algorithm to approximate ground states of nearest-neighbor local Hamiltonians on any lattice or graph of infinite size. By introducing the structural-matrix which…
We propose a measurement setup reaching Heisenberg scaling precision for the estimation of any distributed parameter $\varphi$ (not necessarily a phase) encoded into a generic $M$-port linear network composed only of passive elements. The…
We investigate quantum-inspired tensor networks (QTNs) for approximating flow maps of hydrodynamic partial differential equations (PDEs). Motivated by the effective low-rank structure that emerges after tensorization of discretized…
In this paper, we propose new learning algorithms for approximating high-dimensional functions using tree tensor networks in a least-squares setting. Given a dimension tree or architecture of the tensor network, we provide an algorithm that…
We present a new method for online prediction and learning of tensors ($N$-way arrays, $N >2$) from sequential measurements. We focus on the specific case of 3-D tensors and exploit a recently developed framework of structured tensor…
We present a brief survey on the modern tensor numerical methods for multidimensional stationary and time-dependent partial differential equations (PDEs). The guiding principle of the tensor approach is the rank-structured separable…
Although tensor networks are powerful tools for simulating low-dimensional quantum physics, tensor network algorithms are very computationally costly in higher spatial dimensions. We introduce quantum gauge networks: a different kind of…
We revisit the accuracy of the variational Monte Carlo (VMC) method by taking an example of ground state properties for the one-dimensional Hubbard model. We start from the variational wave functions with the Gutzwiller and long-range…
In this work, we present the tree tensor network Nystr\"om (TTNN), an algorithm that extends recent research on streamable tensor approximation, such as for Tucker and tensor-train formats, to the more general tree tensor network format,…
Tensor network states form a variational ansatz class widely used, both analytically and numerically, in the study of quantum many-body systems. It is known that if the underlying graph contains a cycle, e.g. as in projected entangled pair…
This article introduces a tensor network subspace algorithm for the identification of specific polynomial state space models. The polynomial nonlinearity in the state space model is completely written in terms of a tensor network, thus…
We propose a new statistical model suitable for machine learning of systems with long distance correlations such as natural languages. The model is based on directed acyclic graph decorated by multi-linear tensor maps in the vertices and…
We use TensorNetwork [C. Roberts et al., arXiv: 1905.01330], a recently developed API for performing tensor network contractions using accelerated backends such as TensorFlow, to implement an optimization algorithm for the Multi-scale…