Related papers: Renormalization of tensor networks using graph ind…
Deep unfolding methods---for example, the learned iterative shrinkage thresholding algorithm (LISTA)---design deep neural networks as learned variations of optimization methods. These networks have been shown to achieve faster convergence…
The Renormalization Group is crucial for understanding systems across scales, including complex networks. Renormalizing networks via network geometry, a framework in which their topology is based on the location of nodes in a hidden metric…
This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…
We propose a scalable tensorization framework for neural network compression based on slice-wise feature distillation. Unlike conventional tensor decomposition methods that rely on costly global finetuning, our approach decomposes the…
The full-density-matrix numerical renormalization group (NRG) has evolved as a systematic and transparent setting for the cal- culation of thermodynamical quantities at arbitrary temperatures within the NRG framework. It directly evaluates…
Graph reconstruction can efficiently detect the underlying topology of massive networks such as the Internet. Given a query oracle and a set of nodes, the goal is to obtain the edge set by performing as few queries as possible. An algorithm…
We continue our study of rigorous renormalization group (RG) maps for tensor networks that was begun in arXiv:2107.11464. In this paper we construct a rigorous RG map for 2D tensor networks whose domain includes tensors that represent the…
We introduce a method for extracting meaningful entanglement measures of tensor network states in general dimensions. Current methods require the explicit reconstruction of the density matrix, which is highly demanding, or the contraction…
In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model…
Contracting tensor networks is often computationally demanding. Well-designed contraction sequences can dramatically reduce the contraction cost. We explore the performance of simulated annealing and genetic algorithms, two common discrete…
The higher-order tensor renormalization group (HOTRG) is a fundamental method to calculate the physical quantities by using a tensor network representation. This method is based on the singular value decomposition (SVD) to take the…
In the framework of tensor spaces, we consider orthogonalization kernels to generate an orthogonal basis of a tensor subspace from a set of linearly independent tensors. In particular, we experimentally study the loss of orthogonality of…
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…
The era of data deluge has sparked the interest in graph-based learning methods in a number of disciplines such as sociology, biology, neuroscience, or engineering. In this paper, we introduce a graph recurrent neural network (GRNN) for…
Traditional network analysis focuses on single-layer networks, real-world systems often form multilayer networks with multiple relationship types. However, existing methods typically fail to capture complex inter-layer dependencies by…
Graph Neural Networks (GNNs) have demonstrated significant achievements in processing graph data, yet scalability remains a substantial challenge. To address this, numerous graph coarsening methods have been developed. However, most…
Network backbones provide useful sparse representations of weighted networks by keeping only their most important links, permitting a range of computational speedups and simplifying network visualizations. A key limitation of existing…
The evaluation of partition functions is a central problem in statistical physics. For lattice systems and other discrete models the partition function may be expressed as the contraction of a tensor network. Unfortunately computing such…
Recently, there has been a growing interest in efficient numerical algorithms based on tensor networks and low-rank techniques to approximate high-dimensional functions and solutions to high-dimensional PDEs. In this paper, we propose a new…
We consider the problem of optimally allocating resources across a set of transmitters and receivers in a wireless network. The resulting optimization problem takes the form of constrained statistical learning, in which solutions can be…