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Backtracking has been widely used for solving problems in artificial intelligence (AI), including constraint satisfaction problems and combinatorial optimization problems. Good branching heuristics can efficiently improve the performance of…

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost…

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…

This paper explores the application of tensor networks (TNs) to the simulation of material deformations within the framework of linear elasticity. Material simulations are essential computational tools extensively used in both academic…

We provide a simple new randomized contraction approach to the global minimum cut problem for simple undirected graphs. The contractions exploit 2-out edge sampling from each vertex rather than the standard uniform edge sampling. We…

There is a significant expansion in both volume and range of applications along with the concomitant increase in the variety of data sources. These ever-expanding trends have highlighted the necessity for more versatile analysis tools that…

We propose a neural embedding algorithm called Network Vector, which learns distributed representations of nodes and the entire networks simultaneously. By embedding networks in a low-dimensional space, the algorithm allows us to compare…

This work discusses tensor network embeddings, which are random matrices ($S$) with tensor network structure. These embeddings have been used to perform dimensionality reduction of tensor network structured inputs $x$ and accelerate…

We introduce complex-valued tensor network models for sequence processing motivated by correspondence to probabilistic graphical models, interpretability and resource compression. Inductive bias is introduced to our models via network…

Belief Propagation is a well-studied message-passing algorithm that runs over graphical models and can be used for approximate inference and approximation of local marginals. The resulting approximations are equivalent to the Bethe-Peierls…

Given a network, the critical node detection problem finds a subset of nodes whose removal disrupts the network connectivity. Since many real-world systems are naturally modeled as graphs, assessing the vulnerability of the network is…

Modern quantum optical systems such as photonic quantum computers and quantum imaging devices require great precision in their designs and implementations in the hope to realistically exploit entanglement and reach a real quantum advantage.…

Tensor network methods are a conceptually elegant framework for encoding complicated datasets, where high-order tensors are approximated as networks of low-order tensors. In practice, however, the numeric implementation of tensor network…

Theoretical neuroscientists often try to understand how the structure of a neural network relates to its function by focusing on structural features that would either follow from optimization or occur consistently across possible…

We present an overview of the key ideas and skills necessary to begin implementing tensor network methods numerically, which is intended to facilitate the practical application of tensor network methods for researchers that are already…

We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based…

Large-scale tensor network simulations are crucial for developing robust complexity-theoretic bounds on classical quantum simulation, enabling circuit cutting approaches, and optimizing circuit compilation, all of which aid efficient…

Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. In a recent paper [arXiv:0907.2994v1] we discussed how to…

Combinatorial optimization is of general interest for both theoretical study and real-world applications. Fast-developing quantum algorithms provide a different perspective on solving combinatorial optimization problems. In this paper, we…

Classical simulations of quantum circuits play a vital role in the development of quantum computers and for taking the temperature of the field. Here, we classically simulate various physically-motivated circuits using 2D tensor network…