Related papers: Approximate optimization, sampling and spin-glass …

We consider the task of decentralized minimization of the sum of smooth strongly convex functions stored across the nodes of a network. For this problem, lower bounds on the number of gradient computations and the number of communication…

We demonstrate that a recently introduced heuristic optimization algorithm [Phys. Rev. E 83, 046709 (2011)] that combines a local search with triadic crossover genetic updates is capable of sampling nearly uniformly among ground-state…

In this paper we study the problem of discovering a timeline of events in a temporal network. We model events as dense subgraphs that occur within intervals of network activity. We formulate the event-discovery task as an optimization…

We present a simple algorithm that perfectly samples configurations from the unique Gibbs measure of a spin system on a potentially infinite graph $G$. The sampling algorithm assumes strong spatial mixing together with subexponential growth…

We introduce a change of perspective on tensor network states that is defined by the computational graph of the contraction of an amplitude. The resulting class of states, which we refer to as tensor network functions, inherit the…

We propose that chaotic Glass networks (a class of piecewise-linear Ordinary Differential Equations) are good candidates for the design of true random number generators. A Glass network design has the advantage of involving only standard…

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…

Efficient quantum circuit optimization schemes are central to quantum simulation of strongly interacting quantum many body systems. Here, we present an optimization algorithm which combines machine learning techniques and tensor network…

We propose an efficient meta-algorithm for Bayesian estimation problems that is based on low-degree polynomials, semidefinite programming, and tensor decomposition. The algorithm is inspired by recent lower bound constructions for…

We propose a hybrid quantum-classical algorithm for approximating the ground state of two-dimensional quantum systems using an isometric tensor network ansatz, which maps naturally to quantum circuits. Inspired by the density matrix…

A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions…

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…

The ability to differentiate through optimization problems has unlocked numerous applications, from optimization-based layers in machine learning models to complex design problems formulated as bilevel programs. It has been shown that…

In this paper, we adopt a probability distribution estimation perspective to explore the optimization mechanisms of supervised classification using deep neural networks. We demonstrate that, when employing the Fenchel-Young loss, despite…

In this paper, we propose a method for the approximation of the solution of high-dimensional weakly coercive problems formulated in tensor spaces using low-rank approximation formats. The method can be seen as a perturbation of a minimal…

Deep Neural Networks and Reinforcement Learning methods have empirically shown great promise in tackling challenging combinatorial problems. In those methods a deep neural network is used as a solution generator which is then trained by…

Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the…

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.…

Nearest-neighbor search in large vector databases is crucial for various machine learning applications. This paper introduces a novel method using tensor-train (TT) low-rank tensor decomposition to efficiently represent point clouds and…

Simulation of quantum systems is challenging due to the exponential size of the state space. Tensor networks provide a systematically improvable approximation for quantum states. 2D tensor networks such as Projected Entangled Pair States…