The mean-field theory of spin glass models has been used as a prototype of systems with frustration and disorder. One of the most interesting related systems are models of associative memories. In these lectures we review the main concepts developed to solve the Sherrington-Kirkpatrick model and ...
Spin glass, the travelling salesman problem, neural networks and all thatTheoretical or Mathematical/ lattice theory and statisticsneural netsrandom processesspin glassesstatistical mechanics/ travelling salesman problemneural networksstatistical mechanicsspin glass...
This book contains most of the invited contributions to the Heidelberg Colloquium on Glassy Dynamics, held in June 1986 and covering the three topics: spin glasses, optimization and neural networks. It includes experimental papers on spin glasses and glasses as well as theoretical work on the spin...
We study a family of diluted attractor neural networks with a finite average number of (symmetric) connections per neuron. As in finite connectivity spin glasses, their equilibrium properties are described by order parameter functions, for which we derive an integral equation in replica symmetric ...
The key technology is machine learning, which is supported by successful examples of the use of deep neural networks (DNNs)1. Deep neural networks have achieved state-of-the-art results in a wide variety of tasks, including computer vision, natural language processing, and reinforcement learning2...
Machine learning plays an increasingly important role in many areas of chemistry and materials science, being used to predict materials properties, accelerate simulations, design new structures, and predict synthesis routes of new materials. Graph neural networks (GNNs) are one of the fastest growing ...
Researchers at the Amazon Quantum Solutions Lab, part of the AWS Intelligent and Advanced Computer Technologies Labs, have recently developed a new tool to tacklecombinatorial optimization problems, based on graph neural networks (GNNs). The approach developed by Schuetz, Brubaker and Katzgraber, publi...
Our approach is broadly applicable to canonical NP-hard problems in the form of quadratic unconstrained binary optimization problems, such as maximum cut, minimum vertex cover, maximum independent set, as well as Ising spin glasses and higher-order generalizations thereof in the form of polynomial ...
Spin-glassesNeural networksReplica symmetryIn this paper we continue our investigation of the analogical neural network, by introducing and studying its replica symmetric approximation in the absence of external fields. Bridging the neural network to a bipartite spin-glass, we introduce and apply a ...
We propose a quantum generalisation of a classical neural network. The classical neurons are firstly rendered reversible by adding ancillary bits. Then they are generalised to being quantum reversible, i.e., unitary (the classical networks we generalise