Related papers: Ising models of deep neural networks
It is well established that neural networks with deep architectures perform better than shallow networks for many tasks in machine learning. In statistical physics, while there has been recent interest in representing physical data with…
We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e.,…
Network science provides very powerful tools for extracting information from interacting data. Although recently the unsupervised detection of phases of matter using machine learning has raised significant interest, the full prediction…
Whether deep neural networks can exhibit emergent behaviour is not only relevant for understanding how deep learning works, it is also pivotal for estimating potential security risks of increasingly capable artificial intelligence systems.…
Over the past several years, there have been many studies demonstrating the ability of deep neural networks to identify phase transitions in many physical systems, notably in classical statistical physics systems. One often finds that the…
A thermodynamically motivated neural network model is described that self-organizes to transport charge associated with internal and external potentials while in contact with a thermal reservoir. The model integrates techniques for rapid,…
The Ising model in small-world networks generated from two- and three-dimensional regular lattices has been studied. Monte Carlo simulations were carried out to characterize the ferromagnetic transition appearing in these systems. In the…
Computation with the Ising model is central to future computing technologies like quantum annealing, adiabatic quantum computing, and thermodynamic classical computing. Traditionally, computed values have been equated with ground states.…
We introduce varying spin strengths to the Ising model, a central pillar of statistical physics. With inhomogeneous physical systems in mind, but also anticipating interdisciplinary applications, we present the model on network structures…
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…
We consider Ising model on edge-dual of uncorrelated random networks with arbitrary degree distribution. These networks have a finite clustering in the thermodynamic limit. High and low temperature expansions of Ising model on the edge-dual…
Dynamic networks are structured interconnections of dynamical systems (modules) driven by external excitation and disturbance signals. In order to identify their dynamical properties and/or their topology consistently from measured data, we…
We demonstrate the capability of a convolutional deep neural network in predicting the nearest-neighbor energy of the 4x4 Ising model. Using its success at this task, we motivate the study of the larger 8x8 Ising model, showing that the…
We study a model for a statistical network formed by interactions between its nodes and links. Each node can be in one of two states (Ising spin up or down) and the node-link interaction facilitates linking between the like nodes. For high…
Neural networks are known to be effective function approximators. Recently, deep neural networks have proven to be very effective in pattern recognition, classification tasks and human-level control to model highly nonlinear realworld…
Equations of State model relations between thermodynamic variables and are ubiquitous in scientific modelling, appearing in modern day applications ranging from Astrophysics to Climate Science. The three desired properties of a general…
Multilayer networks provide a framework to study complex systems with multiple types of interactions, multiple dynamical processes, and/or multiple subsystems. When studying a dynamical process on a multilayer network, it is important to…
This article describes a complex network model whose weights are proportional to the difference between uniformly distributed ``fitness'' values assigned to the nodes. It is shown both analytically and experimentally that the strength…
An information theoretic approach inspired by quantum statistical mechanics was recently proposed as a means to optimize network models and to assess their likelihood against synthetic and real-world networks. Importantly, this method does…
Understanding the training dynamics of deep neural networks remains a major open problem, with physics-inspired approaches offering promising insights. Building on this perspective, we develop a thermodynamic framework to describe the…