Related papers: From Dyson to Hopfield: Processing on hierarchical…
The modern Hopfield network, proposed by Krotov and Hopfield, is a mathematical generalization of the Hopfield network, which is a basic model of associative memory that employs higher-order interactions. This study introduces an open…
There has been increasing interest in methodologies that incorporate physics priors into neural network architectures to enhance their modeling capabilities. A family of these methodologies that has gained traction are Hamiltonian neural…
Over the past decade, deep neural networks have proven to be adept in image classification tasks, often surpassing humans in terms of accuracy. However, standard neural networks often fail to understand the concept of hierarchical…
Learning and the ability to learn are important factors in development and evolutionary processes [1]. Depending on the level, the complexity of learning can strongly vary. While associative learning can explain simple learning behaviour…
In this work we approach attractor neural networks from a machine learning perspective: we look for optimal network parameters by applying a gradient descent over a regularized loss function. Within this framework, the optimal…
We introduce a general class of mean-field-like spin systems with random couplings that comprises both the Ising model on inhomogeneous dense random graphs and the randomly diluted Hopfield model. We are interested in quantitative estimates…
In this work, we propose a nonlinear stochastic model of a network of stochastic spiking neurons. We heuristically derive the mean-field limit of this system. We then design a Monte Carlo method for the simulation of the microscopic system,…
We consider a generalization of the Hopfield model, where the entries of patterns are Gaussian and diluted. We focus on the high-storage regime and we investigate analytically the topological properties of the emergent network, as well as…
In neural circuits, synaptic strengths influence neuronal activity by shaping network dynamics, and neuronal activity influences synaptic strengths through activity-dependent plasticity. Motivated by this fact, we study a recurrent-network…
Large-scale deep neural networks consume expensive training costs, but the training results in less-interpretable weight matrices constructing the networks. Here, we propose a mode decomposition learning that can interpret the weight…
This work presents a statistical mechanics characterization of neural networks, motivated by the replica symmetry breaking (RSB) phenomenon in spin glasses. A Hopfield-type spin glass model is constructed from a given feedforward neural…
The intricate relations between elements in natural and human-made systems sustain the complex processes that shape our world, forming multiscale networks of interactions. These networks can be represented as graphs composed of nodes…
The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle…
The neuronal paradigm of studying the brain has left us with limitations in both our understanding of how neurons process information to achieve biological intelligence and how such knowledge may be translated into artificial intelligence…
The Hepp-Lieb-Dicke model is ubiquitous in cavity quantum electrodynamics, describing spin-cavity coupling which does not conserve excitation number. Coupling the closed spin-cavity system to an environment realizes the open Dicke model,…
We propose a statistical mechanics approach to a coevolving spin system with an adaptive network of interactions. The dynamics of node states and network connections is driven by both spin configuration and network topology. We consider a…
We study analytically and numerically a Hopfield fully-connected network with $d$-dimensional vector spins. These networks are models of associative memory that generalize the standard Hopfield with Ising spins, where $P$ examples are…
We study the synchronous dynamics of the Hopfield model when a random antisymmetric part is added to the otherwise symmetric synaptic matrix. We use a generating functional technique to derive analytical expressions for the order parameters…
We consider the slow and athermal deformations of amorphous solids and show how the ensuing sequence of discrete plastic rearrangements can be mapped onto a directed network. The network topology reveals a set of highly connected regions…
We present a Hopfield-like autoassociative network for memories representing examples of concepts. Each memory is encoded by two activity patterns with complementary properties. The first is dense and correlated across examples within…