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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…

Disordered Systems and Neural Networks · Physics 2012-09-28 Elena Agliari , Lorenzo Asti , Adriano Barra , Raffaella Burioni , Guido Uguzzoni

The Hopfield recurrent neural network is a classical auto-associative model of memory, in which collections of symmetrically-coupled McCulloch-Pitts neurons interact to perform emergent computation. Although previous researchers have…

Adaptation and Self-Organizing Systems · Physics 2015-06-09 Christopher Hillar , Ngoc M. Tran

Restricted Boltzmann Machines are key tools in Machine Learning and are described by the energy function of bipartite spin-glasses. From a statistical mechanical perspective, they share the same Gibbs measure of Hopfield networks for…

Mathematical Physics · Physics 2017-08-02 Elena Agliari , Adriano Barra , Chiara Longo , Daniele Tantari

A spontaneously active neural system that is capable of continual learning should also be capable of homeostasis of both firing rate and connectivity. Experimental evidence suggests that both types of homeostasis exist, and that…

Neurons and Cognition · Quantitative Biology 2007-10-15 David Hsu , Aonan Tang , Murielle Hsu , John M. Beggs

In this paper we introduce and exploit the real replica approach for a minimal generalization of the Hopfield model, by assuming the learned patterns to be distributed accordingly to a standard unit Gaussian. We consider the high storage…

Disordered Systems and Neural Networks · Physics 2009-11-19 Adriano Barra , Francesco Guerra

We introduce and study a new model of interacting neural networks, incorporating the spatial dimension (e.g. position of neurons across the cortex) and some learning processes. The dynamic of each neural network is described via the elapsed…

Analysis of PDEs · Mathematics 2020-09-03 Delphine Salort , Nicolas Torres

Neuromorphic computing with spiking neural networks is promising for energy-efficient artificial intelligence (AI) applications. However, different from humans who continually learn different tasks in a lifetime, neural network models…

Neural and Evolutionary Computing · Computer Science 2024-02-20 Mingqing Xiao , Qingyan Meng , Zongpeng Zhang , Di He , Zhouchen Lin

In this work we develop analytical techniques to investigate a broad class of associative neural networks set in the high-storage regime. These techniques translate the original statistical-mechanical problem into an analytical-mechanical…

Disordered Systems and Neural Networks · Physics 2020-04-17 Elena Agliari , Francesco Alemanno , Adriano Barra , Alberto Fachechi

Hopfield networks are an attractive choice for solving many types of computational problems because they provide a biologically plausible mechanism. The Self-Optimization (SO) model adds to the Hopfield network by using a biologically…

Adaptation and Self-Organizing Systems · Physics 2024-03-06 Natalya Weber , Werner Koch , Ozan Erdem , Tom Froese

In this work we study a Hebbian neural network, where neurons are arranged according to a hierarchical architecture such that their couplings scale with their reciprocal distance. As a full statistical mechanics solution is not yet…

Disordered Systems and Neural Networks · Physics 2016-01-26 Elena Agliari , Adriano Barra , Andrea Galluzzi , Francesco Guerra , Daniele Tantari , Flavia Tavani

Recently, the original storage prescription for the Hopfield model of neural networks -- as well as for its dense generalizations -- has been turned into a genuine Hebbian learning rule by postulating the expression of its Hamiltonian for…

Disordered Systems and Neural Networks · Physics 2024-10-04 Linda Albanese , Adriano Barra , Pierluigi Bianco , Fabrizio Durante , Diego Pallara

When an object moves smoothly across a field of view, the identify of the object is unchanged, but the activation pattern of the photoreceptors on the retina changes drastically. One of the major computational roles of our visual system is…

Neurons and Cognition · Quantitative Biology 2014-04-23 Minjoon Kouh

The aim of the present paper is to study the effects of Hebbian learning in random recurrent neural networks with biological connectivity, i.e. sparse connections and separate populations of excitatory and inhibitory neurons. We furthermore…

Neurons and Cognition · Quantitative Biology 2007-06-19 Benoit Siri , Mathias Quoy , Bruno Delord , Bruno Cessac , Hugues Berry

Theoretical models of neuronal function consider different mechanisms through which networks learn, classify and discern inputs. A central focus of these models is to understand how associations are established amongst neurons, in order to…

Neurons and Cognition · Quantitative Biology 2015-05-19 Harold P. de Vladar , Eörs Szathmáry

In this work we reevaluate and elaborate Crick-Mitchison's proposal that REM-sleep corresponds to a self-organized process for unlearning attractors in neural networks. This reformulation is made at the face of recent findings concerning…

Disordered Systems and Neural Networks · Physics 2010-07-13 Osame Kinouchi , Renato Rodrigues Kinouchi

Understanding the theoretical foundations of how memories are encoded and retrieved in neural populations is a central challenge in neuroscience. A popular theoretical scenario for modeling memory function is the attractor neural network…

Neurons and Cognition · Quantitative Biology 2016-02-17 Alireza Alemi , Carlo Baldassi , Nicolas Brunel , Riccardo Zecchina

We consider dense, associative neural-networks trained by a teacher (i.e., with supervision) and we investigate their computational capabilities analytically, via statistical-mechanics of spin glasses, and numerically, via Monte Carlo…

Disordered Systems and Neural Networks · Physics 2023-08-16 Elena Agliari , Linda Albanese , Francesco Alemanno , Andrea Alessandrelli , Adriano Barra , Fosca Giannotti , Daniele Lotito , Dino Pedreschi

Associative memory is a fundamental function in the brain. Here, we generalize the standard associative memory model to include long-range Hebbian interactions at the learning stage, corresponding to a large synaptic integration window. In…

Disordered Systems and Neural Networks · Physics 2021-12-21 Jianwen Zhou , Zijian Jiang , Tianqi Hou , Ziming Chen , K Y Michael Wong , Haiping Huang

We present results for two different kinds of high order connections between neurons acting as corrections to the Hopfield model. Equilibrium properties are analyzed using the replica mean-field theory and compared with numerical…

Condensed Matter · Physics 2009-10-22 J. J. Arenzon , R. M. C. de Almeida

We present a mathematical analysis of the effects of Hebbian learning in random recurrent neural networks, with a generic Hebbian learning rule including passive forgetting and different time scales for neuronal activity and learning…

Chaotic Dynamics · Physics 2008-04-07 Benoit Siri , Hugues Berry , Bruno Cessac , Bruno Delord , Mathias Quoy