Related papers: A Spin Glass Characterization of Neural Networks
Understanding the glassy nature of neural networks is pivotal both for theoretical and computational advances in Machine Learning and Theoretical Artificial Intelligence. Keeping the focus on dense associative Hebbian neural networks, the…
Neural networks are nowadays both powerful operational tools (e.g., for pattern recognition, data mining, error correction codes) and complex theoretical models on the focus of scientific investigation. As for the research branch, neural…
In the past decade, significant strides in deep learning have led to numerous groundbreaking applications. Despite these advancements, the understanding of the high generalizability of deep learning, especially in such an over-parametrized…
Some interesting recent advances in the theoretical understanding of neural networks have been informed by results from the physics of disordered many-body systems. Motivated by these findings, this work uses the replica technique to study…
Spin glasses, generally defined as disordered systems with randomized competing interactions, are a widely investigated complex system. Theoretical models describing spin glasses are broadly used in other complex systems, such as those…
We discuss replica symmetry breaking (RSB) in spin glasses. We update work in this area, from both the analytical and numerical points of view. We give particular attention to the difficulties stressed by Newman and Stein concerning the…
The 2024 Nobel Prize in Physics was awarded for pioneering contributions at the intersection of artificial neural networks (ANNs) and spin-glass physics, underscoring the profound connections between these fields. The topological…
In this paper we study, via equilibrium statistical mechanics, the properties of the internal energy of an Hopfield neural network whose patterns are stored continuously (Gaussian distributed). The model is shown to be equivalent to a…
Spin glass theory, as a paradigm for describing disordered magnetic systems, constitutes a prominent subject of study within statistical physics. Replica symmetry breaking (RSB), as one of the pivotal concepts for the understanding of spin…
Recent results are reviewed on both the time evolution and retrieval properties of multi-state neural networks that are based upon spin-glass models. In particular, the properties of models with neuron states having Q-Ising symmetry are…
Spiking neural networks (SNN) are a biologically inspired model of neural networks with certain brain-like properties. In the past few decades, this model has received increasing attention in computer science community, owing also to the…
We explore a one-to-one correspondence between a neural network (NN) and a statistical mechanical spin model where neurons are mapped to Ising spins and weights to spin-spin couplings. The process of training an NN produces a family of spin…
Spin-glasses are universal models that can capture complex behavior of many-body systems at the interface of statistical physics and computer science including discrete optimization, inference in graphical models, and automated reasoning.…
In this paper we continue our investigation on the high storage regime of a neural network with Gaussian patterns. Through an exact mapping between its partition function and one of a bipartite spin glass (whose parties consist of Ising and…
In this work we study numerically a short range p-spin glass model in three dimensions. The behaviour of the model appears to be remarkably different from mean field predictions. In fact it shares some features typical of models with full…
In this work we study numerically the out of equilibrium dynamics of the Hopfield model for associative memory inside its spin-glass phase. Besides its interest as a neural network model it can also be considered as a prototype of fully…
The concept of replica symmetry breaking found in the solution of the mean-field Sherrington-Kirkpatrick spin-glass model has been applied to a variety of problems in science ranging from biological to computational and even financial…
We study the chaotic behavior of the Gibbs state of spin-glasses under the application of an external magnetic field, in the crossover region where the field intensity scales proportional to $1/\sqrt{N}$, being $N$ the system size. We show…
In the present paper, I describe a spiking neural network (SNN) architecture which, can be used in wide range of supervised learning classification tasks. It is assumed, that all participating signals (the classified object description,…
We study the Hopfield model on a random graph in scaling regimes where the average number of connections per neuron is a finite number and where the spin dynamics is governed by a synchronous execution of the microscopic update rule…