Related papers: The Ashkin-Teller neural network near saturation
We introduce a machine-learning density-functional-theory formalism for the spinless Hubbard model in one dimension at both zero and finite temperature. In the zero-temperature case this establishes a one-to-one relation between the site…
We consider a multi-layer Sherrington-Kirkpatrick spin-glass as a model for deep restricted Boltzmann machines and we solve for its quenched free energy, in the thermodynamic limit and allowing for a first step of replica symmetry breaking.…
Networks of spiking neurons with adaption have been shown to be able to reproduce a wide range of neural activities, including the emergent population bursting and spike synchrony that underpin brain disorders and normal function. Exact…
We study a quantum double model whose degrees of freedom are Ising anyons. The terms of the Hamiltonian of this system give rise to a competition between single and double topologies. By studying the energy spectra of the Hamiltonian at…
We revisit the dynamics of a prototypical model of balanced activity in networks of spiking neutrons. A detailed investigation of the thermodynamic limit for fixed density of connections (massive coupling) shows that, when inhibition…
Hopfield networks are artificial neural networks which store memory patterns on the states of their neurons by choosing recurrent connection weights and update rules such that the energy landscape of the network forms attractors around the…
Replica-mean-field models have been proposed to decipher the activity of neural networks via a multiply-and-conquer approach. In this approach, one considers limit networks made of infinitely many replicas with the same basic neural…
The brain can reproduce memories from partial data; this ability is critical for memory recall. The process of memory recall has been studied using auto-associative networks such as the Hopfield model. This kind of model reliably converges…
Can Spiking Neural Networks (SNNs) approximate the dynamics of Recurrent Neural Networks (RNNs)? Arguments in classical mean-field theory based on laws of large numbers provide a positive answer when each neuron in the network has many…
It has been shown that a neural network model recently proposed to describe basic memory performance is based on a ternary/binary coding/decoding algorithm which leads to a new neural network assembly memory model (NNAMM) providing…
Aubry-Andre Harper (AAH) lattice models, characterized by reflection-asymmetric, sinusoidally varying nearest-neighbor tunneling profile, are well-known for their topological properties. We consider the fate of such models in the presence…
We study extremely diluted spin models of neural networks in which the connectivity evolves in time, although adiabatically slowly compared to the neurons, according to stochastic equations which on average aim to reduce frustration. The…
Unsupervised learning in a generalized Hopfield associative-memory network is investigated in this work. First, we prove that the (generalized) Hopfield model is equivalent to a semi-restricted Boltzmann machine with a layer of visible…
Neural mass models describe the mean-field dynamics of populations of neurons. In this work we illustrate how fundamental ideas of physics, such as energy and conserved quantities, can be explored for such models. We show that…
This study investigates the suitability of the annealed approximation in high-dimensional systems characterized by dense networks with quenched link disorder, employing models of coupled oscillators. We demonstrate that dynamic equations…
Recurrent neural networks have been widely used in sequence learning tasks. In previous studies, the performance of the model has always been improved by either wider or deeper structures. However, the former becomes more prone to…
This paper look at how the Hopfield neural network can be used to store and recall patterns constructed from natural language sentences. As a pattern recognition and storage tool, the Hopfield neural network has received much attention.…
Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…
The information that a pattern of firing in the output layer of a feedforward network of threshold-linear neurons conveys about the network's inputs is considered. A replica-symmetric solution is found to be stable for all but small amounts…
Asymptotic synchronization is one of the essential differences between artificial neural networks and biologically inspired neural networks due to mismatches from dynamical update of weight parameters and heterogeneous activations. In this…