Related papers: Formalized Hopfield Networks and Boltzmann Machine…
Leveraging advances in variational inference, we propose to enhance recurrent neural networks with latent variables, resulting in Stochastic Recurrent Networks (STORNs). The model i) can be trained with stochastic gradient methods, ii)…
The Hamiltonian formalism plays a central role in classical and quantum physics. Hamiltonians are the main tool for modelling the continuous time evolution of systems with conserved quantities, and they come equipped with many useful…
This article presents an innovative approach to integrating port-Hamiltonian systems with neural network architectures, transitioning from deterministic to stochastic models. The study presents novel mathematical formulations and…
This paper is concerned with the modeling and analysis of two of the most commonly used recurrent neural network models (i.e., Hopfield neural network and firing-rate neural network) with dynamic recurrent connections undergoing Hebbian…
Probabilistic Boolean Networks (PBNs) have been previously proposed so as to gain insights into complex dy- namical systems. However, identification of large networks and of the underlying discrete Markov Chain which describes their…
Recently a daily routine for associative neural networks has been proposed: the network Hebbian-learns during the awake state (thus behaving as a standard Hopfield model), then, during its sleep state, optimizing information storage, it…
Capturing the dynamics of active particles, i.e., small self-propelled agents that both deform and are deformed by a fluid in which they move is a formidable problem as it requires coupling fine scale hydrodynamics with large scale…
These lecture notes introduce some topics of classical statistical physics, particularly those that are relevant for neural networks and deep learning. Statistical physics is treated as a branch of probability theory or statistics, with the…
We consider a general class of stochastic networks and ask which network nodes need to be controlled, and how, to stabilize and switch between desired metastable (target) states in terms of the first and second statistical moments of the…
Graphical models are powerful tools for modeling high-dimensional data, but learning graphical models in the presence of latent variables is well-known to be difficult. In this work we give new results for learning Restricted Boltzmann…
We discuss probabilistic neural networks with a fixed internal representation as models for machine understanding. Here understanding is intended as mapping data to an already existing representation which encodes an {\em a priori}…
A modern challenge of Artificial Intelligence is learning multiple patterns at once (i.e.parallel learning). While this can not be accomplished by standard Hebbian associative neural networks, in this paper we show how the Multitasking…
Learning or memory formation are associated with the strengthening of the synaptic connections between neurons according to a pattern reflected by the input. According to this theory a retained memory sequence is associated to a dynamic…
We introduce probabilistic neural networks that describe unsupervised synchronous learning on an atomic Hardy space and space of bounded real analytic functions, respectively. For a stationary ergodic vector process, we prove that the…
This paper contributes to a development of randomized methods for neural networks. The proposed learner model is generated incrementally by stochastic configuration (SC) algorithms, termed as Stochastic Configuration Networks (SCNs). In…
Content-addressable memories such as Modern Hopfield Networks (MHN) have been studied as mathematical models of auto-association and storage/retrieval in the human declarative memory, yet their practical use for large-scale content storage…
This work introduces a new framework integrating port-Hamiltonian systems (PHS) and neural network architectures. This framework bridges the gap between deterministic and stochastic modeling of complex dynamical systems. We introduce new…
The standard Hopfield model for associative neural networks accounts for biological Hebbian learning and acts as the harmonic oscillator for pattern recognition, however its maximal storage capacity is $\alpha \sim 0.14$, far from the…
Large-scale recurrent networks have drawn increasing attention recently because of their capabilities in modeling a large variety of real-world phenomena and physical mechanisms. This paper studies how to identify all authentic connections…
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…