Related papers: A new mathematical model for brain memory working.…
In this paper we develop conditions for various types of stability in social networks governed by Imitation of Success principle. Considering so-called Prisoner's Dilemma as the base of node-to-node game in the network we obtain well-known…
Associative memory models such as the Hopfield network and its dense generalizations with higher-order interactions exhibit a "blackout catastrophe" -- a discontinuous transition where stable memory states abruptly vanish when the number of…
We propose a new framework to understand how quantum effects may impact on the dynamics of neural networks. We implement the dynamics of neural networks in terms of Markovian open quantum systems, which allows us to treat thermal and…
Many models used in artificial intelligence and cognitive science rely on multi-element patterns stored in "slots" - dedicated storage locations - in a digital computer. As biological brains likely lack slots, we consider how they might…
In this work we propose an energy functional along the lines of Modern Hopfield Networks (MNH), the stationary points of which correspond to the attention due to Vaswani et al. [12], thus unifying both frameworks. The minima of this…
Recurrent neural networks (RNNs) provide a theoretical framework for understanding computation in biological neural circuits, yet classical results, such as Hopfield's model of associative memory, rely on symmetric connectivity that…
The principled design and discovery of biologically- and physically-informed models of neuronal dynamics has been advancing since the mid-twentieth century. Recent developments in artificial intelligence (AI) have accelerated this progress.…
A gauge model of neural network is introduced, which resembles the Z(2) Higgs lattice gauge theory of high-energy physics. It contains a neuron variable $S_x = \pm 1$ on each site $x$ of a 3D lattice and a synaptic-connection variable…
Associative memory, a form of content-addressable memory, facilitates information storage and retrieval in many biological and physical systems. In statistical mechanics models, associative memory at equilibrium is represented through…
Motivated by recent applications of the Lyapunov's method in artificial neural networks, which could be considered as dynamical systems for which the convergence of the system trajectories to equilibrium states is a necessity. We re-look at…
We present an interacting branching model of neural network dynamics, incorporating key biological features such as inhibition with several types of inhibitory interactions. We establish a hierarchy of analytical mean-field approximations…
Attractor dynamics are a fundamental computational motif in neural circuits, supporting diverse cognitive functions through stable, self-sustaining patterns of neural activity. In these lecture notes, we review four key examples that…
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…
Neural dynamics of energy-based models are governed by energy minimization and the patterns stored in the network are retrieved when the system reaches equilibrium. However, when the system is driven by time-varying external input, the…
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…
Understanding how receptive fields emerge and organize within brain networks and how neural dynamics couple with stimuli space is fundamental to neuroscience. Models often rely on fine-tuning connectivity to match empirical data, which may…
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…
We solve the dynamics of Hopfield-type neural networks which store sequences of patterns, close to saturation. The asymmetry of the interaction matrix in such models leads to violation of detailed balance, ruling out an equilibrium…
We consider a system of two-level quantum quasi-spins and gauge bosons put on a 3+1D lattice. As a model of neural network of the brain functions, these spins describe neurons quantum-mechanically, and the gauge bosons describes weights of…
We examine a previouly introduced attractor neural network model that explains the persistent activities of neurons in the anterior ventral temporal cortex of the brain. In this model, the coexistence of several attractors including…