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Sequential learning involves learning tasks in a sequence, and proves challenging for most neural networks. Biological neural networks regularly conquer the sequential learning challenge and are even capable of transferring knowledge both…
A neuron transforms its input into output spikes, and this transformation is the basic unit of computation in the nervous system. The spiking response of the neuron to a complex, time-varying input can be predicted from the detailed…
Many mathematical models of synaptic plasticity have been proposed to explain the diversity of plasticity phenomena observed in biological organisms. These models range from simple interpretations of Hebb's postulate, which suggests that…
Among the performance-enhancing procedures for Hopfield-type networks that implement associative memory, Hebbian Unlearning (or dreaming) strikes for its simplicity and its clear biological interpretation. Yet, it does not easily lend…
We investigate the computational limits of the memory retrieval dynamics of modern Hopfield models from the fine-grained complexity analysis. Our key contribution is the characterization of a phase transition behavior in the efficiency of…
The dynamics and the stationary states for the competition between pattern reconstruction and asymmetric sequence processing are studied here in an exactly solvable feed-forward layered neural network model of binary units and patterns near…
Networks in machine learning offer examples of complex high-dimensional dynamical systems reminiscent of biological systems. Here, we study the learning dynamics of Generalized Hopfield networks, which permit a visualization of internal…
Adaptation plays a pivotal role in the evolution of natural and artificial complex systems, and in the determination of their functionality. Here, we investigate the impact of adaptive inter-layer processes on intra-layer synchronization in…
The models in statistical physics such as an Ising model offer a convenient way to characterize stationary activity of neural populations. Such stationary activity of neurons may be expected for recordings from in vitro slices or…
Dense Hopfield networks are known for their feature to prototype transition and adversarial robustness. However, previous theoretical studies have been mostly concerned with their storage capacity. We bridge this gap by studying the phase…
Bottom-up models of functionally relevant patterns of neural activity provide an explicit link between neuronal dynamics and computation. A prime example of functional activity pattern is hippocampal replay, which is critical for memory…
We investigated how the stability of macroscopic states in the associative memory model is affected by synaptic depression. To this model, we applied the dynamical mean-field theory, which has recently been developed in stochastic neural…
The problem of synchronization in networks of neural mass model populations with discrete couplings is considered. The considered network is hybrid one, therefore Mikheev approach is applied to transform it to the network with time-varying…
Several approaches to cognition and intelligence research rely on statistics-based models testing, namely factor analysis. In the present work we exploit the emerging dynamical systems perspective putting the focus on the role of the…
Dynamical balance of excitation and inhibition is usually invoked to explain the irregular low firing activity observed in the cortex. We propose a robust nonlinear balancing mechanism for a random network of spiking neurons, which works…
In statistical mechanics, the Potts model is a model for interacting spins with more than two discrete states. Neural networks which exhibit features of learning and associative memory can also be modeled by a system of Potts spins. A…
A set of fixed points of the Hopfield type neural network was under investigation. Its connection matrix is constructed with regard to the Hebb rule from a highly symmetric set of the memorized patterns. Depending on the external parameter…
Hebbian learning of excitatory synapses plays a central role in storing activity patterns in associative memory models. Furthermore, interstimulus Hebbian learning associates multiple items in the brain by converting temporal correlation to…
Motifs are patterns of subgraphs of complex networks. We studied the impact of such patterns of connectivity on the level of correlated, or synchronized, spiking activity among pairs of cells in a recurrent network model of integrate and…
One of the paramount challenges in neuroscience is to understand the dynamics of individual neurons and how they give rise to network dynamics when interconnected. Historically, researchers have resorted to graph theory, statistics, and…