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Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of…

Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active…

Spiking activity of neurons engaged in learning and performing a task show complex spatiotemporal dynamics. While the output of recurrent network models can learn to perform various tasks, the possible range of recurrent dynamics that…

In recurrent networks of leaky integrate-and-fire (LIF) neurons, mean-field theory has proven successful in describing various statistical properties of neuronal activity at equilibrium, such as firing rate distributions. Mean-field theory…

Cortical networks are strongly recurrent, and neurons have intrinsic temporal dynamics. This sets them apart from deep feed-forward networks. Despite the tremendous progress in the application of feed-forward networks and their theoretical…

For spiking neural networks we consider the stability problem of global synchrony, arguably the simplest non-trivial collective dynamics in such networks. We find that even this simplest dynamical problem -- local stability of synchrony --…

Single trial analyses of ensemble activity in alert animals demonstrate that cortical circuits dynamics evolve through temporal sequences of metastable states. Metastability has been studied for its potential role in sensory coding, memory…

Cortical neurons emit seemingly erratic trains of action potentials or "spikes," and neural network dynamics emerge from the coordinated spiking activity within neural circuits. These rich dynamics manifest themselves in a variety of…

We present a complete mean field theory for a balanced state of a simple model of an orientation hypercolumn. The theory is complemented by a description of a numerical procedure for solving the mean-field equations quantitatively. With our…

Spin models of neural networks and genetic networks are considered elegant as they are accessible to statistical mechanics tools for spin glasses and magnetic systems. However, the conventional choice of variables in spin systems may cause…

Cortical neurons are characterized by irregular firing and a broad distribution of rates. The balanced state model explains these observations with a cancellation of mean excitatory and inhibitory currents, which makes fluctuations drive…

The robustness of dynamical properties of neuronal networks against structural damages is a central problem in computational and experimental neuroscience. Research has shown that the cortical network of a healthy brain works near a…

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…

The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain's network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain…

The architecture of a neural network constrains the potential dynamics that can emerge. Some architectures may only allow for a single dynamic regime, while others display a great deal of flexibility with qualitatively different dynamics…

Although individual neurons and neural populations exhibit the phenomenon of representational drift, perceptual and behavioral outputs of many neural circuits can remain stable across time scales over which representational drift is…

Self-sustained neural activity in the absence of ongoing external input is a fundamental feature of nervous system dynamics, yet the conditions under which it can emerge in biophysically grounded network models remain incompletely…

The branching process is the minimal model for propagation dynamics, avalanches and criticality, broadly used in neuroscience. A simple extension of it, adding inhibitory nodes, induces a much-richer phenomenology, including, an…

The observation of critical-like behavior in cortical networks represents a major step forward in elucidating how the brain manages information. Understanding the origin and functionality of critical-like dynamics, as well as their…

The recently introduced continuous Hopfield network (see Ramsauer et al.) exhibits large memorization capabilities, which manifest as attractive fixed points of its update rule -- a differentiable function consisting of two linear mappings…