Related papers: Slow Transition to Low-Dimensional Chaos in Heavy-…
The criticality hypothesis posits that biological neural networks operate near a phase transition, yet within standard Gaussian mean-field theories this regime appears fragile and requires fine tuning. Here we show that heavy-tailed…
We propose an analytically tractable neural connectivity model with power-law distributed synaptic strengths. When threshold neurons with biologically plausible number of incoming connections are considered, our model features a continuous…
This paper is a review dealing with the study of large size random recurrent neural networks. The connection weights are selected according to a probability law and it is possible to predict the network dynamics at a macroscopic scale using…
Firing patterns in the central nervous system often exhibit strong temporal irregularity and heterogeneity in their time averaged response properties. Previous studies suggested that these properties are outcome of an intrinsic chaotic…
This article studies the dynamics of the mean-field approximation of continuous random networks. These networks are stochastic integrodifferential equations driven by Gaussian noise. The kernels in the integral operators are realizations of…
Biological neural networks can operate in qualitatively distinct dynamical regimes, and transitions between these regimes are thought to underlie changes in computation and behavior. The seminal work of Sompolinsky, Crisanti, and Sommers…
Deep neural networks (DNNs) have been successfully applied to many real-world problems, but a complete understanding of their dynamical and computational principles is still lacking. Conventional theoretical frameworks for analysing DNNs…
The dynamics of an extremely diluted neural network with high order synapses acting as corrections to the Hopfield model is investigated. As in the fully connected case, the high order terms may strongly improve the storage capacity of the…
We introduce a model of randomly connected neural populations and study its dynamics by means of the dynamical mean-field theory and simulations. Our analysis uncovers a rich phase diagram, featuring high- and low-dimensional chaotic…
In neural circuits, statistical connectivity rules strongly depend on neuronal type. Here we study dynamics of neural networks with cell-type specific connectivity by extending the dynamic mean field method, and find that these networks…
Autonomous randomly coupled neural networks display a transition to chaos at a critical coupling strength. We here investigate the effect of a time-varying input on the onset of chaos and the resulting consequences for information…
Recurrent neural networks (RNNs) are non-linear dynamic systems. Previous work believes that RNN may suffer from the phenomenon of chaos, where the system is sensitive to initial states and unpredictable in the long run. In this paper,…
While most models of randomly connected networks assume nodes with simple dynamics, nodes in realistic highly connected networks, such as neurons in the brain, exhibit intrinsic dynamics over multiple timescales. We analyze how the…
High-dimensional chaotic dynamics can emerge in a large random recurrent neural network when the synaptic gain crosses a threshold. Recent works showed that the kinetic energy of neural activity links the chaotic dynamics and the supporting…
Recurrent Neural Networks (RNNs) frequently exhibit complicated dynamics, and their sensitivity to the initialization process often renders them notoriously hard to train. Recent works have shed light on such phenomena analyzing when…
Random neural networks are dynamical descriptions of randomly interconnected neural units. These show a phase transition to chaos as a disorder parameter is increased. The microscopic mechanisms underlying this phase transition are unknown,…
We consider a two-node fluid network with batch arrivals of random size having a heavy-tailed distribution. We are interested in the tail asymptotics for the stationary distribution of a two-dimensional queue-length process. The tail…
Neurons in the brain communicate with spikes, which are discrete events in time and value. Functional network models often employ rate units that are continuously coupled by analog signals. Is there a qualitative difference implied by these…
We study the large-width asymptotics of random fully connected neural networks with weights drawn from $\alpha$-stable distributions, a family of heavy-tailed distributions arising as the limiting distributions in the Gnedenko-Kolmogorov…
Recurrent neural networks (RNNs) are powerful dynamical models, widely used in machine learning (ML) and neuroscience. Prior theoretical work has focused on RNNs with additive interactions. However, gating - i.e. multiplicative -…