相关论文: Neural Fields and Noise-Induced Patterns in Neuron…

We consider the long-time behavior of a population of mean-field oscillators modeling the activity of interacting excitable neurons in large population. Each neuron is represented by its voltage and recovery variables, which are solution to…

We study numerically and analytically first- and second-order phase transitions in neuronal networks stimulated by shot noise (a flow of random spikes bombarding neurons). Using an exactly solvable cortical model of neuronal networks on…

Large networks of sparsely coupled, excitatory and inhibitory cells occur throughout the brain. A striking feature of these networks is that they are chaotic. How does this chaos manifest in the neural code? Specifically, how variable are…

Neurons and networks in the cerebral cortex must operate reliably despite multiple sources of noise. To evaluate the impact of both input and output noise, we determine the robustness of single-neuron stimulus selective responses, as well…

This paper is concerned with the study of synchronization and consensus phenomena in complex networks of diffusively-coupled nodes subject to external disturbances. Specifically, we make use of stochastic Lyapunov functions to provide…

A neural network is a powerful tool that can uncover hidden laws beyond human intuition. However, it often appears as a black box due to its complicated nonlinear structures. By drawing upon the Gutzwiller mean-field theory, we can showcase…

We consider a fully-connected network of leaky integrate-and-fire neurons with spike-timing-dependent plasticity. The plasticity is controlled by a parameter representing the expected weight of a synapse between neurons that are firing…

We propose a novel learning framework based on neural mean-field dynamics for inference and estimation problems of diffusion on networks. Our new framework is derived from the Mori-Zwanzig formalism to obtain an exact evolution of the node…

The analysis of neural network training beyond their linearization regime remains an outstanding open question, even in the simplest setup of a single hidden-layer. The limit of infinitely wide networks provides an appealing route forward…

Circadian rhythmicity lies at the center of various important physiological and behavioral processes in mammals, such as sleep, metabolism, homeostasis, mood changes and more. It has been shown that this rhythm arises from self-sustained…

The mathematical theory of pattern formation in electrically coupled networks of excitable neurons forced by small noise is presented in this work. Using the Freidlin-Wentzell large deviation theory for randomly perturbed dynamical systems…

Exactly solvable neural network models with asymmetric weights are rare, and exact solutions are available only in some mean-field approaches. In this article we find exact analytical solutions of an asymmetric spin-glass-like model of…

We study the effect of width on the dynamics of feature-learning neural networks across a variety of architectures and datasets. Early in training, wide neural networks trained on online data have not only identical loss curves but also…

We investigate two-dimensional neural fields as a model of the dynamics of macroscopic activations in a cortex-like neural system. While the one-dimensional case has been treated comprehensively by Amari 30 years ago, two-dimensional neural…

Starting from a microscopic model for a system of neurons evolving in time which individually follow a stochastic integrate-and-fire type model, we study a mean-field limit of the system. Our model is described by a system of SDEs with…

We propose a theoretical understanding of neural networks in terms of Wilsonian effective field theory. The correspondence relies on the fact that many asymptotic neural networks are drawn from Gaussian processes, the analog of…

As it stands, a robust mathematical framework to analyse and study various topics in deep learning is yet to come to the fore. Nonetheless, viewing deep learning as a dynamical system allows the use of established theories to investigate…

A major challenge in neuroscience is posed by the need for relating the emerging dynamical features of brain activity with the underlying modular structure of neural connections, hierarchically organized throughout several scales. The…

Mean-field models provide a link between microscopic neuronal activity and macroscopic brain dynamics. Their derivation depends on simplifying assumptions, such as all-to-all connectivity, limiting their biological realism. To overcome…

The amplitude of fluctuation-induced patterns might be expected to be proportional to the strength of the driving noise, suggesting that such patterns would be difficult to observe in nature. Here, we show that a large class of…