相关论文: Practical Approximation Method for Firing Rate Mod…

The dynamics of neural networks is often characterized by collective behavior and quasi-synchronous events, where a large fraction of neurons fire in short time intervals, separated by uncorrelated firing activity. These global temporal…

This paper proposes to study neural networks through neuronal correlation, a statistical measure of correlated neuronal activity on the penultimate layer. We show that neuronal correlation can be efficiently estimated via weight matrix, can…

How do neuronal populations encode time-dependent stimuli in their population firing rate? To address this question, I consider the quasi-renewal equation and the event-based expansion, two theoretical approximations proposed recently, and…

Cortical synapse organization supports a range of dynamic states on multiple spatial and temporal scales, from synchronous slow wave activity (SWA), characteristic of deep sleep or anesthesia, to fluctuating, asynchronous activity during…

Partial synchronization plays a crucial role in the functioning of neuronal networks: selective, coordinated activation of neurons enables information processing that flexibly adapts to a changing computational context. Since the structure…

We study the computational task of detecting and estimating correlated signals in a pair of spiked matrices $$ X=\tfrac{\lambda}{\sqrt{n}} xu^{\top}+W, \quad Y=\tfrac{\mu}{\sqrt{n}} yv^{\top}+Z $$ where the spikes $x,y$ have correlation…

Coupling is a widely used technique in the theoretical study of interacting stochastic processes. In this paper I present an example demonstrating its usefulness also in the efficient computer simulation of such processes. I first describe…

The continuous integration of experimental data into coherent models of the brain is an increasing challenge of modern neuroscience. Such models provide a bridge between structure and activity, and identify the mechanisms giving rise to…

Neurons subject to a common non-stationary input may exhibit a correlated firing behavior. Correlations in the statistics of neural spike trains also arise as the effect of interaction between neurons. Here we show that these two situations…

Since loose-fitting clothing contains dynamic modes that have proven to be difficult to predict via neural networks, we first illustrate how to coarsely approximate these modes with a real-time numerical algorithm specifically designed to…

In large-scale excitatory neuronal networks, rapid synchronization manifests as {multiple firing events (MFEs)}, mathematically characterized by a finite-time blow-up of the neuronal firing rate in the mean-field Fokker-Planck equation.…

The correlated variability in the responses of a neural population to the repeated presentation of a sensory stimulus is a universally observed phenomenon. Such correlations have been studied in much detail, both with respect to their…

Recently, it has been shown that spiking neural networks (SNNs) can be trained efficiently, in a supervised manner, using backpropagation through time. Indeed, the most commonly used spiking neuron model, the leaky integrate-and-fire…

Latent position models are widely used for the analysis of networks in a variety of research fields. In fact, these models possess a number of desirable theoretical properties, and are particularly easy to interpret. However, statistical…

A fundamental inequality governing the spike activity of peripheral neurons is derived and tested against auditory data. This inequality states that the steady-state firing rate must lie between the arithmetic and geometric means of the…

The synergy between spiking neural networks and neuromorphic hardware holds promise for the development of energy-efficient AI applications. Inspired by this potential, we revisit the foundational aspects to study the capabilities of…

Training of neural networks is a computationally intensive task. The significance of understanding and modeling the training dynamics is growing as increasingly larger networks are being trained. We propose in this work a model based on the…

To understand how neural networks process information, it is important to investigate how neural network dynamics varies with respect to different stimuli. One challenging task is to design efficient statistical approaches to analyze…

Consider a compound Poisson process with jump measure $\nu$ supported by finitely many positive integers. We propose a method for estimating $\nu$ from a single, equidistantly sampled trajectory and develop associated statistical…

Comparing different neural network representations and determining how representations evolve over time remain challenging open questions in our understanding of the function of neural networks. Comparing representations in neural networks…