Related papers: Firing rate and spatial correlation in a stochasti…
Stability arguments are often used to prevent learning algorithms from having ever increasing activity and weights that hinder generalization. However, stability conditions can clash with the sparsity required to augment the energy…
In a spiking neural network, is it enough for each neuron to spike at most once? In recent work, approximation bounds for spiking neural networks have been derived, quantifying how well they can fit target functions. However, these results…
Neural field models are commonly used to describe wave propagation and bump attractors at a tissue level in the brain. Although motivated by biology, these models are phenomenological in nature. They are built on the assumption that the…
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…
Mean field approximation is a popular method to study the behaviour of stochastic models composed of a large number of interacting objects. When the objects are asynchronous, the mean field approximation of a population model can be…
The synaptic connectivity of cortex is plastic, with experience shaping the ongoing interactions between neurons. Theoretical studies of spike timing-dependent plasticity (STDP) have focused on either just pairs of neurons or large-scale…
We investigate a stochastic network composed of Integrate-and-Fire spiking neurons, focusing on its mean-field asymptotics. We consider an invariant probability measure of the McKean-Vlasov equation and establish an explicit sufficient…
In a generic neuron model, we present the linear response theory for the firing rate in response to both time dependent input currents and noise amplitudes. In both cases the signal transmission is strongly attenuated for frequencies above…
In recent years, there has been increasing interest in developing models and tools to address the complex patterns of connectivity found in brain tissue. Specifically, this is due to a need to understand how emergent properties emerge from…
Most neurons in the primary visual cortex initially respond vigorously when a preferred stimulus is presented, but adapt as stimulation continues. The functional consequences of adaptation are unclear. Typically a reduction of firing rate…
Neurons process sensory stimuli efficiently, showing sparse yet highly variable ensemble spiking activity involving structured higher-order interactions. Notably, while neural populations are mostly silent, they occasionally exhibit highly…
We deal with the problem of bridging the gap between two scales in neuronal modeling. At the first (microscopic) scale, neurons are considered individually and their behavior described by stochastic differential equations that govern the…
We analyze the dynamics of networks of spiking neural oscillators. First, we present an exact linear stability theory of the synchronous state for networks of arbitrary connectivity. For general neuron rise functions, stability is…
The presence of correlated noise, arising from a mixture of independent fluctuations and a common noisy input shared across the neural population, is a ubiquitous feature of neural circuits, yet its impact on collective network dynamics…
In this note, we develop semi-analytical techniques to obtain the full correlational structure of a stochastic network of nonlinear neurons described by rate variables. Under the assumption that pairs of membrane potentials are jointly…
Mean-field theory is a powerful tool for studying large neural networks. However, when the system is composed of a few neurons, macroscopic differences between the mean-field approximation and the real behavior of the network can arise.…
The dynamics of spatially-structured networks of $N$ interacting stochastic neurons can be described by deterministic population equations in the mean-field limit. While this is known, a general question has remained unanswered: does…
Learning is based on synaptic plasticity, which affects and is driven by neural activity. Because pre- and postsynaptic spiking activity is shaped by randomness, the synaptic weights follow a stochastic process, requiring a probabilistic…
While spike timing has been shown to carry detailed stimulus information at the sensory periphery, its possible role in network computation is less clear. Most models of computation by neural networks are based on population firing rates.…
Recent studies have shown how spiking networks can learn complex functionality through error-correcting plasticity, but the resulting structures and dynamics remain poorly studied. To elucidate how these models may link to observed dynamics…