Related papers: On Leaky-Integrate-and Fire as Spike-Train-Quantiz…

We consider a single Leaky integrate-and-fire neuron stimulated with Poisson process. We develop a method, which allows one to obtain the first passage time probability density function without any additional approximations.

Quantitative information flow (QIF) is concerned with assessing the leakage of information in computational systems. In QIF there are two main perspectives for the quantification of leakage. On one hand, the static perspective considers all…

The Network of Noisy Leaky Integrate and Fire (NNLIF) model describes the behavior of a neural network at mesoscopic level. It is one of the simplest self-contained mean-field models considered for that purpose. Even so, to study the…

We study a class of planar integrate and fire (IF) models called adaptive integrate and fire (AIF) models, which possesses an adaptation variable on top of membrane potential, and whose subthreshold dynamics is piecewise linear (PWL). These…

We introduce an exactly integrable version of the well-known leaky integrate-and-fire (LIF) model, with continuous membrane potential at the spiking event, the c-LIF. We investigate the dynamical regimes of a fully connected network of…

When stimulated by a very large number of Poisson-like presynaptic current input spikes, the temporal dynamics of the soma membrane potential $V(t)$ of a leaky integrate-and-fire (LIF) neuron is typically modeled in the diffusion limit and…

We present a mathematical analysis of a networks with Integrate-and-Fire neurons and adaptive conductances. Taking into account the realistic fact that the spike time is only known within some \textit{finite} precision, we propose a model…

Multi-state spiking neurons combine sparse binary activations with rich second-order nonlinear recurrent dynamics, making them a promising alternative to standard deep learning models. However, gradient propagation through these dynamics…

Spiking Neural Networks (SNNs) offer a promising, biologically inspired approach for processing spatiotemporal data, particularly for time series forecasting. However, conventional neuron models like the Leaky Integrate-and-Fire (LIF)…

Spiking transformers achieve competitive accuracy with conventional transformers while offering $38$-$57\times$ energy efficiency on neuromorphic hardware, yet no theoretical framework guides their design. This paper establishes the first…

We investigate a large ensemble of Quadratic Integrate-and-Fire (QIF) neurons with heterogeneous input currents and adaptation variables. Our analysis reveals that for a specific class of adaptation, termed quadratic spike-frequency…

A synfire chain is a simple neural network model which can propagate stable synchronous spikes called a pulse packet and widely researched. However how synfire chains coexist in one network remains to be elucidated. We have studied the…

In this paper we analyze a neuromorphic controller, inspired by the leaky integrate-and-fire neuronal model, in closed-loop with a single-input single-output linear time-invariant system. The controller consists of two neuron-like variables…

Pairs of neurons in brain networks often share much of the input they receive from other neurons. Due to essential non-linearities of neuronal dynamics, the consequences for the correlation of the output spike trains are not well understood…

We study the collective dynamics of a Leaky Integrate and Fire network in which precise relative phase relationship of spikes among neurons are stored, as attractors of the dynamics, and selectively replayed at differentctime scales. Using…

Population equations for infinitely large networks of spiking neurons have a long tradition in theoretical neuroscience. In this work, we analyze a recent generalization of these equations to populations of finite size, which takes the form…

Computationally expensive neural networks are ubiquitous in computer vision and solutions for efficient inference have drawn a growing attention in the machine learning community. Examples of such solutions comprise quantization, i.e.…

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…

The relative timing of action potentials in neurons recorded from local cortical networks often shows a non-trivial dependence, which is then quantified by cross-correlation functions. Theoretical models emphasize that such spike train…

In this paper, we introduce a novel self-calibrating integrate-and-fire time encoding machine (S-IF-TEM) that enables simultaneous parameter estimation and signal reconstruction during sampling, thereby effectively mitigating mismatch…