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In this paper, we propose a shot noise-based leaky integrated and firing neuron model and provide a detailed analysis of the performance of this model compared to the traditional diffusion approximated model. In theoretical neuroscience,…

Spiking Neural Networks (SNNs) capture the information processing mechanism of the brain by taking advantage of spiking neurons, such as the Leaky Integrate-and-Fire (LIF) model neuron, which incorporates temporal dynamics and transmits…

Spiking Neural Networks (SNNs) are valued for their ability to process spatio-temporal information efficiently, offering biological plausibility, low energy consumption, and compatibility with neuromorphic hardware. However, the commonly…

Providing an analytical treatment to the stochastic feature of neurons' dynamics is one of the current biggest challenges in mathematical biology. The noisy leaky integrate-and-fire model and its associated Fokker-Planck equation are…

This paper investigates the classification capability of small-scale spiking neural networks based on the Leaky Integrate-and-Fire (LIF) neuron model. We analyze the relationship between classification accuracy and three factors: the number…

This work reports a transfer function-based approach to characterizing the operation of single neuronal cells in terms of the instantaneous frequency of the input and output signals. We adopt the leaky integrate-and-fire model. The transfer…

Spiking neural networks (SNNs) offer biologically inspired computation but remain underexplored for continuous regression tasks in scientific machine learning. In this work, we introduce and systematically evaluate Quadratic…

The response of neurons is highly sensitive to the stimulus. The stimulus can be associated with a direct injection in vitro experimentation (e.g., time dependent and independent inputs); or post-synaptic potentials resulting from the…

Up to now, modern Machine Learning is mainly based on fitting high dimensional functions to enormous data sets, taking advantage of huge hardware resources. We show that biologically inspired neuron models such as the…

One of the most important challenges in mathematical neuroscience is to properly illustrate the stochastic nature of neurons. Among different approaches, the noisy leaky integrate-and-fire and the escape rate models are probably the most…

The efficiency of the human brain in performing classification tasks has attracted considerable research interest in brain-inspired neuromorphic computing. Hardware implementations of a neuromorphic system aims to mimic the computations in…

Deep Neural Networks (DNNs) are the current state-of-the-art models in many speech related tasks. There is a growing interest, though, for more biologically realistic, hardware friendly and energy efficient models, named Spiking Neural…

Biologically plausible and energy-efficient frameworks such as Spiking Neural Networks (SNNs) have not been sufficiently explored in low-level vision tasks. Taking image deraining as an example, this study addresses the representation of…

In this paper, the hardware implementation of a neuromorphic system is presented. This system is composed of a Leaky Integrate-and-Fire with Latency (LIFL) neuron and a Spike-Timing Dependent Plasticity (STDP) synapse. LIFL neuron model…

We investigate numerically the dynamics of large networks of $N$ globally pulse-coupled integrate and fire neurons in a noise-induced synchronized state. The powerspectrum of an individual element within the network is shown to exhibit in…

Multispectral and Hyperspectral Image Fusion (MHIF) is a practical task that aims to fuse a high-resolution multispectral image (HR-MSI) and a low-resolution hyperspectral image (LR-HSI) of the same scene to obtain a high-resolution…

We propose a novel framework for representing neural fields on triangle meshes that is multi-resolution across both spatial and frequency domains. Inspired by the Neural Fourier Filter Bank (NFFB), our architecture decomposes the spatial…

Leaky integrate-and-fire (LIF) models are mean-field limits, with a large number of neurons, used to describe neural networks. We consider inhomogeneous networks structured by a connec-tivity parameter (strengths of the synaptic weights)…

Implementations of spiking neural networks on neuromorphic hardware promise orders of magnitude less power consumption than their non-spiking counterparts. The standard neuron model for spike-based computation on such systems has long been…

In large-scale neural networks, coherent limit cycle oscillations usually coexist with unstable incoherent equilibrium states, which are not observed experimentally. We implement a first-order dynamic controller to stabilize unknown…