Related papers: An integrate-and-fire model to generate spike trai…
Generalized linear models are one of the most efficient paradigms for predicting the correlated stochastic activity of neuronal networks in response to external stimuli, with applications in many brain areas. However, when dealing with…
Long-range dependence and non-Gaussianity are ubiquitous in many natural systems like ecosystems, biological systems and climate. However, it is not always appreciated that both phenomena may occur together in natural systems and that…
We study the random processes with non-local memory and obtain new solutions of the Mori-Zwanzig equation describing non-markovian systems. We analyze the system dynamics depending on the amplitudes $\nu$ and $\mu_0$ of the local and…
Synaptic noise plays a major role in setting up coexistence of various firing patterns, but the precise mechanisms whereby these synaptic noise contributes to coexisting firing activities are subtle and remain elusive. To investigate these…
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…
In this paper we propose using a nonparametric model specification test for parametric time series with long-range dependence (LRD). To establish asymptotic distributions of the proposed test statistic, we develop new central limit theorems…
Recurrent neural networks are powerful tools for understanding and modeling computation and representation by populations of neurons. Continuous-variable or "rate" model networks have been analyzed and applied extensively for these…
We study in this paper the effect of an unique initial stimulation on random recurrent networks of leaky integrate and fire neurons. Indeed given a stochastic connectivity this so-called spontaneous mode exhibits various non trivial…
We consider the problem of efficiently performing simulation and inference for stochastic kinetic models. Whilst it is possible to work directly with the resulting Markov jump process, computational cost can be prohibitive for networks of…
The neural dynamics generating sensory, motor, and cognitive functions are commonly understood through field theories for neural population activity. Classic neural field theories are derived from highly simplified models of individual…
Simple spiking neural network models, such as those built from interacting integrate-and-fire (IF) units, exhibit rich emergent behaviours but remain notoriously difficult to analyse, particularly in terms of their pattern-forming…
Interspike intervals describe the output of neurons. Signal transmission in a neuronal network implies that the output of some neurons becomes the input of others. The output should reproduce the main features of the input to avoid a…
The goal of this paper is to extend the nonparametric estimation of Impulse Response Functions (IRF) by means of local projections in the nonlinear dynamic framework. We discuss the existence of a nonlinear autoregressive representation for…
The Spiking Neural Network (SNN) has drawn increasing attention for its energy-efficient, event-driven processing and biological plausibility. To train SNNs via backpropagation, surrogate gradients are used to approximate the…
Statistical properties of spike trains measured from a sensory neuron in-vivo are studied experimentally and theoretically. Experiments are performed on an identified neuron in the visual system of the blowfly. It is shown that the spike…
In this paper, the question how spiking neural network (SNN) learns and fixes in its internal structures a model of external world dynamics is explored. This question is important for implementation of the model-based reinforcement learning…
Reinforcement Learning (RL) for training Large Language Models is notoriously unstable. While recent studies attribute this to "training inference mismatch stemming" from inconsistent hybrid engines, standard remedies, such as Importance…
We consider the deterministic evolution of a time-discretized spiking network of neurons with connection weights having delays, modeled as a discretized neural network of the generalized integrate and fire (gIF) type. The purpose is to…
This study investigates the behaviors of Large Language Models (LLMs) when faced with conflicting prompts versus their internal memory. This will not only help to understand LLMs' decision mechanism but also benefit real-world applications,…
Personalized Large Language Models (LLMs) facilitate more natural, human-like interactions in human-centric applications. However, existing personalization methods are constrained by limited controllability and high resource demands.…