Why Poisson? A Dynamical Systems Perspective on Neural Spiking

Abstract: Neural spike trains are frequently modeled as Poisson or conditionally Poisson processes, despite the complex, nonlinear and interacting dynamics underlying neuronal activity. In this talk, I will present the different modelling regimes most frequently used in computational neuroscience and examine when and why such models provide a useful approximation. Starting from noisy integrate-and-fire dynamics, I will discuss how different dynamical regimes shape spiking variability, and how large interacting networks motivate latent process descriptions through mean-field reasoning. By comparing biophysical, stochastic, and statistical viewpoints side by side, the goal is to clarify when and why Poisson models are justified, what assumptions underlie them, and what their limitations reveal about neural dynamics.