We compute the typical number of equilibria of the generalized Lotka-Volterra equations
describing species-rich ecosystems with random, nonreciprocal interactions using the …

We present some recent investigations resulting from the modeling of neural networks as
dynamical systems, and deal with the following questions, adressed in the context of specific …

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 …

Random neural networks are dynamical descriptions of randomly interconnected neural
units. These show a phase transition to chaos as a disorder parameter is increased. The …

Recurrent neural networks (RNNs) are powerful dynamical models, widely used in machine
learning (ML) and neuroscience. Prior theoretical work has focused on RNNs with additive …

We derive rigorous results describing the asymptotic dynamics of a discrete time model of
spiking neurons introduced in Soula et al.(Neural Comput. 18, 1, 2006). Using symbolic …

We study the behavior of weight-tied multilayer vanilla autoencoders under the assumption
of random weights. Via an exact characterization in the limit of large dimensions, our …

We present a mathematical analysis of a networks with Integrate-and-Fire neurons with
conductance based synapses. Taking into account the realistic fact that the spike time is only …

Dynamical systems driven by strong external signals are ubiquitous in nature and
engineering. Here we study “echo state networks,” networks of a large number of randomly …

In this article, we study the asymptotic dynamics of a noisy discrete time neural network, with
random asymmetric couplings and thresholds. More precisely, we focus our interest on the …