On large networks of integrate-and-fire neurons with short-term synaptic plasticity

What the math gives to ML

The paper gives a constructive way to analyze recurrent spiking dynamics with synaptic depression by reducing local stability to the zeros of a Laplace-transformed linear-response function. The transferable asset is not the specific neuron model, but the combination of regenerative resets, a hidden fatigue state, and a computable frequency-domain stability test for the closed-loop interaction strength. A practical neural-network adaptation is to add a depression state to a recurrent or state-space layer and regularize the learned recurrent gain so that the empirical characteristic function has no unstable right-half-plane zeros. The paper's auxiliary ODEs also provide a route to estimating response transforms without differentiating through long network trajectories.