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# Séminaire du CIMMUL – Marina Vegué Llorente

## 25 mars 2022 @ 13 h 00 min - 14 h 00 min

## Firing rate and synaptic weight distributions in plastic networks of spiking neurons

### Marina Vegué Llorente

Stagiaire postdoctorale, Dynamica

Département de physique, génie physique et d’optique, Université Laval

**Résumé**

Networks of spiking neurons have been widely used as models to represent neuronal activity in the brain. These models are reasonably realistic but they are also difficult to treat analytically. Mean-field theory has nevertheless proven to be successful as a method for deriving some of their statistical properties at equilibrium, such as the distribution of firing rates, both in homogeneous networks and in networks which exhibit a large heterogeneity in their structure. However, these models lack realism in the sense that they assume a fixed connectivity, whereas the connection strengths in brain networks evolve in time according to plasticity rules that depend on the neuronal activity.

In this talk I will present a way to extend the mean-field formalism to networks with synaptic weights that are prone to plastic, activity-dependent modulation. The plasticity in our model is mediated by the introduction of spike traces. A trace associated to one neuron represents a chemical signal that is released every time the neuron emits a spike and which is degraded over time. Mathematically, it is a stochastic variable that can be rescaled to be an approximation to the neuron’s firing rate. The temporal evolution of the trace is controlled by its degradation speed (i.e., a measure of how fast the spiking “memory” is lost) and by the mean temporal separation between consecutive spikes (i.e., the inverse of the neuron’s firing rate). These time scales jointly determine a shift from a regime characterized by highly noisy traces to a regime of accurate traces.

Our mean-field formalism provides a set of equations whose solution specifies the firing rate and synaptic weight distributions at equilibrium. The equations are exact in the limit of traces with infinite memory but I will show that they already provide accurate results when the degradation speed is of the order of a few seconds. Overall, this work offers a new perspective to explore and better understand the way in which plasticity shapes both activity and structure in neural networks.