Mean-field models

Tilo Schwalger discusses population-level descriptions of neural dynamics and how mean-field models can be derived from underlying network mechanisms.

Mean-field models of neuronal populations in the brain have proven extremely useful to understand network dynamics and response to stimuli, but these models generally lack a faithful description of the fluctuations in the biologically relevant case of finite network size and connection probabilities $p<1$ (non-full connectivity). To gain insight into the mechanisms underlying the response and variability of the dynamics of populations of spiking neurons, we derive here a nonlinear stochastic mean-field model for a network of spiking Poisson neurons with quenched random connectivity. We treat

The intensity and features of sensory stimuli are encoded in the activity of neurons in the cortex. In the visual and piriform cortices, the stimulus intensity re-scales the activity of the population without changing its selectivity for the stimulus features. The cortical representation of the stimulus is therefore intensity-invariant. This emergence of network invariant representations appears robust to local changes in synaptic strength induced by synaptic plasticity, even though: i) synaptic plasticity can potentiate or depress connections between neurons in a feature-dependent manner, and

Firing-rate (FR) or neural-mass models are widely used for studying computations performed by neural populations. Despite their success, classical firing-rate models do not capture spike timing effects on the microscopic level such as spike synchronization and are difficult to link to spiking data in experimental recordings. For large neuronal populations, the gap between the spiking neuron dynamics on the microscopic level and coarse-grained FR models on the population level can be bridged by mean-field theory formally valid for infinitely many neurons. It remains however challenging to exten