  Recently, low-dimensional models of neuronal activity have been exactly
derived for large networks of deterministic, Quadratic Integrate-and-Fire (QIF)
neurons. Such firing rate models (FRM) describe the emergence of fast
collective oscillations (>30~Hz) via the frequency-locking of a subset of
neurons to the global oscillation frequency. However, the suitability of such
models to describe realistic neuronal states is seriously challenged by fact
that during episodes of fast collective oscillations, neuronal discharges are
often very irregular and have low firing rates compared to the global
oscillation frequency. Here we extend the theory to derive exact FRM for QIF
neurons to include noise, and show that networks of stochastic neurons
displaying irregular discharges at low firing rates during episodes of fast
oscillations, are governed by exactly the same evolution equations as
deterministic networks. Our results reconcile two traditionally confronted
views on neuronal synchronization, and upgrade the applicability of exact FRM
to describe a broad range of biologically realistic neuronal states.
