  Low-dimensional descriptions of spiking neural network dynamics are an
effective tool for bridging different scales of organization of brain structure
and function. Recent advances in deriving mean-field descriptions for networks
of coupled oscillators have sparked the development of a new generation of
neural mass models. Of notable interest are mean-field descriptions of
all-to-all coupled quadratic integrate-and-fire (QIF) neurons, which have
already seen numerous extensions and applications. These extensions include
different forms of short-term adaptation (STA) considered to play an important
role in generating and sustaining dynamic regimes of interest in the brain. It
is an open question, however, whether the incorporation of pre-synaptic forms
of synaptic plasticity driven by single neuron activity would still permit the
derivation of mean-field equations using the same method. Here, we discuss this
problem using an established model of short-term synaptic plasticity at the
single neuron level, for which we present two different approaches for the
derivation of the mean-field equations. We compare these models with a recently
proposed mean-field approximation that assumes stochastic spike timings. In
general, the latter fails to accurately reproduce the macroscopic activity in
networks of deterministic QIF neurons with distributed parameters. We show that
the mean-field models we propose provide a more accurate description of the
network dynamics, although they are mathematically more involved. Thus, we
provide novel insight into the macroscopic effects of short-term synaptic
plasticity in spiking neural networks, as well as two different mean-field
descriptions for future investigations of such networks.
