  When an action potential is transmitted to a postsynaptic neuron, a small
change in the postsynaptic neuron's membrane potential occurs. These small
changes, known as a postsynaptic potentials (PSPs), are highly variable, and
current models assume that this variability is corrupting noise. In contrast,
we show that this variability could have an important computational role:
representing a synapse's uncertainty about the optimal synaptic weight (i.e.
the best possible setting for the synaptic weight). We show that this link
between uncertainty and variability, that we call synaptic sampling, leads to
more accurate estimates of the uncertainty in task relevant quantities, leading
to more effective decision making. Synaptic sampling makes four predictions,
all of which have some experimental support. First the more variable a synapse
is, the more it should change during LTP protocols. Second, variability should
increase as the presynpatic firing rate falls. Third, PSP variance should be
proportional to PSP mean. Fourth, variability should increase with distance
from the cell soma. We provide support for the first two predictions by
reanalysing existing datasets, and we find preexisting data in support of the
last two predictions.
