  The space of possible behaviors complex biological systems may exhibit is
unimaginably vast, and these systems often appear to be stochastic, whether due
to variable noisy environmental inputs or intrinsically generated chaos. The
brain is a prominent example of a biological system with complex behaviors. The
number of possible patterns of spikes emitted by a local brain circuit is
combinatorially large, though the brain may not make use of all of them.
Understanding which of these possible patterns are actually used by the brain,
and how those sets of patterns change as properties of neural circuitry change
is a major goal in neuroscience. Recently, tools from information geometry have
been used to study embeddings of probabilistic models onto a hierarchy of model
manifolds that encode how model behaviors change as a function of their
parameters, giving a quantitative notion of "distances" between model
behaviors. We apply this method to a network model of excitatory and inhibitory
neural populations to understand how the competition between membrane and
synaptic response timescales shapes the network's information geometry. The
hyperbolic embedding allows us to identify the statistical parameters to which
the model behavior is most sensitive, and demonstrate how the ranking of these
coordinates changes with the balance of excitation and inhibition in the
network.
