Abstract
There is a wealth of approaches to understanding the ways that populations of
neurons encode static, unchanging, stimuli in their spiking activity and how the
code thus generated may support relevant computations in neural networks. Bar
some notable exceptions, substantially less effort has been devoted to the
dynamic case in which the stimuli follow trajectories, changing over the same
timescale as the production of the spikes.
One instructive instance concerns a population of independent inhomogenous
Poisson neurons whose instantaneous firing rates are determined by the immediate
value of an evolving stimulus. Decoding the spikes generated by the population
is formally an ill-posed problem, whose solution, a posterior distribution over
possible stimulus trajectories, depends crucially on prior knowledge about such
trajectories. We show that the ideal observer in this case has a simple and
intuitive structure, with a posterior mean of the stimulus value that is a
weighted average of the preferred stimulus values of the neurons that recently
spiked. The prior distribution over trajectories controls how the weights in the
average decrease as a function of elapsed time since the spikes.
In such population codes, the stimulus trajectory induces strong dependencies
among the population of spikes, which the observer needs to take into account
when decoding. Thus the code is very complicated, even in this extremely simple,
instantaneous encoding scheme. Downstream neurones would need access to many
spikes from the entire population to process any individual spike consistently.
We show how the implied distribution can be recoded by population spikes that
can be treated independently, and finally discuss the relationship between this
process of recoding and adaptation.
