Abstract
Many neural areas, notably, the hippocampus, show structured, dynamical, population behavior such as coordinated oscillations. It has long been observed that
such oscillations provide a substrate for representing analog information in the
firing phases of neurons relative to the underlying population rhythm. However,
it has become increasingly clear that it is essential for neural populations to rep-
resent uncertainty about the information they capture, and the substantial recent
work on neural codes for uncertainty has omitted any analysis of oscillatory systems. Here, we observe that, since neurons in an oscillatory network need not only
fire once in each cycle (or even at all), uncertainty about the analog quantities each
neuron represents by its firing phase might naturally be reported through the degree of concentration of the spikes that it fires. We apply this theory to memory in a model of oscillatory associative recall in hippocampal area CA3. Although it is not well treated in the literature, representing and manipulating uncertainty is fundamental to competent memory; our theory enables us to view CA3 as an effective uncertainty-aware, retrieval system.
