Spiking Boltzmann Machines

We first show how to represent sharp posterior probability distribu(cid:173) tions using real valued coefficients on broadly-tuned basis functions. Then we show how the precise times of spikes can be used to con(cid:173) vey the real-valued coefficients on the basis functions quickly and accurately. Finally we describe a simple simulation in which spik(cid:173) ing neurons learn to model an image sequence by fitting a dynamic generative model. A perceived object is represented in the brain by the activities of many neurons, but there is no general consensus on how the activities of individual neurons combine to represent the multiple properties of an object. We start by focussing on the case of a single object that has multiple instantiation parameters such as position, velocity, size and orientation. We assume that each neuron has an ideal stimulus in the space of instantiation parameters and that its activation rate or probability of activation falls off monotonically in all directions as the actual stimulus departs from this ideal.