Distributed Phase Codes

David MacKay and Seb Wills

I gave a talk on October 1st 2004 on an idea about how brains work.

You can see the slides of the talk.

Or watch a movie (WMV, 50 minutes, 56M) | huge movie (WMV, 153M)

The PhD thesis of Seb Wills, "Computation with Spiking Neurons", is also available.

In due course I may even finish a paper.

A distributed phase code represents objects by the times of neuronal action potentials in a large number of neurons. If the object has {\em instantiation parameters\/} (for example, scale and pose, in the case of visual objects), the timings and probabilities of the action potentials are smoothly-varying functions of those parameters. If multiple objects are present, their associated action potential patterns are simply superposed in the distributed phase code. A simple learning rule that could be applied to a distributed phase code is {\em high-order suspicious-coincidence detection}: we posit neurons that notice that conjunctions of several temporal propositions are true more often than would be expected by chance; these neurons become detectors of these coincidences, and respond to them with temporal precision. These coincidence detectors can be used to instantiate associative memory and prediction. The resulting associative memory can store and recall continuous-valued memories, singly or concurrently. Point attractors, line attractors, and manifold attractors are all learned by the same rules. If the elementary objects stimulating the neurons are associated together into higher-order objects, the coincidence detectors automatically take on the role of distributed higher-order-object detectors. The firing times of the coincidence detectors automatically encode latent variables associated with the instantiation parameters of the higher-order objects. Thus distributed phase codes for elementary objects give rise, via coincidence detectors, to distributed phase codes for higher-order objects. By iterating this learning principle, a single assembly of cells can discover a hierarchy of objects that explain and predict the sensory world, the organism's motor actions, and the relations between them.

David J.C. MacKay
3rd October 2004