  In recent years it has become clear that the brain maintains a temporal
memory of recent events stretching far into the past. This paper presents a
neurally-inspired algorithm to use a scale-invariant temporal representation of
the past to predict a scale-invariant future. The result is a scale-invariant
estimate of future events as a function of the time at which they are expected
to occur. The algorithm is time-local, with credit assigned to the present
event by observing how it affects the prediction of the future. To illustrate
the potential utility of this approach, we test the model on simultaneous
renewal processes with different time scales. The algorithm scales well on
these problems despite the fact that the number of states needed to describe
them as a Markov process grows exponentially.
