ABSTRACT
The previous representations were based on the abstraction of a whole temporal sequence that served as input of the system. Since the full models work incrementally, a representation that makes explicit how a previously established context influences future decisions would be useful. We have to ignore here any influence of new incoming data back to the previously processed results, which is a reduction for both models. In the full process model of the connectionist quantizer we can ‘clamp’ the whole of the network state to the partial solution obtained and study what would happen to a new incoming onset. This virtual new onset, acting as a measuring probe, will be moved by the model to an earlier or a later time. If it is given a positive time shift to a later time, the model clearly had not yet ‘expected’ an event. If we postulate a measure of expectation of an event, it has to be larger at a later time for this ‘early’ event. Vice versa: a negative movement, a shift to an earlier time, indicates a dropping expectancy: the event is late. So we can integrate the movement to yield an expectancy measure. It forms a curve with peaks at places where an event, were it to happen there, would stay in place. We could also rephrase this explanation in terms of potential and energy. The potential curve projected into the future by the network is then the inverse of the expectancy. But in the context of cognitive models expectancy seems a more appropriate concept. This process
of calculating an expectancy can even be done in an incremental way: the expectancy is calculated until a real new event happens, that event is added to the context, and the process starts all over again. In figure 6 this curve is shown for a rhythm in 2/4 and the peaks in between and at the note onsets clearly are positioned at important metrical boundaries. Note that for the sake of clarity the input sequence is already idealized here to a metronomical performance.
