Stochastic searching networks
J. M. Bishop · 1989
A fundamental difficulty when using neural net-works applied to problems of pattern recognition is that of stimulus equivalence: the ability to clas-sify a pattern, independent of position, rotation or scale, within the search space. This paper will de-scribe how a network of stochastic cells can be used to find an efficient solution to such problems. 1 Hinton Mapping The problem of stimulus equivalence is a spe-cific example of a best fit constraint satisfaction search, where the model being searched for has been mapped into the search space, using either a translational, rotational or scale transformation. The goal of a system to solve such problems is thus to assertain the inverse mapping from the search space back to the model. For example, in a prob-lem where the model has been rotated in the search space, the solution would be the angle of rotation; where the model has been translated, its XY coor-dinates etc. One solution to the problem, suggested by Hinton [1], is to define a set of functional units corresponding to different mappings into the search space. These are connected to two sets of feature detectors, canonical and retinocentric, by mutually excitory connections. Interactive activation and competition [2] between cells ensures that the mapping which yields the best fit of the model into the search space will receive the most activation. Hinton shows that such a network will rapidly converge to the best mapping of the model in the search space. A problem with Hinton Mapping is that it re-quires one mapping cell for each potential map-ping into the search space. Searching for a model of size N in a search space of size M requires M mapping cells and this value increases polynomi-ally with the number of degrees of freedom of the search. Stochastic Searching uses N cells indepen-dent of the size of the search space [3]. 2