An analysis of the Map Seeking Circuit and Monte Carlo extensions

The Map Seeking Circuit (MSC) has been suggested to address the inverse problem of transformation discovery as found in signal processing, vision, inverse kinematics and many other natural tasks. According to this idea, a parallel search in the transformation space of a high dimensional problem can be decomposed into parts efficiently using the ordering property of superpositions. Deterministic formulations of the circuit have been suggested. Here, we provide a probabilistic interpretation of the architecture whereby the superpositions of the circuit are seen as a series of marginalisations over parameters of the transform. Based on this, we interpret the weights of the MSC as importance weights. The latter suggests the incorporation of Monte-Carlo approaches in the MSC, providing improved resolution of parameter estimates within resource constrained implementations. As a final contribution, we model mixed serial/parallel search strategies of biological vision to reduce the problem of collusions, a common problem in the standard MSC approach.