The temporal correlation hypothesis for self-organizing feature maps

Feature maps, in which one or more aspects of the environment are systematically represented over the surface of the cerebral cortex, are of ten found in primary sensory and motor cortical regions of the vertebrate brain. They have inspired a great deal of computational modelling, and this has provided evidence that such maps are emergent properties of the interactions of numerous cortical neurons and their adaptive, nonlinear connections. In this paper, we address the issue of how multiple feature maps that coexist in the same region of cerebral cortex align with each other. We hypothesize that such alignment is governed by temporal correlations : features in one map that are temporally correlated with those in another come to occupy the same spatial locations over time. To examine the feasibility of this hypothesis and to establish some of its detailed implications, we initially studied a computational model of primary sensorimotor cortex. Coexisting sensory and motor maps formed and generally aligned in a fashion consistent with the temporal correlation hypothesis. We summarize these results, and then mathematically analyse a simplified model of self-organization during unsupervised learning. We show that the properties observed computationally are quite general : that temporally correlated inputs become spatially correlated (i.e. aligned), while input patterns that are temporally anti-correlated tend to result in mutually exclusive (i.e. unaligned) spatial distributions. This work provides a framework in which to interpret and understand future experimental studies of map relationships.