Topographic Map Formation as Statistical Inference

Neurons representing similar aspects of the world are often found close together in the cortex. It is proposed that this phenomenon can be modelled using a statistical approach. We start by using a neural network to nd the \features" that were most likely to have generated the observed probability distribution of inputs. These features can be found using a Boltzmann machine architecture, but the results of this simple network are unsatisfactory. By adding two additional constraints (priors), that all representational units have the same probability of being true, and that nearby representational units are correlated, the network is shown to be capable of extracting distributed, spatially localised topographic representations based on an input of natural images. This is believed to be the rst network capable of achieving this. As a model of topographic map formation, this framework has a number of strengths: 1) The framework is a general one, in which winner-takes-all and distributed representations are special cases. 2) Though slow, the learning is simple and approximately Hebbian. 3) The network can extract topographic representations based on distributed input such as natural images.