According to Wilson and Bednar, there are four main families of theories concerning topological feature maps:
According to Wilson and Bednar, wire-length optimization presupposes that neurons need input from other neurons with similar feature selectivity. Under that assumption, wire length is minimized if neurons with similar selectivities are close to each other. Thus, the kind of continuous topological feature maps we see optimize wire length.
The idea that neurons should especially require input from other neurons with similar spatial receptive fields is unproblematic. However, Wilson and Bednar argue that it is unclear why neurons should especially require input from neurons with similar non-spatial feature preferences (like orientation, spatial frequency, smell, etc.).⇒
Koulakov and Chklovskii assume that sensory neurons in cortex preferentially connect to other neurons whose feature-preferences do not differ more than a certain amount from their own feature-preferences. Further, they argue that long connections between neurons incur a metabolic cost. From this, they derive the hypothesis that the patterns of feature selectivity seen in neural populations are the result of minimizing the distance between similarly selective neurons.⇒
Koulakov and Chklovsky show that various selectivity patterns emerge from their theorized cost minimization, given different parameterizations of preference for connections to similarly-tuned neurons.⇒
Pooling the activity of a set of similarly-tuned neurons is useful for increasing the sharpness of tuning. A neuron which pools from a set of similarly-tuned neurons would have to make shorter connections if these neurons are close together. Thus, there is a reason why it can be useful to connect preferentially to a set of similarly-tuned neurons. This reason might be part of the reason behind topographic maps.⇒