Show Reference: "What, if anything, are topological maps for?"

What, if anything, are topological maps for? Developmental Neurobiology (1 February 2015), pp. n/a-n/a, doi:10.1002/dneu.22281 by Stuart P. Wilson, James A. Bednar
@article{wilson-and-bednar-2015,
    abstract = {What, if anything, is the functional significance of spatial patterning in cortical feature maps? We ask this question of four major theories of cortical map formation: self-organizing maps, wiring optimization, place coding, and reaction-diffusion. We argue that (i) self-organizing maps yield spatial patterning only as a by-product of efficient mechanisms for developing environmentally appropriate distributions of feature preferences, (ii) wiring optimization assumes rather than explains a map-like organization, (iii) place-coding mechanisms can at best explain only a subset of maps in functional terms, and (iv) reaction-diffusion models suggest two factors in the evolution of maps, the first based on efficient development of feature distributions, and the second based on generating feature-specific long-range recurrent cortical circuitry. None of these explanations for the existence of topological maps requires spatial patterning in maps to be useful. Thus despite these useful frameworks for understanding how maps form and how they are wired, the possibility that patterns are merely epiphenomena in the evolution of mammalian neocortex cannot be rejected. The article is intended as a nontechnical introduction to the assumptions and predictions of these four important classes of models, along with other possible functional explanations for maps. {\copyright} 2015 Wiley Periodicals, Inc. Develop Neurobiol, 2015},
    author = {Wilson, Stuart P. and Bednar, James A.},
    citeulike-article-id = {13527341},
    citeulike-linkout-0 = {http://dx.doi.org/10.1002/dneu.22281},
    day = {1},
    doi = {10.1002/dneu.22281},
    journal = {Developmental Neurobiology},
    keywords = {biology, models, som, topographic-maps},
    month = feb,
    pages = {n/a},
    posted-at = {2015-02-25 09:14:56},
    priority = {2},
    title = {What, if anything, are topological maps for?},
    url = {http://dx.doi.org/10.1002/dneu.22281},
    year = {2015}
}

See the CiteULike entry for more info, PDF links, BibTex etc.

Wilson and Bednar distinguish between topological feature maps and topographic maps. The topology of topographic maps tends to correspond to the spatial properties of sensory surfaces (like the retina or the skin) whereas topological feature maps correspond to the similarity of higher-order features of sensory input (like spatial frequency or orientation in vision).

Wilson and Bednar discuss the usefulness of topological feature maps, implying that they may not be useful at all but a byproduct of neural development and adaptation processes.

According to Wilson and Bednar, there are four main families of theories concerning topological feature maps:

  • input-driven self-organization,
  • minimal-wire length,
  • place-coding theory,
  • Turing pattern formation.

Wilson and Bednar argue that input-driven self-organization and turing pattern formation explain how topological maps may arise from useful processes, but they do not explain why topological maps are useful in themselves.

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.).