What, if anything, are topological maps for?

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.

Cortical Maps

“…In primates, cells with nonlinear phase responses are first found in V1 (Hubel and Wiesel 1962), and selforganizing models have explained this emergent property as a process of local pooling in V1 from cells that are selective for similar orientations (because of primate V1's topological map of orientation) but different phases (due to local variability in receptive field structure; Antolik and Bednar 2011;Hyvärinen and others 2009;Weber 2001). This finding raises the intriguing possibility that orientation preference maps may not emerge at the cortical level in rodents, simply because such nonlinear cells are already present at the LGN level (in line with the hypotheses of Nielsen 2014, andBednar 2015).…”

“…We do not yet know whether the intriguing spatial patterns they make on the cortical surface are important for neural computation (Purves and others 1992;Wilson and Bednar 2015), but the following section shows that these patterns do help reveal the underlying processes that generate receptive fields as the building blocks of cortical representation.…”

Self-organising Thermoregulatory Huddling in a Model of Soft Deformable Littermates

“…Metrics of huddling were i) the average body temperature T b maintained by the group, ii) one minus the proportion of the exposed surface area (note that using 1 − A means that larger values indicate increased aggregation levels, i.e., stronger huddling), iii) the number of different subgroups, where a subgroup comprises all individuals that are connected either directly or via intermediaries, and iv) 'pup flow', computed as the absolute value of the derivative of the exposed body surface (see [16,10]). Figure 2 reveals a phase transition in the self-organisation of huddling behaviours in the group.…”

“…This is revealed as raised body temperatures and low exposed surface areas at cool ambient temperatures, and a transition to the opposite profile as the temperature is increased. A central prediction of the thermodynamic description of huddling in related models is that at the critical temperature of the phase transition there should be a peak in the pup flow metric [16]. This prediction dervies from an analogy between huddling (measured as 1 − A) as the energy of the system and pup flow as the heat capacity of the system, as these terms are defined in statistical physics [10].…”

“…The simulation is shown here to recreate the phase transition in huddling as a function of the ambient temperature, as measured experimentally by [3]. The modelling approach could thus be used to generate complex naturalistic patterns of sensory and motor input for models of neural development [13][14][15][16][17], which are expected to vary systematically with the environment temperature as an underlying control parameter.…”