Expansion and contraction of resource allocation in sensory bottlenecks

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Abstract

Topographic sensory representations often do not scale proportionally to the size of their input regions, with some expanded and others contracted. In vision, the foveal representation is magnified cortically, as are the fingertips in touch. What principles drive this allocation, and how should receptor density, e.g. the high innervation of the fovea or the fingertips, and stimulus statistics, e.g. the higher contact frequencies on the fingertips, contribute? Building on work in efficient coding, we address this problem using linear models that optimally decorrelate the sensory signals. We introduce a sensory bottleneck to impose constraints on resource allocation and derive the optimal neural allocation. We find that bottleneck width is a crucial factor in resource allocation, inducing either expansion or contraction. Both receptor density and stimulus statistics affect allocation and jointly determine convergence for wider bottlenecks. Furthermore, we show a close match between the predicted and empirical cortical allocations in a well-studied model system, the star-nosed mole. Overall, our results suggest that the strength of cortical magnification depends on resource limits.

Data availability

No data was generated for this study. All equations and model parameters are included in the manuscript and supporting files. Additionally, code implementing the model equations has been made available on Github at https://github.com/lauraredmondson/expansion_contraction_sensory_bottlenecks (see also Methods section in manuscript).

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Laura R Edmondson

Department of Psychology, University of Sheffield, Sheffield, United Kingdom

Competing interests
The authors declare that no competing interests exist.

"This ORCID iD identifies the author of this article:" 0000-0001-9886-1121
Alejandro Jiménez Rodríguez

Sheffield Robotics, University of Sheffield, Sheffield, United Kingdom

Competing interests
The authors declare that no competing interests exist.
Hannes P Saal

Department of Psychology, University of Sheffield, Sheffield, United Kingdom

For correspondence
h.saal@sheffield.ac.uk

Competing interests
The authors declare that no competing interests exist.

"This ORCID iD identifies the author of this article:" 0000-0002-7544-0196

Funding

Wellcome Trust (209998/Z/17/Z)

Hannes P Saal

European Commission (HBP-SGA2,785907)

Alejandro Jiménez Rodríguez

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

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This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.