Expansion and contraction of resource allocation in sensory bottlenecks

  1. Laura R Edmondson
  2. Alejandro Jiménez Rodríguez
  3. Hannes P Saal  Is a corresponding author
  1. Active Touch Laboratory, Department of Psychology, University of Sheffield, United Kingdom
  2. Sheffield Robotics, University of Sheffield, United Kingdom
  3. Department of Computer Science, University of Sheffield, United Kingdom
6 figures, 1 table and 1 additional file

Figures

Illustration of the resource allocation problem and solution outline.

(A) Abstract problem setup. When two regions vary in their receptor densities and activation, how should a shared resource be allocated between them when that resource is limited, as in a sensory …

Figure 2 with 4 supplements
Optimal resource allocation for heterogeneous receptor densities or input statistics leads to complex trade-offs.

(A) Illustration of resource allocation for heterogeneous receptor density but homogeneous stimulus statistics over all bottleneck sizes. Orange denotes the lower density region and blue the higher …

Figure 2—figure supplement 1
Effect of different values of γ on the covariance function decay.

Smaller γ leads to a slower decay and therefore a larger extent of spatial correlations. When the sigma is large, receptors have less similar responses to their neighbours, and therefore co-vary …

Figure 2—figure supplement 2
Resource allocation for heterogeneous receptor densities and variations in input statistics in 1D.

(A) Examples of allocation for two input regions with differing receptor densities and activation (see insets) for different bottleneck widths, demonstrating complex trade-offs in resource …

Figure 2—figure supplement 3
Illustration of eigenvalue sorting and resulting allocation.

Main panels: eigenvalues for heterogeneous density (A), heterogeneous activation (B), or combined (C). For each, the manipulated ratio is set as 1:2. For simplicity, the example considers 1D …

Figure 2—figure supplement 4
Limit on information rather than number of neurons.

Resource allocations where the bottleneck is expressed as variance explained. Because eigenvalues decrease dramatically in size, this re-expression results in a ’squashing’ of the allocation curve …

Figure 3 with 1 supplement
Interactions between heterogeneous statistics and density.

(A) Allocations with both heterogeneous density and activation ratios. Expansion and contraction for a baseline region where relative density and activation is varied over the other region. All …

Figure 3—figure supplement 1
Comparison between 1D and 2D results for heterogeneous activation and density.

(A) Effect of changing both the density and activation ratios, and possible resource allocations for two regions. Plots show the same density ratio, 1:5, considering 1D (left) and 2D (right) …

Re-allocation to account for changes in stimulus statistics.

(A) Top left: illustration of problem setup. Increased stimulation is applied to the middle digit (yellow symbols), leading to changes in optimal allocations. Top right: optimal allocations for …

Allocations for other monotonically decreasing covariance functions.

(A) Three covariance functions of different smoothness taken from the Matérn class, differing in the parameter ν (see ‘Methods’). (B) Examples of numerically determined allocation for the covariance …

Figure 6 with 1 supplement
Resource allocation in the star-nosed mole.

(A) Star-nosed moles have two sets of 11 tactile rays used for detecting and capturing prey. (B) Fibre innervation densities for each ray. (C) Typical usage percentages for each ray during foraging. …

Figure 6—figure supplement 1
Additional figures for the star-nosed mole.

(A) Fits across all bottleneck sizes for each model. Lowest root-mean-square error (RMSE) is indicated for each model. Dashed line indicates lowest RMSE (excluded for densities-only model as RMSE is …

Tables

Table 1
Model parameters for the star-nosed mole.
Ray1234567891011
Size1.141.211.211.171.081.021.001.131.050.871.10
Density45.7847.1445.8245.6945.246.9143.344.0144.2647.9250.46
Activation0.030.010.020.010.020.010.020.020.040.080.11
γ0.991.001.021.011.001.010.991.041.101.161.27

Additional files

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