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Eigenspectra of renormalization group (RG)-inspired clustering, direct functional region sampling (FSap), and random sampling (RSap) in ERM. (A, D) RG clustered eigenspectra of ERM. The size of the cluster is denoted by N , which is the number of neurons in each cluster. We adopt the RG approach (Meshulam et al., 2018; Meshulam et al., 2019), but with a specific modification (Appendix 1). (B, E) Direct spatial sampling in the functional space (FSap) and the corresponding ERM eigenspectra. We began our analysis with a set of N0 neurons distributed in the functional space. Initially, we chose N=N0/2 neurons that were located exclusively on one side of the x-axis of this space. We then proceeded to select N=N0/4 neurons from 4 quadrants. This sampling process was repeated iteratively, generating successively smaller subsets of neurons. (C, F) Random sampled (RSap) eigenspectra of ERM. ERM parameters: (A–C) Exponential function f(x⃗ )=e−∥x⃗ ∥/b where b=1 , ρ=10.24 and dimension d=2 . (D–F) Approximate power law Equation 11 with μ=0.5 , ρ=10.24 and dimension d=2 . Other parameters are the same as Figure 3. The standard error of the mean (SEM) across the clusters is represented by the shaded area of each line. |