Figure 2.

Nonlinear RFs could be estimated by CNN encoding models for simulated simple cells and complex cells. (a,b) Scheme of response generation for simulated simple cells (a) and simulated complex cells (b) (See Methods for details). The Gabor-shaped filters of simulated simple cell A and complex cell B are displayed. (c) Left: comparison of the response predictions among the following encoding models: the L1-regularised linear regression model (Lasso), L2-regularised linear regression model (Ridge), support vector regression model (SVR), hierarchical structural model (HSM), and CNN. Data are presented as the mean ± s.e.m. (N = 30 simulated simple cells and N = 70 simulated complex cells). Right: cumulative distribution of CNN prediction similarity. Simulated cells with a CNN prediction similarity ≤0.3 (indicated as the red arrow) were removed from the following receptive field (RF) analysis. (d,f) Results of iterative CNN RF estimations for simulated simple cell A (d) and complex cell B (f). Only 20 of the 100 generated RF images are shown in these panels. Grids are depicted in cyan. Although the simulated simple cell A had RFs in nearly identical positions, the simulate complex cell B had RFs in shifted positions. (e,g) Linearly estimated RFs (linear RFs) of simulated simple cell A (e) and complex cell B (g), using a regularised pseudoinverse method. (h) Gabor-fitting similarity of CNN RFs, defined as the Pearson correlation coefficient between the CNN RF and fitted Gabor kernel. (i) Maximum similarity between each generator filter and 100 CNN RFs. (j) Maximum similarity between linear RFs and CNN RFs. Similarity was defined as the normalised pixelwise dot product between the linear RF and CNN RF. (k) Relationship of the Gabor orientations between generator filters and CNN RFs. (l) Distribution of complexness. Only cells with a CNN prediction similarity >0.3 were analysed in (h–l) (N = 19 simple cells and N = 47 complex cells).