Table 1.

Experiment 1: Emergence of CSFs from biodistortion compensation (computational goal and error in CSFs). The achievement of the computational goal is described by ${\varepsilon }_{LMS}$ (error of the reconstructed signal in LMS) for batches of images of the independent test set (averages and standard deviations from 20 realizations with 50 images/batch). The distance between the CSFs of the networks and the human CSFs is measured by the RMSE between the functions, Equation 10. Uncertainty of the RMSE was estimated only in two cases (two layer ReLU and six layer sigmoid) and is represented here by the standard error of the corresponding means. It is interesting to note that the optimal linear solution (computed from the train set) has worse performance in the test set than the linearized versions of the networks.

	Comput. goal		CSFs		Comput. goal		CSFs
	${\varepsilon }_{LMS}$		RMSE		${\varepsilon }_{LMS}$		RMSE
Distortion	$15.5\pm 0.2$
Linear net	$\mathbf{13}.\mathbf{1}\pm 0.1$		$\mathbf{24}.\mathbf{4}$
CNNs	Sigmoid	ReLU	Sigmoid	ReLU	Sigmoid	ReLU	Sigmoid	ReLU
	nonlinear	nonlinear	nonlinear	nonlinear	linearized	linearized	linearized	linearized
2 Layers	$\mathbf{10}.\mathbf{3}\pm 0.1$	$\mathbf{10}.\mathbf{8}\pm 0.1$	$\mathbf{26}.\mathbf{9}$	$\mathbf{24}.\mathbf{5}\pm 0.3$	$12.5\pm 0.1$	$12.6\pm 0.2$	24.1	22.8
4 Layers	$\mathbf{8}.\mathbf{9}\pm 0.1$	$\mathbf{9}.\mathbf{1}\pm 0.1$	$\mathbf{26}.\mathbf{6}$	$\mathbf{28}.\mathbf{5}$	$12.5\pm 0.1$	$12.5\pm 0.1$	23.2	23.1
6 Layers	$\mathbf{8}.\mathbf{7}\pm 0.1$	$\mathbf{8}.\mathbf{5}\pm 0.1$	$\mathbf{29}.\mathbf{7}\pm 0.7$	$\mathbf{33}.\mathbf{1}$	$12.5\pm 0.2$	$12.5\pm 0.2$	23.2	23.1
8 Layers	$\mathbf{8}.\mathbf{9}\pm 0.2$	$\mathbf{8}.\mathbf{7}\pm 0.1$	$\mathbf{31}.\mathbf{2}$	$\mathbf{31}.\mathbf{6}$	$12.6\pm 0.1$	$12.7\pm 0.1$	27.0	27.4

Numbers in bold style refer to nonlinear networks and numbers in regular style refer to linearized networks.