The accuracy of the non-linear deep neural network is tested. We assume a four layers network with, respectively, N1 = 784, N2, N3 = 120, N4 = 10; N2 is changed so as to enlarge the set of parameters to be trained. The red line refers to the spectral training, with N2 + N3 + N4 adjusted eigenvalues. The blue line stands for a neural network trained in direct space, the target of the optimisation being a subset made of N2 + N3 + N4 weights, randomly selected from the available pool of N1N2 + N2N3 + N3N4 tunable parameters. The black line reports the accuracy of the linear neural network when training the full set of N1N2 + N2N3 + N3N4 weights. The green line refers to the spectral learning when eigenvalues and eigenvectors are simultaneously trained.