Matrix losses as a function of the choice of the banding parameter k for the toy model. The dashed (red), dotted (blue) and solid (green) lines correspond to the KL, ||CΔΩ|| and ||ΔΩ||_F losses, respectively. The losses are all normalized to the minimum value of the loss. Recall that k is defined including the main diagonal (e.g. k = 2 corresponds to one-off diagonal element). All of these are computed for d = 500 simulations. We find a well-defined minimum here, although for two of the three norms, it is at k = 3 and not k = 2.