A common point you brought up

Thank you very much for your detailed reviews and comments. The simplest version of our toy landscape is constructed as follows. As such, our toy model serves us well, albeit it doesn't In real nets, we find a large number of weight-space directions in which we can move very far, while the loss doesn't We find the full low-loss manifold to be a union of those in different directions and orientations. We will include this extended discussion in the paper. In all cases the results supported our landscape model and we will include them in the final version.