For all authors... (a) Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope? If you ran experiments... (a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [No] (b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)?

See Appendix A.9 for the derivation of the Hessian. We have proved the statement (a). Notice that this is a contradiction because any point with WL+1 = 0 is in the set S. Hence, there exists no point at which the Hessian is negative semidefinite. Because the negative semidefiniteness is a necessary condition for a local maximum, every critical point is then either a local minimum or a saddle point. We have proved the statement (b).