We would like to thank all the reviewers for their comprehensive reviews. We clarify the major comments below. As noted in Sec.6 (and suggested by As discussed in Sec.1, 1.1, 2-4, and Figure 1, TensorNOODL accomplishes Therefore, it seems that leveraging tensor structure may increase the computational complexity. Thank you for this insight. Further, TensorNOODL requires the initial dictionary estimate to follow A.2. for exact recovery at a linear Initializations which do not meet these conditions may still converge, albeit not at a linear rate.

The robust training built upon the loose guarantees limits the improvement of model robustness.

The right to be forgotten calls for efficient machine unlearning techniques that make trained machine learning models forget a cohort of data.

Atypically to standard NN applications, financial industry practitioners use such models equally to replicate market prices and to value other financial instruments. In other words, low training losses are as important as generalization capabilities.

In this section we provide a proof of Theorem 9 and a numerical comparison with the P AC-Bayes-Bernstein inequality. The proof is based on the standard change of measure argument. The second ingredient is Bennett's lemma, which is a bound on the moment generating function used Now we are ready to prove the theorem. Therefore, for µ < 0 .5 we have null In this section we provide technical details on minimization of the bounds in Theorems 12 and 15. As most of the other P AC-Bayesian works, we take π to be a union distribution over the hypotheses 14 in both cases.