We thank the reviewers for their comments and suggestions. Hereafter, we list reviewers' (sometimes paraphrased) Each answer will translate into a clarification in the final version. Reviewer #2 and #3 felt that our message was lacking clarity. A.2). We will add more pointers to their statistical analysis, from the existing literature (e.g. L81-90 in the main paper, often α(m) = 1/ m in these works).

Modern neural networks often have great expressive power and can be trained to overfit the training data, while still achieving a good test performance.

We focus on a stochastic learning model where the learner observes a finite set of training examples and the output of the learning process is a data-dependent distribution over a space of hypotheses.