# Response to Reviewer yfXT (3)

We thank Reviewer yfXT for the feedback on our work.

> My main concern is the paper’s writing and clarity. I found the flow of the paper lacking and, in general, the message the authors tried to convey did not pass clearly. In addition, there are many sloppy typos throughout the draft. Doing a very thorough revision and improving the writing flow would greatly benefit the paper and make the message much clearer.

**Typos and clarity of writing**: We have made substantial improvements in the exposition of the paper, detailed in the general comments, which as we hope conveys our message much clearer.

> The observations and conclusions from each of the experiments should be clearly stated.

**Discussion of the experiments**: The submitted paper states the main take-aways for each experiment in the respective figure caption. In addition to those, we provide a detailed interpretation of each result in the main text. A detailed description of the experimental setting is in the supplementary material. We kindly ask Reviewer yfXT to point out which experiments were unclear in particular, so that we can point to the respective explanation, improve those explanations, and/or provide clarifying remarks.

> The Theorems are very technical, and some explanations will help better understand the results. For example, how is the function m behaves as a function of z? What this means on B and V depends on $\lambda$? There is some discussion in the paper, but I found it insufficient.

**Intuition for theorems**: While both theorems are rather technical, we additionally provide intuition that can help to understand their significance. For example, we plot the asymptotic values for the standard and the robust risks from Theorems 3.1 and 4.1 in Figures 2 and 4 respectively. In both cases we show that regularization helps to achieve a lower asymptotic robust risk and that the trend is closely matched by simulations for finite $d$ and $n$. Furthermore, in Sections 3.4 and 4.4, we conduct additional experiments in order to gain further insights on the phenomena causing robust overfitting for linear and logistic regression (see Figures 3 and 5, respectively).

**Interpretation of the quantities $B,V,m(z)$ that appear in Theorem 3.1**: As we mention in the main text, Theorem 3.1 is an extension for the robust risk of a result originally derived by Hastie et al. for the standard risk. Therefore, many of the quantities in Theorem 3.1 have been introduced in [1]. In particular, $B$ and $V$ represent the asymptotic bias and variance, respectively, as we mention in the theorem statement. Furthermore, the function $m(z)$ is the Stieltjes transform of the Marchenko-Pastur law. We added a comment on this in a revised version of our paper.

[1]: Surprises in High-Dimensional Ridgeless Least Squares Interpolation. Trevor Hastie, Andrea Montanari, Saharon Rosset, Ryan J. Tibshirani. Arxiv 18.