of the paper: Overall the paper is reasonably well-written but the writing can improve in certain aspects. Some comments and questions below. 1. It is not apparent to the reader why the authors choose an asymptotic regime to focus on. My understanding is that the primary reason is easier theoretical tractability. It would help the reader to know why the paper focuses on the asymptotic setting. 2. It is unclear in the write-up if sample-wise descent occurs only in the over-parameterized regime or not. Pointing this explicitly in the place where you list your contributions would help. More broadly, it is important to have a discussion around these regimes in the main body and also a discussion around how they are defined in the asymptotic regime would help. 3. The paper is written in a very technical manner with very little proof intuition provided in the main body. It would benefit from having more intuition on the tools used and the reasons the main theorems hold. 4. Given that prior work already theoretically shows that sample-wise multiple descent can occur in linear regression, the main contribution of the paper appears to be the result that optimal regularization can remove double descent even in certain anisotropic settings. If this is not the case, the paper should do a better job of highlighting the novelty of their result in relation to prior results.
I am not too familiar with the particular techniques and tools used in the paper and could not verify the claims but they seem correct.
4. Given that prior work already theoretically shows that sample-wise multiple descent can occur in linear regression, the main contribution of the paper appears to be the result that optimal regularization can remove double descent even in certain anisotropic settings. If this is not the case, the paper should do a better job of highlighting the novelty of their result in relation to prior results. I am not too familiar with the particular techniques and tools used in the paper and could not verify the claims but they seem correct.