Revisiting Critical Learning Periods in Deep Neural Networks

• While I appreciate the notion of the effective gradient, the derivation of it takes up a lot of space in the paper. Effectively, this could have been a simple statement of 'alignment between current gradient and $(w_final - w_i)$. As far as I can tell, the takeaway from the theory is that the effective gradient converges 0 while the actual gradient doesn't, hence while the effective gradient is large the model can be tripped up by bad data? In that case, it might help to start with a motivation / summary of the argument rather than building the argument up from the parts.
• The effective gradient provides good grounding for the experiments in this paper, but it's only available for post-hoc analysis. It seems to me that it might be correlated to per-step loss reduction, albeit not perfectly. Metrics like these might be measurable while training and provide actionable insights at what training phase to be extra careful about data quality.
• The experimental evaluation clearly supports the main argument of the paper. However, some details are unclear. For instance, the 'optimum' used to compute the effective gradient, is it the same between the different models, or do they each get their own, individual optima? Also, the claim that models with defective training reach a different basin would benefit from more support, e.g. by computing the mode connectivity between the clean/defective solution.
• The paper is generally well-written and carries a clear message. However, there seems to be some unnecessary math like on page 2 the KL. In the interest of clarity, I would recommend dropping it unless it helps make the argument.

• The paper does not define memorization clearly but starts using this term. This vague use can be very confusing to the reader. A suggested place to consider to define memorization is at the start of Section 2.

• The paper uses mutual information (MI) to measure memorization in Section 3.2. It would be beneficial to define this even before the mathematical preliminaries in prior subsections (also see first point). More importantly, there is no justification on why MI is a good definition of memorization in neural networks. A quick read of one of the references (Kleinman et al.)[https://arxiv.org/abs/2010.02459] appears to suggest that other/better metrics are preferred over MI to quantify memorization. The paper could benefit from a discussion of why MI is preferred in the current work over other metrics.

• (continuing with memorization metrics) There is vast literature that appears to define and use memorization measures some of which relates to noisy labels while others may related to noisy inputs. The paper would benefit if the paper includes a proper discussion of prior work to help both new and experienced readers to understand the current work's viewpoint

• There are other references that talk about memorization and Fisher Information (FI) that needs to be discussed in the paper. See (Jastrz ̨ebski et al.)[https://arxiv.org/abs/2012.14193] for instance. These prior works suggest that trace of FIM is good enough memorization measure. A discussion on preferring MI over other proposed measures could be useful.

• Certain sections on the paper are hard to follow. For instance it is hard for me to pick up the explanation in Sections 2.2 and 2.3 on FI and memorization.

• The paper proposes effective gradient. However, this metric is non-measurable so an approximation is used. However, the paper uses an approximation that relies on knowing the final solution (weights) which severely reduces the usefulness of this quantity both in concept as well as practice. The paper notes that the effective gradient is ``practically inaccessible''. However, the lack of access to effective gradient is not just in practice but also in theory in the case of online learning-like settings. A clarification on what settings effective gradient applies to would help clarify claims made in the paper.

(1) The experiments lack statistical analysis of the variance in metrics and model performance during CLPs, especially given that it is the "stochastic" gradient descent that behinds the research problem and motivates the proposed novel metrics. The authors are encouraged to add variance plots to the figures and conduct statistical tests to help readers better evaluate the consistency of the key findings.

(2) The explanation of experiment results regarding the relationship between FI dynamics and the memory phase seems questionable. In both Fig. 1 (b)(c), there is a slight initial increase followed by a decrease in FI at the beginning of training, although the change is not as large as in the defective training periods. Do these small changes of FI, at the beginning of the training, align well with the existing explanations of memorization and forgetting phases? Can one then simply conclude that "the surge in FI is a consequence of defective training"? The authors are encouraged to provide more explanations and discussion on this.

(3) Given the challenge of precisely defining CLPs in the training of deep learning models, the authors are encouraged to provide a clear problem setting for the CLPs that this paper aims to investigate and address, ideally in the first paragraph of the introduction. Personally, I found myself a bit lost in Sections 2.2 and 2.3, trying to understand what CLPs should be without considering FI dynamics, and then gained a much clearer understanding when I reached the discussion section, particularly the paragraph, "Critical learning periods are not time windows with clear boundaries." Additionally, the authors mentioned "The CLPs refer to the phenomenon where ..." in Section 4.2 but did not provide references there. In summary, previewing some key findings (like potentially a new "definition" and "understanding" of CLPs) in the early part of the introduction would help strengthen the writing and clarify the definition of CLPs in this paper.

1. All experiments were conducted only on CIFAR-10 dataset, without validation on larger-scale datasets like ImageNet. Also, there is no exploration of domains beyond image classification. Testing on more complex datasets and more types of defective data could further validate the generality of the effective gradient metric. Do the authors expect their findings to generalize to larger datasets or other domains?

2. The calculation of effective gradients, as discussed, relies on access to the full gradient, which is challenging to obtain in real-time during training. Although the paper acknowledges this limitation, it lacks concrete solutions or approximations that could make the effective gradient metric feasible in practical scenarios. How would the authors propose to calculate effective gradients during actual training, rather than post-hoc? Or is it true that effective gradient can only be used as a post-training analysis tool and not for actual guidance in training? Could the authors discuss any existing methods for approximating full gradients that might be applicable, or outline potential research directions for developing such approximations?

3. The paper claims to "shed light on enhancing model performance and robustness through such periods" in the abstract. Could the authors provide examples or guidelines on how this understanding of CLPs could be used to improve training strategies?

4. What are the computational requirements for calculating effective gradients in large-scale training scenarios? Could you provide a complexity analysis? Or could you provide an estimate of the additional computational overhead (e.g., in terms of time or memory) required to calculate effective gradients for a typical training run on your experimental setup?

I'd be happy to raise the score if the author could address my concerns.