Empirically Characterizing Overparameterization Impact on Convergence
A long-held conventional wisdom states that larger models train more slowly when using gradient descent. This work challenges this widely-held belief, showing that larger models can potentially train faster despite the increasing computational requirements of each training step. In particular, we study the effect of network structure (depth and width) on halting time and show that larger models---wider models in particular---take fewer training steps to converge. We design simple experiments to quantitatively characterize the effect of overparametrization on weight space traversal. Results show that halting time improves when growing model*s width for three different applications, and the improvement comes from each factor: The distance from initialized weights to converged weights shrinks with a power-law-like relationship, the average step size grows with a power-law-like relationship, and gradient vectors become more aligned with each other during traversal.
 This paper presents an empirical analysis of the convergence of deep NN training (in particular in language models and speech). Studying the effect of various hyperparameters on the convergence is certainly of great interest. However, the issue with this paper is that its analyses are mostly *descriptive*, rather than conclusive or even suggestive. For example, in Figure 2, it is shown that the convergence slope of Adam is steeper than that of SGD, when the x-axis is the model size. Very naturally I would be interested in a hypothesis like “Adam converges quicker than SGD as we increase the model size”, but there is no discussion like that. Throughout the paper there are many experimental results, but results are presented one after another, without many conclusions or suggestions made for practice. I don’t have a good take-away after reading it. The writing of this paper also needs to be improved significantly. In particular, lots of statements are made casually without justification. For example, “If hidden dimension is wide enough to absorb all the information within the input data, increasing width obviously would not affect convergence” -- Not so obvious to me, any reference? “Figure 4 shows a sketch of a model’s convergence curve ...” -- it’s not a fact but only a hypothesis. For example, what if for super large models the convergence gets slow and the curve gets back up again? In general, I think the paper is asking an interesting, important question, but more developments are needed from these initial experimental results.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Empirically Characterizing Overparameterization Impact on Convergence
A long-held conventional wisdom states that larger models train more slowly when using gradient descent. This work challenges this widely-held belief, showing that larger models can potentially train faster despite the increasing computational requirements of each training step. In particular, we study the effect of network structure (depth and width) on halting time and show that larger models---wider models in particular---take fewer training steps to converge. We design simple experiments to quantitatively characterize the effect of overparametrization on weight space traversal. Results show that halting time improves when growing model*s width for three different applications, and the improvement comes from each factor: The distance from initialized weights to converged weights shrinks with a power-law-like relationship, the average step size grows with a power-law-like relationship, and gradient vectors become more aligned with each other during traversal.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



 This paper presents an empirical analysis of the convergence of deep NN training (in particular in language models and speech). Studying the effect of various hyperparameters on the convergence is certainly of great interest. However, the issue with this paper is that its analyses are mostly *descriptive*, rather than conclusive or even suggestive. For example, in Figure 2, it is shown that the convergence slope of Adam is steeper than that of SGD, when the x-axis is the model size. Very naturally I would be interested in a hypothesis like “Adam converges quicker than SGD as we increase the model size”, but there is no discussion like that. Throughout the paper there are many experimental results, but results are presented one after another, without many conclusions or suggestions made for practice. I don’t have a good take-away after reading it. The writing of this paper also needs to be improved significantly. In particular, lots of statements are made casually without justification. For example, “If hidden dimension is wide enough to absorb all the information within the input data, increasing width obviously would not affect convergence” -- Not so obvious to me, any reference? “Figure 4 shows a sketch of a model’s convergence curve ...” -- it’s not a fact but only a hypothesis. For example, what if for super large models the convergence gets slow and the curve gets back up again? In general, I think the paper is asking an interesting, important question, but more developments are needed from these initial experimental results.
assistant
 This paper presents an empirical analysis of the convergence of deep NN training (in particular in language models and speech). Studying the effect of various hyperparameters on the convergence is certainly of great interest. However, the issue with this paper is that its analyses are mostly *descriptive*, rather than conclusive or even suggestive. For example, in Figure 2, it is shown that the convergence slope of Adam is steeper than that of SGD, when the x-axis is the model size. Very naturally I would be interested in a hypothesis like “Adam converges quicker than SGD as we increase the model size”, but there is no discussion like that. Throughout the paper there are many experimental results, but results are presented one after another, without many conclusions or suggestions made for practice. I don’t have a good take-away after reading it. The writing of this paper also needs to be improved significantly. In particular, lots of statements are made casually without justification. For example, “If hidden dimension is wide enough to absorb all the information within the input data, increasing width obviously would not affect convergence” -- Not so obvious to me, any reference? “Figure 4 shows a sketch of a model’s convergence curve ...” -- it’s not a fact but only a hypothesis. For example, what if for super large models the convergence gets slow and the curve gets back up again? In general, I think the paper is asking an interesting, important question, but more developments are needed from these initial experimental results.