An Empirical Analysis of Deep Network Loss Surfaces
The training of deep neural networks is a high-dimension optimization problem with respect to the loss function of a model. Unfortunately, these functions are of high dimension and non-convex and hence difficult to characterize. In this paper, we empirically investigate the geometry of the loss functions for state-of-the-art networks with multiple stochastic optimization methods. We do this through several experiments that are visualized on polygons to understand how and when these stochastic optimization methods find minima.
I appreciate the work but I do not think the paper is clear enough. Moreover, the authors say *local minimia* ~70 times but do not show (except for Figure 11?) that the solutions found are not necessarily local minima. The authors do not talk about that fact that slices of a non-convex problem can look like the ones they show. It is well-known that the first-order methods may just fail to deal with certain non-convex ill-conditioned problems even in low-dimensional noiseless cases, the place/solution where they fail to make progress is not necessarily a local minimum. Some sentences like the one given below suggest that the study is too superficial: *One of the interesting empirical observation is that we often observe is that the incremental improvement of optimization methods decreases rapidly even in non-convex problems.*
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
An Empirical Analysis of Deep Network Loss Surfaces
The training of deep neural networks is a high-dimension optimization problem with respect to the loss function of a model. Unfortunately, these functions are of high dimension and non-convex and hence difficult to characterize. In this paper, we empirically investigate the geometry of the loss functions for state-of-the-art networks with multiple stochastic optimization methods. We do this through several experiments that are visualized on polygons to understand how and when these stochastic optimization methods find minima.
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>



I appreciate the work but I do not think the paper is clear enough. Moreover, the authors say *local minimia* ~70 times but do not show (except for Figure 11?) that the solutions found are not necessarily local minima. The authors do not talk about that fact that slices of a non-convex problem can look like the ones they show. It is well-known that the first-order methods may just fail to deal with certain non-convex ill-conditioned problems even in low-dimensional noiseless cases, the place/solution where they fail to make progress is not necessarily a local minimum. Some sentences like the one given below suggest that the study is too superficial: *One of the interesting empirical observation is that we often observe is that the incremental improvement of optimization methods decreases rapidly even in non-convex problems.*
assistant
I appreciate the work but I do not think the paper is clear enough. Moreover, the authors say *local minimia* ~70 times but do not show (except for Figure 11?) that the solutions found are not necessarily local minima. The authors do not talk about that fact that slices of a non-convex problem can look like the ones they show. It is well-known that the first-order methods may just fail to deal with certain non-convex ill-conditioned problems even in low-dimensional noiseless cases, the place/solution where they fail to make progress is not necessarily a local minimum. Some sentences like the one given below suggest that the study is too superficial: *One of the interesting empirical observation is that we often observe is that the incremental improvement of optimization methods decreases rapidly even in non-convex problems. *