Demystifying ResNet
We provide a theoretical explanation for the superb performance of ResNet via the study of deep linear networks and some nonlinear variants. We show that with or without nonlinearities, by adding shortcuts that have depth two, the condition number of the Hessian of the loss function at the zero initial point is depth-invariant, which makes training very deep models no more difficult than shallow ones. Shortcuts of higher depth result in an extremely flat (high-order) stationary point initially, from which the optimization algorithm is hard to escape. The 1-shortcut, however, is essentially equivalent to no shortcuts. Extensive experiments are provided accompanying our theoretical results. We show that initializing the network to small weights with 2-shortcuts achieves significantly better results than random Gaussian (Xavier) initialization, orthogonal initialization, and shortcuts of deeper depth, from various perspectives ranging from final loss, learning dynamics and stability, to the behavior of the Hessian along the learning process.
ResNet and other architectures that use shortcuts have shown empirical success in several domains and therefore, studying the optimization for such architectures is very valuable. This paper is an attempt to address some of the properties of networks that use shortcuts. Some of the experiments in the paper are interesting. However, there are two main issues with the current paper: 1- linear vs non-linear: I think studying linear networks is valuable but we should be careful not to extend the results to networks with non-linear activations without enough evidence. This is especially true for Hessian as the Hessian of non-linear networks have very large condition number (see the ICLR submission *Singularity of Hessian in Deep Learning*) even in cases where the optimization is not challenging. Therefore, I don*t agree with the claims in the paper on non-linear networks. Moreover, one plot on MNIST is not enough to claim that non-linear networks behave similar to linear networks. 2- Hessian at zero initial point: The explanation of why we should be interested in Hessain at zero initial point is not acceptable. The zero initial point is not interesting because it is a very particular point that cannot tell us about the Hessian during optimization.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Demystifying ResNet
We provide a theoretical explanation for the superb performance of ResNet via the study of deep linear networks and some nonlinear variants. We show that with or without nonlinearities, by adding shortcuts that have depth two, the condition number of the Hessian of the loss function at the zero initial point is depth-invariant, which makes training very deep models no more difficult than shallow ones. Shortcuts of higher depth result in an extremely flat (high-order) stationary point initially, from which the optimization algorithm is hard to escape. The 1-shortcut, however, is essentially equivalent to no shortcuts. Extensive experiments are provided accompanying our theoretical results. We show that initializing the network to small weights with 2-shortcuts achieves significantly better results than random Gaussian (Xavier) initialization, orthogonal initialization, and shortcuts of deeper depth, from various perspectives ranging from final loss, learning dynamics and stability, to the behavior of the Hessian along the learning process.
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>



ResNet and other architectures that use shortcuts have shown empirical success in several domains and therefore, studying the optimization for such architectures is very valuable. This paper is an attempt to address some of the properties of networks that use shortcuts. Some of the experiments in the paper are interesting. However, there are two main issues with the current paper: 1- linear vs non-linear: I think studying linear networks is valuable but we should be careful not to extend the results to networks with non-linear activations without enough evidence. This is especially true for Hessian as the Hessian of non-linear networks have very large condition number (see the ICLR submission *Singularity of Hessian in Deep Learning*) even in cases where the optimization is not challenging. Therefore, I don*t agree with the claims in the paper on non-linear networks. Moreover, one plot on MNIST is not enough to claim that non-linear networks behave similar to linear networks. 2- Hessian at zero initial point: The explanation of why we should be interested in Hessain at zero initial point is not acceptable. The zero initial point is not interesting because it is a very particular point that cannot tell us about the Hessian during optimization.
assistant
ResNet and other architectures that use shortcuts have shown empirical success in several domains and therefore, studying the optimization for such architectures is very valuable. This paper is an attempt to address some of the properties of networks that use shortcuts. Some of the experiments in the paper are interesting. However, there are two main issues with the current paper: 1- linear vs non-linear: I think studying linear networks is valuable but we should be careful not to extend the results to networks with non-linear activations without enough evidence. This is especially true for Hessian as the Hessian of non-linear networks have very large condition number (see the ICLR submission *Singularity of Hessian in Deep Learning*) even in cases where the optimization is not challenging. Therefore, I don*t agree with the claims in the paper on non-linear networks. Moreover, one plot on MNIST is not enough to claim that non-linear networks behave similar to linear networks. 2- Hessian at zero initial point: The explanation of why we should be interested in Hessain at zero initial point is not acceptable. The zero initial point is not interesting because it is a very particular point that cannot tell us about the Hessian during optimization.