The loss surface of residual networks: Ensembles and the role of batch normalization
Deep Residual Networks present a premium in performance in comparison to conventional networks of the same depth and are trainable at extreme depths. It has recently been shown that Residual Networks behave like ensembles of relatively shallow networks. We show that these ensemble are dynamic: while initially the virtual ensemble is mostly at depths lower than half the network’s depth, as training progresses, it becomes deeper and deeper. The main mechanism that controls the dynamic ensemble behavior is the scaling introduced, e.g., by the Batch Normalization technique. We explain this behavior and demonstrate the driving force behind it. As a main tool in our analysis, we employ generalized spin glass models, which we also use in order to study the number of critical points in the optimization of Residual Networks.
This paper extend the Spin Glass analysis of Choromanska et al. (2015a) to Res Nets which yield the novel dynamic ensemble results for Res Nets and the connection to Batch Normalization and the analysis of their loss surface of Res Nets. The paper is well-written with many insightful explanation of results. Although the technical contributions extend the Spin Glass model analysis of the ones by Choromanska et al. (2015a), the updated version could eliminate one of the unrealistic assumptions and the analysis further provides novel dynamic ensemble results and the connection to Batch Normalization that gives more insightful results about the structure of Res Nets. It is essential to show this dynamic behaviour in a regime without batch normalization to untangle the normalization effect on ensemble feature. Hence authors claim that steady increase in the L_2 norm of the weights will maintain the this feature but setting for Figure 1 is restrictive to empirically support the claim. At least results on CIFAR 10 without batch normalization for showing effect of L_2 norm increase and results that support claims about Theorem 4 would strengthen the paper. This work provides an initial rigorous framework to analyze better the inherent structure of the current state of art Res Net architectures and its variants which can stimulate potentially more significant results towards careful understanding of current state of art models (Rather than always to attempting to improve the performance of Res Nets by applying intuitive incremental heuristics, it is important to progress on some solid understanding too).
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
The loss surface of residual networks: Ensembles and the role of batch normalization
Deep Residual Networks present a premium in performance in comparison to conventional networks of the same depth and are trainable at extreme depths. It has recently been shown that Residual Networks behave like ensembles of relatively shallow networks. We show that these ensemble are dynamic: while initially the virtual ensemble is mostly at depths lower than half the network’s depth, as training progresses, it becomes deeper and deeper. The main mechanism that controls the dynamic ensemble behavior is the scaling introduced, e.g., by the Batch Normalization technique. We explain this behavior and demonstrate the driving force behind it. As a main tool in our analysis, we employ generalized spin glass models, which we also use in order to study the number of critical points in the optimization of Residual Networks.
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 extend the Spin Glass analysis of Choromanska et al. (2015a) to Res Nets which yield the novel dynamic ensemble results for Res Nets and the connection to Batch Normalization and the analysis of their loss surface of Res Nets. The paper is well-written with many insightful explanation of results. Although the technical contributions extend the Spin Glass model analysis of the ones by Choromanska et al. (2015a), the updated version could eliminate one of the unrealistic assumptions and the analysis further provides novel dynamic ensemble results and the connection to Batch Normalization that gives more insightful results about the structure of Res Nets. It is essential to show this dynamic behaviour in a regime without batch normalization to untangle the normalization effect on ensemble feature. Hence authors claim that steady increase in the L_2 norm of the weights will maintain the this feature but setting for Figure 1 is restrictive to empirically support the claim. At least results on CIFAR 10 without batch normalization for showing effect of L_2 norm increase and results that support claims about Theorem 4 would strengthen the paper. This work provides an initial rigorous framework to analyze better the inherent structure of the current state of art Res Net architectures and its variants which can stimulate potentially more significant results towards careful understanding of current state of art models (Rather than always to attempting to improve the performance of Res Nets by applying intuitive incremental heuristics, it is important to progress on some solid understanding too).
assistant
This paper extend the Spin Glass analysis of Choromanska et al. (2015a) to Res Nets which yield the novel dynamic ensemble results for Res Nets and the connection to Batch Normalization and the analysis of their loss surface of Res Nets. The paper is well-written with many insightful explanation of results. Although the technical contributions extend the Spin Glass model analysis of the ones by Choromanska et al. (2015a), the updated version could eliminate one of the unrealistic assumptions and the analysis further provides novel dynamic ensemble results and the connection to Batch Normalization that gives more insightful results about the structure of Res Nets. It is essential to show this dynamic behaviour in a regime without batch normalization to untangle the normalization effect on ensemble feature. Hence authors claim that steady increase in the L_2 norm of the weights will maintain the this feature but setting for Figure 1 is restrictive to empirically support the claim. At least results on CIFAR 10 without batch normalization for showing effect of L_2 norm increase and results that support claims about Theorem 4 would strengthen the paper. This work provides an initial rigorous framework to analyze better the inherent structure of the current state of art Res Net architectures and its variants which can stimulate potentially more significant results towards careful understanding of current state of art models (Rather than always to attempting to improve the performance of Res Nets by applying intuitive incremental heuristics, it is important to progress on some solid understanding too).