Skip Connections Eliminate Singularities
Skip connections made the training of very deep networks possible and have become an indispensable component in a variety of neural architectures. A completely satisfactory explanation for their success remains elusive. Here, we present a novel explanation for the benefits of skip connections in training very deep networks. The difficulty of training deep networks is partly due to the singularities caused by the non-identifiability of the model. Several such singularities have been identified in previous works: (i) overlap singularities caused by the permutation symmetry of nodes in a given layer, (ii) elimination singularities corresponding to the elimination, i.e. consistent deactivation, of nodes, (iii) singularities generated by the linear dependence of the nodes. These singularities cause degenerate manifolds in the loss landscape that slow down learning. We argue that skip connections eliminate these singularities by breaking the permutation symmetry of nodes, by reducing the possibility of node elimination and by making the nodes less linearly dependent. Moreover, for typical initializations, skip connections move the network away from the "ghosts" of these singularities and sculpt the landscape around them to alleviate the learning slow-down. These hypotheses are supported by evidence from simplified models, as well as from experiments with deep networks trained on real-world datasets.
 Paper examines the use of skip connections (including residual layers) in deep networks as a way of alleviating two perceived difficulties in training: 1) when a neuron does not contain any information, and 2) when two neurons in a layer compute the same function. Both of these cases lead to singularities in the Hessian matrix, and this work includes a number of experiments showing the effect of skip connections on the Hessian during training. This is a significant and timely topic. While I may not be the best one to judge the originality of this work, I appreciated how the authors presented clear and concise arguments with experiments to back up their claims.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Skip Connections Eliminate Singularities
Skip connections made the training of very deep networks possible and have become an indispensable component in a variety of neural architectures. A completely satisfactory explanation for their success remains elusive. Here, we present a novel explanation for the benefits of skip connections in training very deep networks. The difficulty of training deep networks is partly due to the singularities caused by the non-identifiability of the model. Several such singularities have been identified in previous works: (i) overlap singularities caused by the permutation symmetry of nodes in a given layer, (ii) elimination singularities corresponding to the elimination, i.e. consistent deactivation, of nodes, (iii) singularities generated by the linear dependence of the nodes. These singularities cause degenerate manifolds in the loss landscape that slow down learning. We argue that skip connections eliminate these singularities by breaking the permutation symmetry of nodes, by reducing the possibility of node elimination and by making the nodes less linearly dependent. Moreover, for typical initializations, skip connections move the network away from the "ghosts" of these singularities and sculpt the landscape around them to alleviate the learning slow-down. These hypotheses are supported by evidence from simplified models, as well as from experiments with deep networks trained on real-world datasets.
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>



 Paper examines the use of skip connections (including residual layers) in deep networks as a way of alleviating two perceived difficulties in training: 1) when a neuron does not contain any information, and 2) when two neurons in a layer compute the same function. Both of these cases lead to singularities in the Hessian matrix, and this work includes a number of experiments showing the effect of skip connections on the Hessian during training. This is a significant and timely topic. While I may not be the best one to judge the originality of this work, I appreciated how the authors presented clear and concise arguments with experiments to back up their claims.
assistant
 Paper examines the use of skip connections (including residual layers) in deep networks as a way of alleviating two perceived difficulties in training: 1) when a neuron does not contain any information, and 2) when two neurons in a layer compute the same function. Both of these cases lead to singularities in the Hessian matrix, and this work includes a number of experiments showing the effect of skip connections on the Hessian during training. This is a significant and timely topic. While I may not be the best one to judge the originality of this work, I appreciated how the authors presented clear and concise arguments with experiments to back up their claims.