Per-Weight Class-Based Learning Rates via Analytical Continuation
We study the problem of training deep fully connected neural networks. Despite much progress in the design of activation functions, novel normalization techniques, and various skip-connection techniques, such networks remain challenging to train due to vanishing or exploding gradients. Our method is based on employing a different class-dependent learning rate to each network weight. Since the learning rates are hyperparameters and not part of the network, we perform an analytical continuation of the network, and create a generalized network. Following this reparameterization, the set of per-class per-weight learning rates are being manipulated during the training iterations. Our results show that the new algorithm leads to improved classification accuracy for both classical and modern activation functions.
 In this paper, the authors propose to have a different learning rate depending on the class of the examples when learning a neural network. This paper*s contribution are quite moderate, as the proposed method seems to be a very natural extension but it is backed up by lots of numerical results. However, it would have been interesting to show the evolution of the learning rates (for every class) along the epochs and to correlate this evolution with the classes ratio or their separability or to analyse more in depths the properties of the obtained networks. It is rather unclear why changing the learning rate affects the performance of the model and it is would have been interesting to discuss. Moreover, it would be interesting to show if this class-based learning rates changes the convergence of the model or if the early stopping occurs earlier etc...
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Per-Weight Class-Based Learning Rates via Analytical Continuation
We study the problem of training deep fully connected neural networks. Despite much progress in the design of activation functions, novel normalization techniques, and various skip-connection techniques, such networks remain challenging to train due to vanishing or exploding gradients. Our method is based on employing a different class-dependent learning rate to each network weight. Since the learning rates are hyperparameters and not part of the network, we perform an analytical continuation of the network, and create a generalized network. Following this reparameterization, the set of per-class per-weight learning rates are being manipulated during the training iterations. Our results show that the new algorithm leads to improved classification accuracy for both classical and modern activation functions.
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>



 In this paper, the authors propose to have a different learning rate depending on the class of the examples when learning a neural network. This paper*s contribution are quite moderate, as the proposed method seems to be a very natural extension but it is backed up by lots of numerical results. However, it would have been interesting to show the evolution of the learning rates (for every class) along the epochs and to correlate this evolution with the classes ratio or their separability or to analyse more in depths the properties of the obtained networks. It is rather unclear why changing the learning rate affects the performance of the model and it is would have been interesting to discuss. Moreover, it would be interesting to show if this class-based learning rates changes the convergence of the model or if the early stopping occurs earlier etc...
assistant
 In this paper, the authors propose to have a different learning rate depending on the class of the examples when learning a neural network. This paper*s contribution are quite moderate, as the proposed method seems to be a very natural extension but it is backed up by lots of numerical results. However, it would have been interesting to show the evolution of the learning rates (for every class) along the epochs and to correlate this evolution with the classes ratio or their separability or to analyse more in depths the properties of the obtained networks. It is rather unclear why changing the learning rate affects the performance of the model and it is would have been interesting to discuss. Moreover, it would be interesting to show if this class-based learning rates changes the convergence of the model or if the early stopping occurs earlier etc...