On orthogonality and learning recurrent networks with long term dependencies
It is well known that it is challenging to train deep neural networks and recurrent neural networks for tasks that exhibit long term dependencies. The vanishing or exploding gradient problem is a well known issue associated with these challenges. One approach to addressing vanishing and exploding gradients is to use either soft or hard constraints on weight matrices so as to encourage or enforce orthogonality. Orthogonal matrices preserve gradient norm during backpropagation and can therefore be a desirable property; however, we find that hard constraints on orthogonality can negatively affect the speed of convergence and model performance. This paper explores the issues of optimization convergence, speed and gradient stability using a variety of different methods for encouraging or enforcing orthogonality. In particular we propose a weight matrix factorization and parameterization strategy through which we we can bound matrix norms and therein control the degree of expansivity induced during backpropagation.
Vanishing and exploding gradients makes the optimization of RNNs very challenging. The issue becomes worse on tasks with long term dependencies that requires longer RNNs. One of the suggested approaches to improve the optimization is to optimize in a way that the transfer matrix is almost orthogonal. This paper investigate the role of orthogonality on the optimization and learning which is very important. The writing is sound and clear and arguments are easy to follow. The suggested optimization method is very interesting. The main shortcoming of this paper is the experiments which I find very important and I hope authors can update the experiment section significantly. Below I mention some comments on the experiment section: 1- I think the experiments are not enough. At the very least, report the result on the adding problem and language modeling task on Penn Treebank. 2- I understand that the copying task becomes difficult with non-lineary. However, removing non-linearity makes the optimization very different and therefore, it is very hard to conclude anything from the results on the copying task. 3- I was not able to find the number of hidden units used for RNNs in different tasks. 4- Please report the running time of your method in the paper for different numbers of hidden units, compare it with the SGD and mention the NN package you have used. 5- The results on Table 1 and Table 2 might also suggest that the orthogonality is not really helpful since even without a margin, the numbers are very close compare to the case when you find the optimal margin. Am I right? 6- What do we learn from Figure 2? It is left without any discussion.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
On orthogonality and learning recurrent networks with long term dependencies
It is well known that it is challenging to train deep neural networks and recurrent neural networks for tasks that exhibit long term dependencies. The vanishing or exploding gradient problem is a well known issue associated with these challenges. One approach to addressing vanishing and exploding gradients is to use either soft or hard constraints on weight matrices so as to encourage or enforce orthogonality. Orthogonal matrices preserve gradient norm during backpropagation and can therefore be a desirable property; however, we find that hard constraints on orthogonality can negatively affect the speed of convergence and model performance. This paper explores the issues of optimization convergence, speed and gradient stability using a variety of different methods for encouraging or enforcing orthogonality. In particular we propose a weight matrix factorization and parameterization strategy through which we we can bound matrix norms and therein control the degree of expansivity induced during backpropagation.
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>



Vanishing and exploding gradients makes the optimization of RNNs very challenging. The issue becomes worse on tasks with long term dependencies that requires longer RNNs. One of the suggested approaches to improve the optimization is to optimize in a way that the transfer matrix is almost orthogonal. This paper investigate the role of orthogonality on the optimization and learning which is very important. The writing is sound and clear and arguments are easy to follow. The suggested optimization method is very interesting. The main shortcoming of this paper is the experiments which I find very important and I hope authors can update the experiment section significantly. Below I mention some comments on the experiment section: 1- I think the experiments are not enough. At the very least, report the result on the adding problem and language modeling task on Penn Treebank. 2- I understand that the copying task becomes difficult with non-lineary. However, removing non-linearity makes the optimization very different and therefore, it is very hard to conclude anything from the results on the copying task. 3- I was not able to find the number of hidden units used for RNNs in different tasks. 4- Please report the running time of your method in the paper for different numbers of hidden units, compare it with the SGD and mention the NN package you have used. 5- The results on Table 1 and Table 2 might also suggest that the orthogonality is not really helpful since even without a margin, the numbers are very close compare to the case when you find the optimal margin. Am I right? 6- What do we learn from Figure 2? It is left without any discussion.
assistant
Vanishing and exploding gradients makes the optimization of RNNs very challenging. The issue becomes worse on tasks with long term dependencies that requires longer RNNs. One of the suggested approaches to improve the optimization is to optimize in a way that the transfer matrix is almost orthogonal. This paper investigate the role of orthogonality on the optimization and learning which is very important. The writing is sound and clear and arguments are easy to follow. The suggested optimization method is very interesting. The main shortcoming of this paper is the experiments which I find very important and I hope authors can update the experiment section significantly. Below I mention some comments on the experiment section: 1- I think the experiments are not enough. At the very least, report the result on the adding problem and language modeling task on Penn Treebank. 2- I understand that the copying task becomes difficult with non-lineary. However, removing non-linearity makes the optimization very different and therefore, it is very hard to conclude anything from the results on the copying task. 3- I was not able to find the number of hidden units used for RNNs in different tasks. 4- Please report the running time of your method in the paper for different numbers of hidden units, compare it with the SGD and mention the NN package you have used. 5- The results on Table 1 and Table 2 might also suggest that the orthogonality is not really helpful since even without a margin, the numbers are very close compare to the case when you find the optimal margin. Am I right? 6- What do we learn from Figure 2? It is left without any discussion.