FastNorm: Improving Numerical Stability of Deep Network Training with Efficient Normalization
We propose a modification to weight normalization techniques that provides the same convergence benefits but requires fewer computational operations. The proposed method, FastNorm, exploits the low-rank properties of weight updates and infers the norms without explicitly calculating them, replacing an computation with an one for a fully-connected layer. It improves numerical stability and reduces accuracy variance enabling higher learning rate and offering better convergence. We report experimental results that illustrate the advantage of the proposed method.
 This paper proposes a computationally fast method to train neural networks with normalized weights. Experiments demonstrate that their method is promising compared to the competitor “NormProp” which explicitly normalizes the weights of neural networks. Pros: (1) The paper is easy to follow. (2) Authors use figures that are easy to understand to explain their core idea, i.e., maintaining a vector which estimates the row norm of weight matrix and implicitly normalizing weights. Cons: (1) If we count the matrix multiplication operation in fc layer along with normalization (in common cases normalization should follow a weighted layer), the whole computation complexity becomes O(mn) rather than O(n+m), so I doubt how fast it could be in the common case. (2) Authors did a MNIST experiment with a 2-fc layer neural network for comparing their FastNorm to NormProp. It is a bit strange that they do not show the difference of speed, but show that FastNorm can outperform NormProp in terms of classification accuracy with a higher learning rate. Since the efficiency is one of the main contributions, I suggest authors add this comparison. (3) The proposed FastNorm improves the stability by observing the standard deviation of validation accuracies in training phase. The authors attribute this to the reduction of accumulated rounding error in training process, which is somewhat against the community’s consensus, i.e., float precision is not that important so we can use float32 or even float16 to train/do inference for neural networks. I’m curious if this phenomenon still holds if authors use float64 in the experiments. Some typos: First line in page 3: “brining” should be “bringing” Overall, I think the current version of the paper is not ready for ICLR conference. Authors need more experiments to show their approach’s effectiveness. For example, batching and convolution as mentioned by authors would be more significant.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
FastNorm: Improving Numerical Stability of Deep Network Training with Efficient Normalization
We propose a modification to weight normalization techniques that provides the same convergence benefits but requires fewer computational operations. The proposed method, FastNorm, exploits the low-rank properties of weight updates and infers the norms without explicitly calculating them, replacing an computation with an one for a fully-connected layer. It improves numerical stability and reduces accuracy variance enabling higher learning rate and offering better convergence. We report experimental results that illustrate the advantage of the proposed method.
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 proposes a computationally fast method to train neural networks with normalized weights. Experiments demonstrate that their method is promising compared to the competitor “NormProp” which explicitly normalizes the weights of neural networks. Pros: (1) The paper is easy to follow. (2) Authors use figures that are easy to understand to explain their core idea, i.e., maintaining a vector which estimates the row norm of weight matrix and implicitly normalizing weights. Cons: (1) If we count the matrix multiplication operation in fc layer along with normalization (in common cases normalization should follow a weighted layer), the whole computation complexity becomes O(mn) rather than O(n+m), so I doubt how fast it could be in the common case. (2) Authors did a MNIST experiment with a 2-fc layer neural network for comparing their FastNorm to NormProp. It is a bit strange that they do not show the difference of speed, but show that FastNorm can outperform NormProp in terms of classification accuracy with a higher learning rate. Since the efficiency is one of the main contributions, I suggest authors add this comparison. (3) The proposed FastNorm improves the stability by observing the standard deviation of validation accuracies in training phase. The authors attribute this to the reduction of accumulated rounding error in training process, which is somewhat against the community’s consensus, i.e., float precision is not that important so we can use float32 or even float16 to train/do inference for neural networks. I’m curious if this phenomenon still holds if authors use float64 in the experiments. Some typos: First line in page 3: “brining” should be “bringing” Overall, I think the current version of the paper is not ready for ICLR conference. Authors need more experiments to show their approach’s effectiveness. For example, batching and convolution as mentioned by authors would be more significant.
assistant
 This paper proposes a computationally fast method to train neural networks with normalized weights. Experiments demonstrate that their method is promising compared to the competitor “NormProp” which explicitly normalizes the weights of neural networks. Pros: (1) The paper is easy to follow. (2) Authors use figures that are easy to understand to explain their core idea, i.e., maintaining a vector which estimates the row norm of weight matrix and implicitly normalizing weights. Cons: (1) If we count the matrix multiplication operation in fc layer along with normalization (in common cases normalization should follow a weighted layer), the whole computation complexity becomes O(mn) rather than O(n+m), so I doubt how fast it could be in the common case. (2) Authors did a MNIST experiment with a 2-fc layer neural network for comparing their FastNorm to NormProp. It is a bit strange that they do not show the difference of speed, but show that FastNorm can outperform NormProp in terms of classification accuracy with a higher learning rate. Since the efficiency is one of the main contributions, I suggest authors add this comparison. (3) The proposed FastNorm improves the stability by observing the standard deviation of validation accuracies in training phase. The authors attribute this to the reduction of accumulated rounding error in training process, which is somewhat against the community’s consensus, i.e., float precision is not that important so we can use float32 or even float16 to train/do inference for neural networks. I’m curious if this phenomenon still holds if authors use float64 in the experiments. Some typos: First line in page 3: “brining” should be “bringing” Overall, I think the current version of the paper is not ready for ICLR conference. Authors need more experiments to show their approach’s effectiveness. For example, batching and convolution as mentioned by authors would be more significant.