ACIQ: Analytical Clipping for Integer Quantization of neural networks
We analyze the trade-off between quantization noise and clipping distortion in low precision networks. We identify the statistics of various tensors, and derive exact expressions for the mean-square-error degradation due to clipping. By optimizing these expressions, we show marked improvements over standard quantization schemes that normally avoid clipping. For example, just by choosing the accurate clipping values, more than 40\% accuracy improvement is obtained for the quantization of VGG-16 to 4-bits of precision. Our results have many applications for the quantization of neural networks at both training and inference time.
 This paper empirically finds that the distribution of activations in quantized networks follow Gaussian or Laplacian distribution, and proposes to determine the optimal clipping factor by minimizing the quantization error based on the distribution assumption. The pros of the work are its simplicity, the proposed clipping and quantization does not need additional re-training. However, while the key of this paper is to determine a good clipping factor, the authors use uniform density function to represent the middle part of both Gaussian and Laplacian distributions where the majority of data points lie in, but exact computation for the tails of the distributions at both ends. Thus the computation of quantization error is not quite convincing. Moreover, the authors do not compare with the other recent works that also clip the activations, thus it is hard to validate the efficacy of the proposed method. For the experiments, the authors mention that a look-up table can be pre-computed for fast retrieval of clipping factors given the mean and sigma of a distribution. However, the mean and sigma are continuous numbers, how is the look-up table made? Moreover, how is the mean and std estimated for each weight tensor and what is the complexity?
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### Title + Abstract
ACIQ: Analytical Clipping for Integer Quantization of neural networks
We analyze the trade-off between quantization noise and clipping distortion in low precision networks. We identify the statistics of various tensors, and derive exact expressions for the mean-square-error degradation due to clipping. By optimizing these expressions, we show marked improvements over standard quantization schemes that normally avoid clipping. For example, just by choosing the accurate clipping values, more than 40\% accuracy improvement is obtained for the quantization of VGG-16 to 4-bits of precision. Our results have many applications for the quantization of neural networks at both training and inference time.
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<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 empirically finds that the distribution of activations in quantized networks follow Gaussian or Laplacian distribution, and proposes to determine the optimal clipping factor by minimizing the quantization error based on the distribution assumption. The pros of the work are its simplicity, the proposed clipping and quantization does not need additional re-training. However, while the key of this paper is to determine a good clipping factor, the authors use uniform density function to represent the middle part of both Gaussian and Laplacian distributions where the majority of data points lie in, but exact computation for the tails of the distributions at both ends. Thus the computation of quantization error is not quite convincing. Moreover, the authors do not compare with the other recent works that also clip the activations, thus it is hard to validate the efficacy of the proposed method. For the experiments, the authors mention that a look-up table can be pre-computed for fast retrieval of clipping factors given the mean and sigma of a distribution. However, the mean and sigma are continuous numbers, how is the look-up table made? Moreover, how is the mean and std estimated for each weight tensor and what is the complexity?
assistant
 This paper empirically finds that the distribution of activations in quantized networks follow Gaussian or Laplacian distribution, and proposes to determine the optimal clipping factor by minimizing the quantization error based on the distribution assumption. The pros of the work are its simplicity, the proposed clipping and quantization does not need additional re-training. However, while the key of this paper is to determine a good clipping factor, the authors use uniform density function to represent the middle part of both Gaussian and Laplacian distributions where the majority of data points lie in, but exact computation for the tails of the distributions at both ends. Thus the computation of quantization error is not quite convincing. Moreover, the authors do not compare with the other recent works that also clip the activations, thus it is hard to validate the efficacy of the proposed method. For the experiments, the authors mention that a look-up table can be pre-computed for fast retrieval of clipping factors given the mean and sigma of a distribution. However, the mean and sigma are continuous numbers, how is the look-up table made? Moreover, how is the mean and std estimated for each weight tensor and what is the complexity?