Zero-shot Mixed Precision Quantization via Joint Optimization of Data Generation and Bit Allocation

Authors: Hoang Anh Dung, Cuong Pham, Trung Le, Jianfei Cai, Thanh-Toan Do
Primary area: transfer learning, meta learning, and lifelong learning
Keywords: Zero-shot Quantization, Post-training quantization, mixed-precision quantization

Abstract:
Mixed-precision quantization (MPQ) aims to identify optimal bit-widths for layers to quantize a model.
On the other hand,
zero-shot quantization (ZSQ) aims to learn a quantized model from a pre-trained full-precision model in a data-free manner, which is commonly done by generating a synthetic calibration set used for quantizing the full-precision model. While it is intuitive that there exists inherent correlation between the quality of the generated calibration dataset
and the bit allocation to the model's layers, 
all existing frameworks treat them as separate problems. This paper proposes a novel method that jointly optimizes both the calibration set and the bit-width of each layer in the context of zero-shot quantization. Specifically, we first propose a novel data optimization approach that takes into consideration the Gram-Gradient matrix constructed from the gradient vectors of calibration samples. We then propose a novel scalable quadratic optimization-based approach to identify the model's bit-widths. These proposals will then be combined into a single framework to jointly optimize both the calibration data and the bit allocation to the model's layers.
Experimental results on the ImageNet dataset demonstrate the proposed method's superiority compared to current state-of-the-art techniques in ZSQ.

Decision: reject
Reviewer scores: 6, 5, 8

Reviews and discussion:
<thread>
creation date:
1730004535976

thread_type:
official_review

<thread_object>
creator: reviewer_mxwe

<content>
summary:
They introduce a jointly optimization framework for zero-shot quantization that alternatively optimize the calibration data and model bit-widths

strengths:
The authors propose a mixed precision quantization method for ZSQ from the perspective of data quality. I support this work on the good topic.

weaknesses:
My main concern is that network optimization from a gradient perspective may be passive given the poor quality of the available data, and the intuition is that bypassing the gradient information and using a gradient-free search method may be a better option.

questions:
1. The quantizer setup. The GDFQ/Qimera/AdaDFQ series compared in this paper all use perchannel quantizer and naive optimization by STE. However, these details are not elaborated for the proposed method.
2. The proposed method also works for conventional PTQ when the calibration data set is assumed not to fit the model statistics, which indicates that the method is not completely limited to ZSQ. Authors should provide more targeted explanations or provide experiments of the proposed method on PTQ for corroboration. Perhaps the proposed method can be used to build benchmarks on PTQ?
3. The traditional benchmark on CIFAR data set has not been adopted, and the authors are requested to add explanations.
4. line235: "When that happens, we call the set X^(T) is k-equivalent to X^(V) . We can optimize this objective, by matching the Gram-Gradient matrix of the two sets, according to Definition 1 and Theorem 3.1" ZSQ does not provide a validation set. I am trying to doubt the assumption in the article that when two samples are from synthetic datasets, their matching does not indicate the correctness of the feature?
5. The generator configuration is not well aligned with the comparison method because Genie's generator is a newer version and this part needs further ablation.
6. Lack of overhead analysis.
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<thread>
creation date:
1730250119360

thread_type:
official_review

<thread_object>
creator: reviewer_lh3r

<content>
summary:
This paper for the first time proposes a mechanism that combines zero-shot quantization and mixed-precision quantization.On the basis, the paper proposes a joint optimization framework between bit-width allocation and synthetic data generation. However, during the entire optimization process, these two parts are carried out alternately and iteratively. There is still a lack of a deeply coupled mechanism for joint optimization.

strengths:
The inherent correlation between the quality of the generated calibration dataset and the bit allocation to the model's layers are considered. The paper is well-organized and clearly stated. I would suggest accepting it after the following concerns are addressed.

weaknesses:
1. The references are all published until 2023. It would be best to provide some references on Mixed-precision Quantization/Zero-shot Quantization in 2024.
2. In Section 3.1, the authors mentioned that “In the realm of zero-shot quantization, the
validation set does not exist, so we only assume it here for explanation”. But the evaluation of model performance is conducted on the ImageNet dataset. Please carefully explain the relation between these two sets. If the validation does not exist, will there be significant changes or simplifications in formulas 6 and 8?
3. Please further explain the derivation process from formula 5 to formula 6.
4. In table 1 & table 2, the bit widths of results obtained using methods from this paper are marked as (*). From quantization setting in section 4.1, weights of some layers are set to 8 bits for initialization. Please calculate the average bit width of these models and fill it in the table, which will be more conducive to comparing the results and demonstrating the superiority of the method.
5. It would be better if the paper could compare the data synthesized in this paper with the data synthesized by existing methods and give deeper explanations or analyses.

questions:
1. The references are all published until 2023. It would be best to provide some references on Mixed-precision Quantization/Zero-shot Quantization in 2024.
2. In Section 3.1, the authors mentioned that “In the realm of zero-shot quantization, the
validation set does not exist, so we only assume it here for explanation”. But the evaluation of model performance is conducted on the ImageNet dataset. Please carefully explain the relation between these two sets. If the validation does not exist, will there be significant changes or simplifications in formulas 6 and 8?
3. Please further explain the derivation process from formula 5 to formula 6.
4. In table 1 & table 2, the bit widths of results obtained using methods from this paper are marked as (*). From quantization setting in section 4.1, weights of some layers are set to 8 bits for initialization. Please calculate the average bit width of these models and fill it in the table, which will be more conducive to comparing the results and demonstrating the superiority of the method.
5. It would be better if the paper could compare the data synthesized in this paper with the data synthesized by existing methods and give deeper explanations or analyses.
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</thread>
<thread>
creation date:
1730447920239

thread_type:
official_review

<thread_object>
creator: reviewer_n47e

<content>
summary:
The paper presents a novel framework for zero-shot mixed-precision quantization (ZMPQ) that combines data generation and bit allocation optimization, focusing on improving quantization outcomes for deep learning models without access to original data. The approach introduces Gram-Gradient matrix-based data optimization and a scalable quadratic optimization for bit-width allocation, outperforming state-of-the-art methods on ImageNet benchmarks.

strengths:
1.	Proposes a unique, joint optimization approach for data generation and bit allocation, filling a gap in zero-shot mixed-precision quantization research.
2.	Demonstrates superior or comparable performance to existing state-of-the-art methods under low-bit settings and varied model budgets, with results verified on multiple architectures (ResNet-18, ResNet-50, MobileNetV2).
3.	As a complex system, the paper offers a well-rounded suite of ablation studies that demonstrate the robustness of the method

weaknesses:
I am not familiar with the work related to Mixed-precision quantization task. This paper is intuitive and reasonable on the whole. However there are some problems of clarity in the writing
1. Certain proofs, such as the explanation of Equation (6) and the construction and application of the Gram-Gradient matrix, are highly technical, demanding considerable background knowledge from the reader. The explanation provided for Equation (6), in particular, feels insufficient for those not deeply versed in the topic.
2. The paper would benefit from additional figures or qualitative results to aid in understanding complex concepts such as gradient matching, which currently lack sufficient illustration.
3. Table 1 and 2, could provide more detail on the W/A notation (e.g., clarifying 2/2 and */2) to enhance interpretability.

questions:
Some of the suggestions for clarity mentioned above.
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creation date:
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thread_type:
official_comment

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creator: authors

<content>
title:
General Response

comment:
# References

[1] Hoang Anh Dung, Cuong Pham, Trung Le, Jianfei Cai, and Thanh-Toan Do. Sharpness-aware data generation for zero-shot quantization. In ICML, 2024.

[2] Ke Xu, Zhongcheng Li, Shanshan Wang, and Xingyi Zhang. Ptmq: Post- training multi-bit quantization of neural networks. In AAAI, 2024.

[3] Yongkweon Jeon, Chungman Lee, and Ho-young Kim. Genie: Show me the data for quantization. In CVPR, 2023.

[4] Yuhang Li, Ruihao Gong, Xu Tan, Yang Yang, Peng Hu, Qi Zhang, Fengwei Yu, Wei Wang, and Shi Gu. Brecq: Pushing the limit of post-training quantization by block reconstruction. ArXiv, abs/2102.05426, 2021.

[5] Yunshan Zhong, Mingbao Lin, Gongrui Nan, Jianzhuang Liu, Baochang Zhang, Yonghong Tian, and Rongrong Ji. Intraq: Learning synthetic im- ages with intra-class heterogeneity for zero-shot network quantization. In CVPR, 2022.

[6] Kanghyun Choi, Deokki Hong, Noseong Park, Youngsok Kim, and Jinho Lee. Qimera: Data-free quantization with synthetic boundary supporting samples. NeurIPS, 2021.

[7] Biao Qian, Yang Wang, Richang Hong, and Meng Wang. Rethinking data- free quantization as a zero-sum game. AAAI, 2023.

[8] Biao Qian, Yang Wang, Richang Hong, and Meng Wang. Adaptive data- free quantization. CVPR, 2023.

[9] Jungwook Choi, Zhuo Wang, Swagath Venkataramani, Pierce I-Jen Chuang, Vijayalakshmi Srinivasan, and K. Gopalakrishnan. Pact: Param- eterized clipping activation for quantized neural networks. ArXiv, 2018.

[10] Yuexiao Ma, Taisong Jin, Xiawu Zheng, Yan Wang, Huixia Li, Yongjian Wu, Guannan Jiang, Wei Zhang, and Rongrong Ji. OMPQ: Orthogonal mixed precision quantization. In AAAI, 2023.

[11] Peijie Dong, Lujun Li, Zimian Wei, Xin-Yi Niu, Zhiliang Tian, and Hengyue Pan. EMQ: Evolving training-free proxies for automated mixed precision quantization. ICCV, 2023.

[12] Yaohui Cai, Zhewei Yao, Zhen Dong, Amir Gholami, Michael W. Mahoney, and Kurt Keutzer. ZeroQ: A novel zero shot quantization framework. CVPR, 2020.

[13] Zhewei Yao, Zhen Dong, Zhangcheng Zheng, Amir Gholami, Jiali Yu, Eric Tan, Leyuan Wang, Qijing Huang, Yida Wang, Michael W. Mahoney, and Kurt Keutzer. HAWQV3: Dyadic neural network quantization. ArXiv, 2020.

[14] Huantong Li, Xiangmiao Wu, Fanbing Lv, Daihai Liao, Thomas H. Li, Yonggang Zhang, Bo Han, and Mingkui Tan. Hard sample matters a lot in zero-shot quantization. In CVPR, 2023.
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<thread>
creation date:
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thread_type:
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creator: authors

<content>
title:
General Response

comment:
**Q3**: *More detailed explanation for Equations 5 and 6*

**Answer**:  
Our optimization objective for the generated dataset is:

\\begin{aligned}[b]
     & X^{\(T\)} = \\arg \\min\_{ X^{\(T\)}}  
     \\mathcal{L}\_{R}\( \\theta\_{Q}^{\*},\\theta\_{FP},X^{\(V\)},B\) \\\\
     &\\text{s.t.:\\ } \\theta\_{Q}^{\*} = \\arg \\min\_{\\theta\_Q} \\mathcal{L}\_{R}\( \\theta\_{Q},\\theta\_{FP},X^{\(T\)},B\),
\\end{aligned}


where \\\( \\theta\_Q^{\*} \\\)  is the model weights after updating \\\( \\theta\_Q \\\) with \\\( X^{\(T\)} \\\) under the bit-width setting \\\( B \\\).  
Define \\\( \\delta\_{\\theta\_{Q}} = \\theta\_{Q}^{\*}-\\theta\_{Q} \\\) as the weight difference of the quantized model \\\( \\theta\_{Q} \\\) before and after quantization with the training dataset \\\( X^{\(T\)} \\\). In practice, we only approximate the calibrated model using a single-step gradient descent, which yields:

\\\( 
\\delta\_\{\\theta\_{Q}} = -\\alpha \\nabla\_{\\theta\_Q} \\mathcal{L}\_{R}\(\\theta\_{Q},\\theta\_{FP},X^{\(T\)},B\), \\\)


where \\\( \\alpha \\\) denotes the learning rate. Using the first-order Taylor expansion for the reconstruction loss \\\( \\mathcal{L}\_{R}\(\\theta\_{Q}^{\*},\\theta\_{FP},X^{\(T\)},B\) \\\) at \\\( \\theta\_{Q} \\\), we have:

\\\[
\\begin{aligned}[b]
     \\arg \\min\_{ X^{\(T\)}}\\mathcal{L}\_{R}\(\\theta^{\*}\_{Q},\\theta\_{FP},X^{\(V\)},B\) 
     &= \\arg \\min\_{ X^{\(T\)}} \\mathcal{L}\_{R}\(\\theta\_{Q},\\theta\_{FP},X^{\(V\)},B\)  + \\nabla\_{\\theta\_Q} \\mathcal{L}\_{R}\(\\theta\_{Q},\\theta\_{FP},X^{\(V\)},B\)^T \(\\theta^{\*}\_{Q} - \\theta\_Q\).
\\end{aligned}
\\\]

The first term \\\( \\mathcal{L}\_{R}\(\\theta\_{Q},\\theta\_{FP},X^{\(V\)},B\) \\\) is independent of \\\( X^{\(T\)} \\\), so we can ignore it:

\\\[
\\begin{aligned}[b]
     \\arg \\min\_{ X^{\(T\)}}\\mathcal{L}\_{R}\(\\theta^{\*}\_{Q},\\theta\_{FP},X^{\(V\)},B\) 
     = \\arg \\min\_{ X^{\(T\)}} \\nabla\_{\\theta\_Q} \\mathcal{L}\_{R}\(\\theta\_{Q},\\theta\_{FP},X^{\(V\)},B\)^T \(\\theta^{\*}\_{Q} - \\theta\_Q\).
\\end{aligned}
\\\]

If we replace \\\( \(\\theta^{\*}\_{Q} - \\theta\_Q\) = \\delta\_{\\theta\_{Q}} = -\\alpha \\nabla\_{\\theta\_Q} \\mathcal{L}\_{R}\(\\theta\_{Q},\\theta\_{FP},X^{\(T\)},B\) \\\), we have:

\\\[
\\begin{aligned}[b]
     \\arg \\min\_{ X^{\(T\)}}\\mathcal{L}\_{R}\(\\theta^{\*}\_{Q},\\theta\_{FP},X^{\(V\)},B\) 
     &= \\arg \\min\_{ X^{\(T\)}} \\nabla\_{\\theta\_Q} \\mathcal{L}\_{R}\(\\theta\_{Q},\\theta\_{FP},X^{\(V\)},B\)^T \\delta\_{\\theta\_{Q}} \\\\
     &= \\arg \\min\_{ X^{\(T\)}} -\\alpha \\nabla\_{\\theta\_Q} \\mathcal{L}\_{R}\(\\theta\_{Q},\\theta\_{FP},X^{\(V\)},B\)^T \\nabla\_{\\theta\_Q} \\mathcal{L}\_{R}\(\\theta\_{Q},\\theta\_{FP},X^{\(T\)},B\).
\\end{aligned}
\\\]

We denote the gradient vector of the model evaluated on the training set as \\\( \\mathcal{J}\_{T}^{\(\\theta\_Q\)} \\\):

\\\[
\\begin{aligned}[b]
     \\mathcal{J}\_{T}^{\(\\theta\_Q\)} = \\nabla\_{\\theta\_Q} \\mathcal{L}\_{R}\(\\theta\_{Q},\\theta\_{FP},X^{\(T\)},B\) = \\frac{1}{|X^{\(T\)}|} \\sum\_{j=1}^{|X^{\(T\)}|} \\mathcal{J}\_{T,j}^{\(\\theta\_Q\)},
\\end{aligned}
\\\]

where \\\( \\mathcal{J}\_{T,j}^{\(\\theta\_Q\)} \\\) denotes the gradient vector of the reconstruction loss evaluated on the \\\( j^{\\text{th}} \\\) sample in the training set \\\( X^{\(T\)} \\\) w.r.t. the model weight \\\( \\theta\_Q \\\). Similarly, we have:

\\\[
\\begin{aligned}[b]
     \\mathcal{J}\_{V}^{\(\\theta\_Q\)} = \\nabla\_{\\theta\_Q} \\mathcal{L}\_{R}\(\\theta\_{Q},\\theta\_{FP},X^{\(V\)},B\) = \\frac{1}{|X^{\(V\)}|} \\sum\_{i=1}^{|X^{\(V\)}|} \\mathcal{J}\_{V,i}^{\(\\theta\_Q\)}.
\\end{aligned}
\\\]

Now, the optimization objective becomes:

\\\[
\\begin{aligned}[b]
     \\arg \\min\_{ X\^{\(T\)}} \\mathcal{L}\_{R}\( \\theta\_{Q}^{\*},\\theta\_{FP},X\^{\(V\)}, B\) 
     &= \\arg \\min\_{ X\^{\(T\)}} -\\alpha {\\mathcal{J}\_{V}\^{\(\\theta\_Q\)}}\^T \\mathcal{J}\_{T}\^{\(\\theta\_Q\)} \\\\
     &= \\arg \\max\_{X^{\(T\)}} \\frac{1}{|X^{\(V\)}|} \\sum\_{i=1}^{|X^{\(V\)}|} \\frac{1}{|X^{\(T\)}|} \\sum\_{j=1}^{|X^{\(T\)}|} {\\mathcal{J}\_{V,i}^{\(\\theta\_Q\)}}^T \\mathcal{J}\_{T,j}^{\(\\theta\_Q\)} \\\\
     &= \\arg \\max\_{X^{\(T\)}} \\frac{1}{|X^{\(V\)}|} \\sum\_{i=1}^{|X^{\(V\)}|} \\frac{1}{|X^{\(T\)}|} \\sum\_{j=1}^{|X^{\(T\)}|} I\(x^{\(V\)}\_i, x^{\(T\)}\_j\),
\\end{aligned}
\\\]

where \\\( I\(x^{\(V\)}\_i, x^{\(T\)}\_j\) = \{\mathcal{J}\_{V,i}^{\(\\theta\_Q\)}}^T \\mathcal{J}\_{T,j}^{\(\\theta\_Q\)} \\\) is a gradient matching score, denoting how well the model can minimize the loss on sample \\\( x^{\(V\)}\_i \\\) indirectly through training sample \\\( x^{\(T\)}\_j \\\). Therefore, we want the gradient matching score of all validation samples \\\( x^{\(V\)}\_i \\\) to remain high throughout the entire training process.
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creation date:
1732167208785

thread_type:
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creator: authors

<content>
title:
General Response

comment:
Q2: Regarding the validation set and visualization.

Answer:
In the context of zero-shot quantization, we have access to the weight of the pretrained model, but do not have access to any real original images during the quantization process. In the derivation of our method, we assume the availability of the validation set in order to derive the optimization objective. In practice, when quantizing the model, we need to circumvent the lack of the real validation set. To this end, we synthesize the validation set as explained from line 270 to line 277 of the paper. Before the optimization process, we warm-up the synthetic training data, by matching its Batch Norm statistics with those of the full-precision model. The synthetic validation set is then generated by sampling data in the neighborhood of the warmed-up training samples. By matching the Batch Norm statistics in the warm-up stage, the validation samples are likely to share features with the real data.
After the model has been quantized, we evaluate the quantized model on the real validation set of the ImageNet dataset to compare to other methods. As we mentioned above, the validation set is synthesized in our framework. Hence, there are no changes to Eqs. (6) and (8).

As described from line 225 to line 231 of the paper, we want to encourage each validation sample to have a high gradient matching score with at least one training sample. To demonstrate the effectiveness of our method, we visualize the distribution of gradient matching scores between the real validation set and our generated training set, compared to that of other zero-shot data generation methods [3,14]. Specifically, for each real validation sample, we compute its maximum gradient matching score with a synthetic sample from the training set generated by each method and plot the score distribution for the entire validation set.
The visualization can be accessed via the following link: [Visualization of Gradient Similarity](https://anonymous.4open.science/r/test_repo-D26B/Visualization_Gradient_Similarity_9.pdf).

The results show that our Gram-Gradient matching approach leads to better gradient matching over the real validation data, compared to other zero-shot quantization methods. This demonstrates that Gram-Gradient matrix matching between the synthetic training set and the synthetic validation set can lead to a better gradient matching between the synthetic training set and the real validation data.
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General Response

comment:
# General Response

**We sincerely thank the Reviewers for the constructive feedback.**

## Question

**Q1**: *Regarding Table 1 and Table 2 of the paper.*

**Answer**:  
Following the feedbacks from the Reviewers, we have updated Tables 1 and 2 below, including adding the average bit, clarification for notations and additional comparison methods. We provide additional methods published in 2024 for zero-shot quantization \(SADAG [1]\) and mixed-precision quantization \(PTMQ [2]\) for comparison in Tables 1 and 2 below.  
It is worth noting that, to the best of our knowledge, there is no available joint optimization method for both mixed-precision quantization and zero-shot quantization published in 2024.

### Table 1: Comparisons of Top-1 classification accuracy (%) with the state-of-the-art zero-shot quantization methods on the ImageNet dataset.

*Genie + MPQ denotes the combining of generated data using Genie[3] model with our bit allocation method. Results marked with $(\dagger)$ are reproduced using the official released code of the corresponding paper. $(\*)$ indicates mixed-precision quantization for models' weights. Methods with $(\diamond)$ use the same quantization setting as BRECQ [4] and Genie [3]. **AverageBit** denotes the average bit of models in the same block, accounting for layers configured to 8 bits. Our method maintains the same model size as other methods in the corresponding settings. FP denotes the full-precision model.*

| **Method**                | **W/A**  | **Resnet-18**             |   | **Resnet-50**             |   | **MobilenetV2**            |   |
|---------------------------|----------|---------------------------|---|---------------------------|---|---------------------------|---|
|                           |          | **AverageBit**   | **Acc**    | **AverageBit**   | **Acc**    | **AverageBit**   | **Acc**    |
|---------------------------|----------|-----------|-----------|-----------|-----------|-----------|-----------|
| FP                        |          | 32/32      | 71.01     |  32/32          | 76.63     |    32/32        | 72.20     |
| SADAG [1]         | 2/2      |           | 54.51     |           | 57.55     |           | 13.01     |
| Genie [3]        | 2/2      |           | 53.74     |           | 56.81     |           | 11.93     |
| Genie [3] + MPQ (Ours)        | */2      | 2.2/2     | 58.33     | 2.48/2    | 63.85     | 4.2/2     | 23.39     |
| Ours                      | */2      |           | **58.60** |           | **64.23** |           | **23.69** |
|---------------------------|----------|-----------|-----------|-----------|-----------|-----------|-----------|
| IntraQ [5]      | 3/3      |           | -         |           | -         |           | -         |
| Qimera [6]      | 3/3      | 3/3       | 1.17      | 3/3       |           | 3/3       | -         |
| AdaSG [7]        | 3/3      |           | 37.04     |           | 16.98     |           | 26.90     |
| AdaDFQ [8]        | 3/3      |           | 38.10     |           | 17.63     |           | 28.99     |
|---------------------------|----------|-----------|-----------|-----------|-----------|-----------|-----------|
| Genie [3]        | 3/3      |           | 66.89     |           | 72.54     |           | $55.13^\dagger$ |
| Genie [3] + MPQ (Ours)        | */3      | 3.2/3     | 67.33     | 3.4/3     | 73.75     | 4.8/3     | 62.45     |
| SADAG [1]        | 3/3      |           | 67.10     |           | 72.62     |           | 56.02     |
| Ours                      | */3      |           | **67.57** |           | **73.83** |           | **62.60** |
|---------------------------|----------|-----------|-----------|-----------|-----------|-----------|-----------|
| Qimera [6]      | 4/4      |           | 63.84     |           | 66.25     |           | 61.62     |
| AdaSG [7]        | 4/4      | 4/4       | 66.50     | 4/4       | 68.58     | 4/4       | 65.15     |
| IntraQ [5]      | 4/4      |           | 66.47     |           | -         |           | 65.10     |
| AdaDFQ [8]          | 4/4      |           | 66.53     |           | 68.38     |           | 65.41         |
|---------------------------|----------|-----------|-----------|-----------|-----------|-----------|-----------|
| Qimera$^{\diamond}$ [6] | 4/4      |           | 67.86     |           | 72.90     |           | 58.33     |
| IntraQ$^{\diamond}$ [5] | 4/4      |           | 68.77     |           | 68.16     |           | 63.78     |
| SADAG [1]        | 4/4      |           | 69.72     |           | 75.7      |           | 68.54     |
| Genie [3]        | 4/4      |  4.17/4         | 69.66     |   4.3/4        | $75.57^\dagger$ |  5.47/4      | 68.38     |
| Genie [3] + MPQ (Ours)        | */4      |           | 69.88     |           | 75.84     |           | 69.95     |
| Ours                      | */4      |           | **70.05** |           | **75.87** |           | **70.07** |
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creation date:
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creator: authors

<content>
title:
Revision

comment:
We sincerely thank the Reviewers for their thoughtful feedback and valuable comments on our work. We have slightly revised the paper to address typos.
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Metareview:
metareview:
This paper proposes a joint optimization approach for both the calibration set and the bit-width of each layer within the context of zero-shot quantization. The scores for this paper are mixed, with one reviewer rating it marginally above acceptance but with low confidence, one rating it marginally below acceptance, and one recommending acceptance. After carefully reviewing the feedback and discussions between the reviewers and authors, the Area Chair (AC) has concluded that the paper cannot be accepted. The approach, which combines joint optimization of calibration data and bit allocation across model layers, lacks novelty. Additionally, the paper fails to compare its methods with recent approaches from 2024, and in some cases, the proposed method performs worse than existing ones under certain configurations. Finally, the overall writing and organization of the paper make it difficult for readers to follow and understand.