TexQ: Zero-shot Network Quantization with Texture Feature Distribution Calibration
Authors: Xinrui Chen
Yizhi Wang
Renao Yan
Yiqing Liu
Tian Guan
Yonghong He
Venue: NeurIPS 2023 poster (2023)
Keywords: Zero-shot quantization
Texture feature calibration
Post-training quantization
low bit width
Neural network compression
TL;DR: We proposed a novel zero-shot quantization method TexQ, which takes advantage of texture feature energy distribution calibration and mixup knowledge distillation, achieving state-of-the-art performance especially in low bit width.

Abstract: Quantization is an effective way to compress neural networks. By reducing the bit width of the parameters, the processing efficiency of neural network models at edge devices can be notably improved. Most conventional quantization methods utilize real datasets to optimize quantization parameters and fine-tune. Due to the inevitable privacy and security issues of real samples, the existing real-data-driven methods are no longer applicable. Thus, a natural method is to introduce synthetic samples for zero-shot quantization (ZSQ). However, the conventional synthetic samples fail to retain the detailed texture feature distributions, which severely limits the knowledge transfer and performance of the quantized model. In this paper, a novel ZSQ method, TexQ is proposed to address this issue. We first synthesize a calibration image and extract its calibration center for each class with a texture feature energy distribution calibration method. Then, the calibration centers are used to guide the generator to synthesize samples. Finally, we introduce the mixup knowledge distillation module to diversify synthetic samples for fine-tuning. Extensive experiments on CIFAR10/100 and ImageNet show that TexQ is observed to perform state-of-the-art in ultra-low bit width quantization. For example, when ResNet-18 is quantized to 3-bit, TexQ achieves a 12.18% top-1 accuracy increase on ImageNet compared to state-of-the-art methods. Code at https://github.com/dangsingrue/TexQ.

TexQ: Zero-shot Network Quantization with Texture Feature Distribution Calibration
Xinrui Chen, Yizhi Wang, Renao Yan', Yiqin Liu, Tian Guan", Yonghong He Tsinghua Shenzhen International Graduate School, Tsinghua University {cxr22, yz-wang22, yra21, liuyiqin20) @mails Emails tsinghua, edu, en {guantian, heyh)@sz. tsinghua. edu. cn
Abstract
Quantization is effective way compress neural networks. By reducing the bit width of the parameters, the processing efficiency of neural network models at edge devices can be notably improved. Most conventional quantization methods utilize real datasets to optimize quantization parameters and fine-tune. Due to the inevitable privacy and security issues of real samples, the existing real-data- driven methods are no longer applicable. Thus, a natural method is to introduce synthetic samples for zero-shot quantization (ZSQ). However, the conventional synthetic samples fail to retain the detailed texture feature distributions, which severely limits the knowledge transfer and performance of the quantized model. In this paper, novel ZSQ method, TexQ is proposed to address this issue. We first synthesize a calibration image and extract its calibration center for each class with a texture feature energy distribution calibration method. Then, the calibration centers are used to guide the generator to synthesize samples. Finally, the mixup knowledge distillation module is introduced to diversifyy the synthetic samples for fine-tuning. Extensive experiments on CIFAR PRRI0/100 10/100 and ImageNet show that TexQ is observed to perform state-of-the-art in low bit width quantization. For example, when ResNet-18 is quantized to 3-bit, TexQ achieves a 12.18% top-1 accuracy increase ImageNet compared to state-of-the-art methods.
Introduction
Limited by the computing capability edge devices such as mobile phones, deep neural network models inevitably require compression for terminal scenarios 2]. Compared to popular pressing methods such as pruning and distillation, quantization is easier to achieve lightweight and hardware compatibility [G. g BJ. By compressing floating-point parameters low-bit fixed-point integer, quantization reduces the resource footprint and improves computing efficiency. For exam- ple, when moving the parameters tensor (weights and activation) from 32 4 bits, the memory consumption is reduced by factor of 8, while the computational overhead of matrix multiplication goes down by factor of 64 a squared rate. Most research on quantization focuses on quantization- aware training (QAT) [7), 8, H [TO] and post-training quantization (PTQ) [[L], 02, IEL I14, II3. 16]. QAT introduces fake quantization nodes when training and achieves performance close to full precision. However, it relies on the full training set and lacks a uniform specification, making it unfriendly deploy. Thus, PTQ has gained attention, which only requires a small part of the training set to statistically optimize the quantization parameters [ [9. [0].
Due to privacy and security constraints, access to certain real data might be prohibited [21]], such as patient medical images, confidential business information, etc. Therefore, zero-shot quantization
Corresponding author
37th Conference on Neural Information Processing Systems (NcurIPS 2023).

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(ZSQ) P2. 2E MA 24 25 is proposed to circumvent this limitations. Among previous studies, syn- thetic sample-base methods [21. 24, - have attracted attention by their excellent performance. Most studies synthesize samples that resemble the distribution of the real samples by extracting statistics in the full precision model, such as antch-oormalization statistics [21]], categorical labels [24]] intermediate features [25], etc. However, despite a good fit to the model statistics and high classification confidence, there is still a huge gap between the texture feature distribution they con- tain and that of real samples. Such phenomenon is likely to result in bad performance, studies show that CNNs rely on texture feature to make decisions, for texture feature is "easy to learn" for CNNs [2G. 27 28 In addition, the conventional multiple-constraint paradigm limits the diversity of synthetic samples [299 [0].
To tackle the above problems, the following exploratory experi- ments were carried out. Firstly, local binary pattern (LBP) [32] was introduced to characterize the texture feature. A batch of real samples and conventional synthetic samples with class confidence above 99.9% were extracted their LBP feature for clustering. As presented in Figure M. the domain gap (point distribution) and di- versity gap (point density) can be observed. We further explored the texture bias of the quantized model to prove the importance of texture feature. As shown in Figure Z same model spectively quantized with real samples and conventional synthetic samples, and tested in four image patterns: original, greyscale (removes color feature), binary (removes color and texture fea- ture), and edge (retains shape feature and restores few texture feature). illustrates that removing texture feature causes a sharp performance decrease. The model quantized with synthetic sam- ples drops off a lot on performance while restoring some of the texture feature in Figure Ed can recover its performance. These experiments imply that the ZSQ model is strongly biased towards texture feature and tends to make decisions with it. Inspired by the experiments, an intuitive idea is to calibrate the synthetic samples to retain the texture feature distribution, which facilitates the model learn and improve its performance.
IntraQ
Real sample
Ours
Figure LBP feature cluster- ing of samples from CIFAR10 10, IntraQ and our method. Visual- ization with t-SNE [S]]
Top Accuracy (%) 79.62
Real samples
Synthetic samples
77.03
69.08
67.03
34.65
35.43
28.19
33.01
(a) Original
(b) Greyscale
(c) Binary
(d) Edge
Figure 2: Test results of real/synthetic samples quantized model on CIFAR1O in 4 image patterns.
In this work, we propose TexQ, a zero-shot quantization method using synthetic calibration centers calibrate samples and retain texture feature distributions. We first generate calibration images and its center for each class. Further, the centers guide the generator to synthesize samples. The two-stage synthetic sample paradigm alleviates the homogeneity caused by multiple constraints. Finally, mixup knowledge distillation is introduced to enhance sample diversity and avoid overfitting. With the above methods, the proposed TexQ performs state-of-the-ard various datasets and model settings.
2
Related work
2.1 Texture feature extraction
Texture feature powerful visual cue that provides useful information identifying objects or regions of interest in images [3]] To make of these cues, texture feature extraction methods

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has been widely used in natural image processing, among which filtering approaches are proven to be successful, including LAWS filters, dyadic Gabor filter banks, wavelet transforms and on [6
Studies [35% 36 [7]] have shown that image texture feature are conductive to image classification
and are class separable. For instance, [38]] introduce GL.CM and Gahor texture feature from regions
of interest for better mammogram classification. Recently, many studies [39, Hn, [ identify the
importance of textures feature for CNNs. [X>]] found that texture representations could capture
the statistical characteristics of images for CNNs. [! showed that classic CNNs were unable to
recognize sketches where textures are missing and shapes are left. Similarly, [8]1L 82] validated that
CNNs were biased towards textures than shapes, for example, ResNet-50 biased 77.9% texture.
2.2 Zero-shot quantization
Most zero-shot quantization (also called data-free quantization) studies try to recover the quantiza- tion error from three perspectives. The first perspective designs quantization parameters by using model properties [22, 2R, T.l. Bi] without acquiring any data. For instance, Nagel et al. [22]] pro- posed a scale-equivariance property of activation functions to equalize the weight ranges of the network. Meller et al. [E highlighted an inversely proportional factorization of convolutional neural networks decrease the degradation caused by quantization. The above methods avoid the access to data but suffer from severe performance degradation in low bit widths. For example, DFQ achieved 0. 1.11% top-1 accuracy the 4-bit MobileNetV2 case [22 221]. Therefore, more ZSQ
methods resort synthetic samples. The second perspective adopts optimization- basod methods to synthesize samples by aligning the statistics in the full-precision network [21,, 30, 29]. ZeroQ [21]] adopted batch normalization statistics alignment to optimize the standard Gaussian noise. DSG [30]] proposed a slack distribution alignment to diversify samples. IntraQ [29]] highlighted the intra-class heterogeneity and retained this property in the synthetic samples for better performance. The third perspective adopts a generator to synthesize samples [22] 85, AБ, H7, H8J. For example, GDFQ [22]] proposed showledge-matchinn
generator to produce synthetic data with labels by introducing the cross-entropy loss. ClusterQ |SS]] utilized the feature distribution alignment to imitate the distribu- tion of real data. AdaDFQ
| proposed zero-sum game to adaptively regulate the adaptability of synthetic samples. The existing studies provide us effective method to statistics in full precisiin models, however, none of these considered texture feature distribution in synthetic samples, though is fundamental for CNNs to learn and make decisions. To the extent of our knowledge, this work is the first consider texture feature in ZSQ, introducing synthetic calibration center to calibrate synthetic samples.
3 Methodology
3.1 Preliminaries
3.1.1 Quantizer
Following ZeroQ [ZT]], asymmetric quantization is adopted. Given a Dhatinng-piim value zy (weights or activations) and quantization bit width BW, the quantized integer T. can be obtained as:
Zq Clip( S 1--ZP,000 2,,,0,2B -)
(I)
where S = BW
is the scaling factor mapping the floating-point number to a fixed-point integer, ZP- If min S is the zero point mapping the floating-point minimum to zero, linpul] rounds its input to the nearest integer. Clip(lensorr; T'min Fmas) clamps the tensor elements to be between min and Tmaz- The dequantized value xg can be obtained as:
max 2f min
Iq + ZP
FA
(2)
S
3

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3.1.2 Data synthesis
PTQ requires small real dataset D (z, v)} containing samples and labels y. Similarly, most
ZSQ introduce synthetic sample sets D { 7) To fit the batch normalization statistics (BNS)
in the full-precision model (F)), basic principle [2T 45 29 using BNS alignment loss in Eq.
1 LBNS = Σllu(Z) 14 112 [|) a1 0l2
(3)
where 14 F and of are the rumning mean and variance stored in the 1-th BN layer of F. The mean and variance of the synthetic sample batch in the I-th layer of F are given by pc(x) and (z)..
Given generator G, standard Gaussian noise 2, and target label y, the synthetic sample can be obtained as 7- = G (2(7). The cross-entropy loss in Eq. is used to generate label-oriented samples
22 19
LCE ((x.)))((E.0) (Crossaeeeeoooooeooeeeee [Cross-enlropy (F(z), 7))
(4)
3.2 Texture feature distríbution calibration
In this section, the calibration method and mixup knowledge distillation module are proposed. The framework of our TexQ is illustrated in Figure
Calibration sample
L LAWS
L
Forward proegaaion Backward gradient
Syuthetic sample
L
Loss calculation
F
Gaussian noise
L
L
Generalor
Calibration Center
LANSS
'DHNNS
L BNS
Full- procision nolwork
Quantized network
LG
2 (
Loss for G//G/ Q
F
CE
Cross entrogy loss
G
L KD
Ls
BNS aligmment
MKD distilation)
Liss
Layerod alignment
4 Das
ENS-distorted
L7 CB
4 Lww
Texture feature energy distribution calibration loss
MKD
Mixup knowledge distillation module
Figure 3: An overview of the proposed framework TexQ. Calibration centers are produced to guide G to synthesize samples. Q is fine-tuned with both calibration samples and synthetic samples.
3.2.1 Texture feature energy distribution calibration loss
To quantitatively measure the texture feature distribution, LAWS texture feature energy [8% 60] is introduced. We select four 1-dimensional filters provided by LAWS: Eş=[-1, -2, 0, 1], S5=[-1, 0. 2, -1J, W5=[-1, 2, 0, -2, 1], R5=[1, -4, 6, -4, 1]. which stand for edge, spot, wave, and ripple. By convolving two 1-dimensional LAWS filters of size x with each other, total of 16 2-dimensional filters of size 5x5 can be obtained. Each filter extracts a basic element of the texture, for example, R₁R; denotes high-frequency point filter, and E,S; denotes V shape filter. To be specific, the calculation procedure of R₂ is given as an example in Eq. EL
1
1
-4
16
-24
16
-4
R3 = R33
Rs
*
#11
4
6 4
1]=
-24
36
-24
6
(5)
-4
16
-24
16
-4
I
-4
6
-4
1

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Original
(Edge) RgRg (High frequency)
EgSg shape)
ImageNet
Dominant
IntraQ
Cat
Proportion (%)
01
Tree
Cloth
Texture elements
Figure Visualization of distribu- tion T' from different samples.
Figure 4: Features extracted with LAWS filters.
Proportion
20-
12-
Number of dominant texture elements
sus
2
(a) ImageNet
(b) Synthetic sample (IntraQ) (c) Calibration sample (Ours) (d) Synthetic sample (Ours)
Figure 6: Dominant texture elements number distribution of samples from the ImageNet training set, IntraQ synthetic samples, calibration images as well as synthetic samples generated by our method. Synthetic samples were obtained with pre-trained ResNet-18.
Straightforward visualization of the texture feature extracted by LAWS texture feature filters pro- vided in Figure Н. It can be observed that different types of images contain different dominant texture feature. For example, the trees with lots of leaves including V-shape, high-frequency points and edge features, and the cat lying on the chair including mainly V-shape and edge features.
reasonable evaluate texture distributions by analyzing basic elements, for complex texture feature are composed of simple elements. We apply 16 filters to obtain the texture feature energy distributions T of sample as shown in Figure E.. Assuming that the top-k elements in T account for more than 80% are the dominant texture elements, the set of these elements is recorded as K. As displayed in Figure E. the real samples (Figure Ea) have at most 9 dominant texture elements, i.e., 9,, while there is almost only in the conventional synthetic samples (Figure Bb). To be detailed, in Figure the distribution curve of the conventional synthetic sample presents a clear peak, indi- cating a single dominant element, which reduces the intra-class heterogeneity and the information contained. Unlike this, the curve of the real sample presents detailed texture distribution. To retain this property, texture feature energy distribution calibration loss of Eq. B is proposed to dynamically adjust the detailed texture feature distribution of calibration images for each class.
CLLWWS max (m Bull2 -, 0) max (Il [[[1-Kmaan Kmax) Oz 12112 E, 0)
(6)
where Kmax is the largest element in K. The hyperparameters Ou Oz, and e control the upper and lower bounds of the elements in K. Specifically, Or the upper bound of Kmax- and 02, is the lower bound of the sum of all elements in K except Kmax. is the softness factor to alleviate convergence problem. Both upper and lower bounds are used together to extract detailed distribution.
To introduce the calibration loss, possible scheme is directly applying constraint to the generator. However, multiple constraints to generator results slow iterations and homogeneous samples. We adopt two-stage method, which includes optimization method to synthesize accurate calibra- tion centers for each class and generation method to synthesize samples with the constraint on calibration centers.
5

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3.2.2 Layered BNS alignment constraint
Considering that neural networks extract glass-independent low-level features (e.g., texture and con- tours) in shallow layers and class-related high-level features in deep layers, the layered BNS align- ment loss (CL-BNs) is proposed. We adopt loose constraints in shallow layers facilitate the expression of texture feature and tightened constraints in deep layers to fit class-related information.
In calibration set generation stage, given the calibration set C { 7)), the L LBBNS of Eq. D constraints to align the BNS in F.
C L-BNS = Σ 1100 (H((Fe) - 14 2111 + |m (oi(Ec)-o7"11 1=1
- 01²)|12
(7)
0.2, <<< _ -
wi =
1.1, 1 - L
where L is the number of BN layers, (fe) and (5.) denote the mean and variance of C' in the 1-th layer of F. wy the loss weight for the 1-th layer. [input] returns the smallest integer greater than its input.
In synthetic sample generation stage, L samples that fit the calibration centers of corresponding class label k.
L L.BNN Eq. constrains the generator to synthesize
L L-BNS- Σ wwy [Au (5ly = 14 (Felee = =k)]ll
(8)
{ 0.1<l<< 41 - 1. 1 <<
+ w |oi (xly k)) 01 (Eel kb] wi
where μ4 (Ily = k) and of (z y = k:) denote the mean and variance of the synthetic samples. 1 (Felye k) and 0,
(Fe ye k) the corresponding mean and variance calibration center.
3.2.3 Mixup knowledge distillation module
Knowledge distillation is commonly used transfer the output distribution from full-precision model F to the quantized model Q in the fine-tuning stage, which requires diversified samples. Some studies introduce Mixup [5.1L [X] augmentation to generate samples with mixed labels to fine- tune the quantized model with cross entropy loss. However, the labels produced by the such methods are not accurate enough, and taking such mixed labels fine-tune the quantized model tends be disastrously misleading. Therefore, we advocate discarding mixed labels and taking only mixed samples to knowledge distillate the quantized model, and name this method mixup knowledge dis- tillation. Specifically, as presented in Eq. B, new sample Umiz is generated by weighted fusion of 2 samples H; and T randomly selected in a batch for distillation. Mixup proportion sampled from standard uniform distribution. The probability p 20% is observed to perform best.
ATT + (1= with probability P A ( 1)
Emiz
(9)
Ti, with probability
3.3 Quantization process
3.3.1 Stepl: Calibration generation
In this stage, the calibration set with Gaussian noise initialization is optimized with the loss in Eq. π capturing the preferred texture of each class from F. We fix F and back pack-propagate the loss to the calibration images. For each class, the calibration image trained for most 1500 iterations individually, with a warm-up of 150 iterations at half learning rate without L LAWS- Their BNS are extracted as the calibration centers to guide the generator in the next step.
CCLWSS C C LAWS ai L L-BNS 02 L CE
(10)

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3.3.2 Step2: Synthetic samples generation
In this stage, generator G synthesize samples of different classes that fit corresponding calibration
centers via L L-BNS. Following FDDA [ distorit loss in Eq. is introduced to avoid overfitting by Gaussian noise interfering with the calibration center. by = 0.5 and Va 1.0 control distortion degree of mean and variance.
1 [ D.BNS - 1|1 IM (J/ k) -N (N (Feli Mn)
(11)
{
0,1< 7 - 1, [
+ w1 (T (ar (Eelic k) v.))
In addition, L CE and C BNS are used to align the label and BNS of Up to this point, the total loss employed by generator G' can be summarized in Eq. M
c = L L CE + tag L BNS + 04 L L-BNS aas L D-BNS.
(12)
3.3.3 Step3: Quantized model fine-tuning
To make full use of the data, we take both samples D and as the input of Q and apply cross-entropy loss _ cg to fine-tune. Subsequently, both samples in 7) and C are input into the mixup knowledge distillation module to produce mixup samples. With the input of mixup samples, Kullback-Leibler loss in Eq. is applied transfer the output of F to Q.
_ KD (e, [Kulbback-Leii (Q(Tmiz). F(Fmiz)))
(13)
At this point, the overall loss for fine-tuning Q can be summarized
- _ a6 L KD
(14)
4 Experiment
4.1 Experimental settings and details
We report top-1 accuracy on validation sets of CIFAR-10/100 |> and ImageNet [ Networks selected include ResNet-20 [54]] for CIFAR-10/100 ResNet- 8, MobileNetV2 [a>] and ResNet-50
for ImageNet. All experiments are implemented with Pytorch [b9i] via the code of FDDA [MC]]] and
IntraQ [29]] and run on an NVIDIA GeForce RTX 3090 GPU. Calibration images are iterated with
a constant learning rate of 0.05. Generator imported from GDFQ [2_4] with a initial learning rate of 1e-3 multiplied by 0.1 every 100 epochs. In fine-tuning, batchsize is 128 for CIFAR- 10/100 and 16 for ImageNet, adjusting by cosine annealing [57]]. We warm up for 50 epochs, then update G and Q for 450 epochs. The optimal configurations trade-off parameters from to og obtained
by grid search are 10, 0.4, 0.02, 1.8, and 20.
4.2 Performance comparison
To demonstrate the efficacy of our TexQ, we conduct experiment in 3/4-bit case, since high accuracy can be easily achieved with a larger bit width. For instance, the advanced AdaDFQ [+7]]] trails full precision with a 0.08% top-1 accuracy in 5-bit ResNet-20 case. In this section, WBAB indicates the weights and activations are quantized B-bit. Best results in boldface.
4.2.1 CIFAR-10/100
We compare the performance against the advanced 7SQ methods CIFAR-10/100. As presented in Table MI our TexQ is observed to achieve state-of-the-arr among the competitors, improving the top-1 accuracy by 3. 1.13%//1.588 in 3-bit CIFAR-10/100 case compared to the advanced AdaDFQ. Similar
7

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results can be observed in the 4-bit case. In particular, the top-1 accuracy of our TexQ exceeds that of the same framework with real data b-bit case, demonstrating that the proposed TexQ can fully extract the feature distribution in simple datasets.
Table I: Results ResNet-20 on CIFAR-10/100
Top-1 Accuracy(%)
Bit width
Method
CIFAR-10
CIFAR-100
Full-precision
93.89
70.33
Real data
91,52
66.80
GDFQ [24]]
(ECCV 2020)
90.11
63.75
ARC |Н (ICAI 2021)
88.55
62.76
Qimera [X]]
(NeurIPS 2021)
91.26
65.10
W4A4
IntraQ 2X (CVPR 2022)
91,49
64.98
ARC+AIT [59]]
(CVPR 2022)
90.49
61.05
AdaSG H+ (AAAI 2023)
92.10
66.42
AdaDFQ [ (CVPR 2023)
92.31
66.81
TexQ (Ours)
92.68
67.18
GDFQ [24], 277 (ECCV 2020)
75.11
47.61
ARC [58] (ICAA 2021)
40.15
Qimera |X
!А (NeurlPS 2021)
74.43
46.13
IntraQ 2S] (CVPR 2022)
77.07
48.25
W3A3
ARC+AIT [5>]]
(CVPR 2022)
41.34
AdaSG [6 (AAAI 2023)
84.14
52.76
AdaDFQ [ (CVPR 2023)
84.89
52.74
TexQ (Ours)
86.47
55.87
4.2.2 ImageNet
We further compare with competitors on challenging ImageNet, the results are presented in Table
Table 2: Results of ResNet-18, MobileNetV2 and ResNet-50 on ImageNet.
Top-1 Accuracy(%)
Bit width
Method
ResNet-
MobileNetV2
ResNet-50
Full-precision
71.47
72.49
77.73
GDFQ [2]]]
(ECCV 2020)
60.60
59.43
54.16
ZAQ
2
(CVPR 2021)
52.64
0.10
53.02
ARC
|
(IJCAI 2021)
61.32
60.13
64.37
Qimera
(NeurIPS 2021)
63.84
61.62
66.25
W4A4
IntraQ A0
(CVPR 2022)
66.47
65.10
ARC+AIT [59]
(CVPR 2022)
65.73
66.47
68.27
AdaSG [ЯБ]
(AAAI 2023)
66.50
65.15
68.58
AdaDFQ [--]]] (CVPR 2023)
66.53
65.41
68.38
TexQ (Ours)
67.73
67.07
70.72
GDFQ I 2 (ECCV 2020)
20.23
1.46
0.31
ARC [حح] (ICAA 2021)
23.37
14.30
1.63
Qimera B8 |ي
(NeurIPS 2021)
1.17
W3A3
AdaSG [А (AAAI 2023)
37.04
26.90
16.98
AdaDFO - (CVPR 2023)
38.10
28.99
17.63
TexQ (Ours)
50.28
32.80
25.27
Bit width For low bit width case, conventional 7SQ methods suffer from huge accuracy loss, while our TexQ performs good generalization capability. Specifically, for 4-bit ResNet- case,

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TexQ achieving 67.73% accuracy, outperforming AdaDFQ by 1.2%. In 3-bit case, TexQ reaches 50.28% outstanding aceuracy, outperforming AdaDFQ by 12.18%, with standard deviation of 0.34 in 5 repeated experiments. Similar results were obtained in MobileNetV2.
Network Size Larger models are likely lead to poor performance with existing ZSQ methods, especially low bit width case. For example, in 3-bit case, Qimera [H8, 27 performs well on the small ResNet-20. while achieves only 1.17% accuracy on the larger ResNet-18. In contrast, our TexQ achieved 55.87% ultra-low when quantizing ResNet-18 to 3-bit, and leads AdaDFQ with 7.64% on 3-bit ResNet50 case. These results again demonstrate the effectiveness of our method.
4.3 Ablation study
Hyperparameters After empirical initialization, the hyperparameters k. 0y. Oz. and searched for their optimal value with grid search by quantizing ResNet-18 to 3-bit on ImageNet, displayed in Figure Ø. The optimal configurations hyperparameter k represents the number dominant texture elements, whose optimal value of k=9 consistent with what observe in the real samples. The sum of the optimal values of fl and 0, is 0.8, which fits our assumptions about the proportion of dominant texture elements. To avoid complex searches, these parameters were used for all experiments. While this may not be optimal for all networks, it is sufficient to exhibit the advanced performance of TexQ.
k=9, =0.3, 02=0.5, and c=0.015. The
50.91
50.4
$1.01
Top1 eccusey (5
50.5-
50.15
90.5
50,02
50,40
50.0
50:07
50.0
49.5
30.94
48.5
50.0
40.39
19.53
48.5
68.77
49.0
49.0
48.5
4887
47.66
48.5
03.23
45.0
48.0
47,81
10
0.1
0.2
0.3
0.4
0.5
47.5
0.3
0.4
01.6
0.100
0.005
0.000
0.015
0.000
dg
(c)
(b) x
Figure 7: Influence of the hyperparameters.
Modules Ablation on key modules including _ LAWS (Eq. 6). CCL-NNS, (Eq, 7) and mixup knowledge distillation (MKD, Eq. 9) is conducted. As presented in Table 3, dropping one or two of them results in an accuracy loss. The largest accuracy loss (8.37%) observed when both _ LAWS and _ L-BNS are removed, which indicates their cooperative relationship: L L-BNS loosens the shallow layers constraint, facilitating L LAWS calibrate.
Table Ablations on modules. We report the top-1 accuracy of 3-bit ResNet-18 on ImageNet.
LAWS
C LBBNS
MKD
Top-1 Accuracy(%)
50.94
49.03
43.31
49.63
V
42.65
49.00
42.57
Discussion
5.1 Why does TexQ work?
Mitigating the domain gap Our synthetic samples with calibration match the real distribution better, as presented in Figure and Figure H. Further, Figure shows our synthetic sample has more detailed texture distribution similar to the real one.

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(a) ImageNet (IntraQ) (b) ImageNet (Ours)
(c) CIEAR1O (IntraQ)
(d) CIRA R10 (Ows) (e) CIFAR100 (IntrQ) (f) CIFAR100 (Ours)
Figure 8: Visualization of synthetic samples. For ImageNet and CIFAR10/100, samples are obtained with ResNet-18 and ResNet-20, respectively. The advanced IntraQ was selected competitor.
Syttwiic sempli
10
34
(a) Without Calibration (b) Introduce Calibration
(a) ImageNet
(b) Ours
(c) IntraQ
stmbanty
Figure 9: Visualization of the running mean BNS in ResNet-20.
Figure 10: Cosine similarity confusion matrix of samples.
Synthetic samples are obtained with ResNet-18.
Increasing inter-class distance As displayed in Figure Pa, the class centers of samples from con- ventional methods is unclear, limiting the inter-class distance. The situation is improved by intro- ducing calibration centers, shown in Figure Db.
Enhancing sample diversity Figure shows our synthetic samples scatter a lot compared with IntraQ, implying the enhancement of sample diversity. To put it bluntly, synthetic images from different methods are visualized Figure & showing the improvement in color and texture diversity of samples. Further, the intra-class diversity is observed through cosine similarity confusion matrix of samples Figure I. showing that our samples reach a similar diversity to the real ones.
5.2 Limitations and future work
This work is built upon the concept of "texture", and the texture filters adopted are designed man- ually. Thus, the application to other tasks with different modality would be limited. We envision adding training process to the filters, which would generalize the calibration method proposed to other modality. Low-bit quantization remains challenge. For instance, TexQ achieve 70.72% curacy by quantizing ResNet-50 to 4-bit, while it drops to 25.27 55.2%% 7 in 3-bit case. The introduction of advanced distillation methods holds promise for more better results.
Conclusion
In this paper, we observe a non-negligible detailed texture distribution in the real samples. To retain this property synthetic samples, we introduce synthetic calibration images and centers calibrate the generator. To diversify the samples, mixup knowledge distillation module is introduce to create diversified samples for fine-tuning. Extensive experiments show our state-of the-art performance on mainstream networks and datasets, especially for low bit width quantization.
Acknowledgment
This work was supported by the Science and Technology Research Program of Shenzhen City (No. XCXFZ02002111322000,, No. WDDZC220000082214444440000 and the Jilin Fuyuan Guan Food Group Co., Ltd.
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14


Reviews:
[{"review_id": "P3YqJUgzqS", "reviewer": "Reviewer_zKQV", "summary": "They suggested a zero-shot quantization method to retain the detailed texture feature distribution and introduced the mixup knowledge distillation module to diversify synthetic samples for finetuning", "questions": "1. please provide more detail on why the texture feature distribution calibration is important when generating synthetic data.\n\n2. PTQ methods such as AdaRound, AdaQuant, and Brecq can employ synthetic data to quantize models. how about adapting these post-training quantization schemes for your methods?\n\n3. I expect to see more evaluation on various models in order to convince the superiority of your work.", "limitations": "It lacks a literature survey.", "rating": 5, "confidence": 5, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "They identified the new feature required when generating synthetic data for quantization.", "weaknesses": "They should compare their work with MixMix [1], Genie[2] and KW[3].\n\nThe authors only empirically showed their superiority. i.e. lt lacks explanations of intuitive or mathematic. The author should give more reasons.\n\nThe image they generated showed a little bit of poor quality to argue that it has captured the texture feature distributions. please see the synthetic images in [1], [2], [3].\n\n[1] Li, Yuhang, et al. \"Mixmix: All you need for data-free compression are feature and data mixing.\" Proceedings of the IEEE/CVF International Conference on Computer Vision. 2021.\n\n[2] Jeon, Yongkweon, Chungman Lee, and Ho-young Kim. \"Genie: Show Me the Data for Quantization.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2023.\n\n[3] Haroush, Matan, et al. \"The knowledge within: Methods for data-free model compression.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2020.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "### We would like to thank the reviewer for the thoughtful reviews that will help strengthen our paper. In the following, we address each individual question in detail. \n\n**Due to characters limit, all tables for supplementary experiments are displayed in the global response area.**\n\n***\n\n**Q1: please provide more detail on why the texture feature distribution calibration is important when generating synthetic data.**\n\n**A1: We agreed to provide more details to make it clearer for future readers.**\n\n* For intuitive explanations, we appreciate the comments of reviewer F97y. We will provide straightforward visualization of the texture feature extracted by filters in Figure 5, after introducing the concept of \"LAWS texture feature energy\" (line 127). In addition, we supplement the actual signal meaning of the filters in Section 3.2.1 (line 126).\n\n* For literature survey and mathematic explanations, we supplement Related work (line 71) on the importance of texture features and the processing details of texture features. \n\n* Many research [4-6] identified the importance of textures feature for CNNs. [4] found that texture representations could capture the statistical characteristics of images for CNNs. [5] showed that classic CNNs were unable to recognize sketches where textures are missing and shapes are left. Similarly, [6-7] validated that CNNs were biased towards textures than shapes, for example, ResNet-50 biased 77.9% texture [6].\n\n* Texture feature extraction is a common method in natural image processing, details can be referred to [8]. Studies [9-10] have shown that image texture features are conductive to image classification and are class separable. We observe that quantized networks suffer from accuracy loss on image that lose texture features (Figure 2). Further, we introduced quantitative indicators of LBP and LAWS texture feature energy to visually demonstrate the texture feature gap between the synthetic and real image (Figure 1,5). Results show that the plug of this gap is beneficial to quantization.\n\n**Q2 and weakness: \nThey should compare their work with MixMix [1], Genie[2] and KW[3]. PTQ methods such as AdaRound, AdaQuant, and Brecq can employ synthetic data to quantize models. how about adapting these post-training quantization schemes for your methods?**\n\n**A2: We have also noted the studies[1-3]. We provide comparisons with MixMix [1], Genie[2] and KW[3] below. However, it should be noted that MixMix [1], KW [3] has looser quantization settings and no open-source code, Genie [2] is not the same type of work as ours on feature extraction, which makes the comparison not fair.**\n\n* As for MixMix [1], it focuses on the generalization of synthetic dataset, and **3 pre-trained models** were used for distilling (Section 5, [1]). However, General **ZSQs allow only 1 pre-trained model** to extract data and quantize itself. For KW [3], they quantized the **first & final layers in 8 bits and 1x1 convolution layers in 8 bits** (Table 1-3, [3]), However, most of works including ours quantize **all layers to the same target bits**. Even under unfair comparison, our method exhibits superior performance. As shown in Table A, **we still lead MixMix with a top1 acc. of 3.06%, and lead KW with acc. loss of 0.39% in the 4 bits MobIleNet-V2 case on ImageNet.**\n\n* Genie [2] is a different type of work. They focus on new quantizer (Section 3.2, [2]) and introduced PTQ (AdaRound and BRECQ) for fine-tuning. However, we focus on verifying the idea of texture calibration, regardless of improving the quantizer even though we may achieve better accuracy by optimizing it. Thus, a naive asymmetric quantizer is adopted to maintain consistency with the same type of works. To reach a fair comparison, we adopted 1000 synthetic samples of Genie [2] and conducted the experiment on the same asymmetric quantizer. Results in Table B show that Genie performs similar results to the contemporaneous work. **We lead Genie with 1.79% top1 acc. on the same quantizer in the 4 bits MobIleNet-V2 case.** One of the factors is that Genie ignored class information but we retain class features with dynamic texture calibration.\n\n* On the issue of image visualization, MixMix [1], Genie[2] and KW[3] generate images that conform to human vision. However, our goal is not to generate beautiful images, and we even drop the scale limit of [-1, 1] of the image tensor to expand the feature representation space. Some methods as L2 norm, clamp/clip to generate smooth and visual images were tried but seem no benefit in quantization. Relevant experimental results are shown in Table C.\n\n**Q3: I expect to see more evaluation on various models in order to convince the superiority of your work.**\n\n**A3: We are providing our results for ResNet50 on ImageNet in Table D.**\n\n* **We continue to show advanced performance on the ResNet50, such as we lead AdaDFQ with 7.64%/2.34% Top1 acc. on 3/4 bits case**. We will supplement this result in Table 2. \n\n* For our experiments, we follow the settings of Section 4.1 except that we raise the weight of L-BNS loss and BNS alignment loss to ensure the convergence of the model.\n\n```\n[1] Mixmix: All you need for data-free compression are feature and data mixing. ICCV. 2021.\n[2] Genie: Show Me the Data for Quantization. CVPR. 2023.\n[3] The knowledge within: Methods for data-free model compression. CVPR. 2020.\n[4] Texture synthesis using convolutional neural networks. NeurIPS. 2015.\n[5] On the performance of GoogLeNet and AlexNet applied to sketches. AAAI. 2016.\n[6] ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness. arXiv, 2018.\n[7] BiasBed-Rigorous Texture Bias Evaluation. CVPR. 2023.\n[8] Filtering for texture classification: A comparative study. TPAMI. 1999.\n[9] Image Classification Using Laws' Texture Energy Measures. 1987.\n[10] Texture and shape biased two-stream networks for clothing classification and attribute recognition. CVPR. 2020.\n```"}, {"review_id": "HbXVNdceTm", "reviewer": "Reviewer_yCFw", "summary": "The paper points out that there is a strong dependency between the performance of CNN and the texture feature of the dataset. For extending this concept to the quantization field, the paper adopts calibration samples which are trained with manually designed texture filters. In addition to synthetic samples which are generally used in ZSQ works (generated by a network that is trained with Batch Normalization layers’ statistics of a full precision model), the paper exploits calibration samples to quantize a model without the original dataset. Furthermore, the paper applies mixup data augmentation to improve the quantized model’s performance.", "questions": "- In equation 1, only a rounding operation is applied to obtain quantized integers without a clip operation?\n\n- The paper design texture filter manually. Is it possible to get texture filters with the training process?\n\n- Calibration samples are obtained without a generator. Is it possible to generate calibration samples with another generator, or the synthetic sample generator by giving the texture feature energy distribution calibration loss?\n\n- How expensive it is to generate both samples, compared to other works that generate synthetic samples only?\n\n- Qimera [1] executed several experiments with mixup and cutmix, similar with 'Mixup knowledge distillation module' described in 3.2.3, claiming that superposed latent embedding works better than mixup and cutmix. Can a comparison with those methods be provided?\n\n\n[1] Choi et al. Qimera: Data-free Quantization with Synthetic Boundary Supporting Samples. In Conference on Neural Information Processing Systems. 2021", "limitations": "Previous ZSQ works which exploit Batch Normalization layers' statistics for generating synthetic samples are hard to apply transformer-based models.\n\nIt is worth analyzing that the proposed method can be applied to those models.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- This paper is well-motivated and easy to follow.\n\n- The paper adopts a concept of texture feature in Zero-shot quantization for the first time.\n\n- The paper demonstrates the proposed method well with several formulas and figures.", "weaknesses": "- It seems costly that generate calibration samples along with synthetic samples for quantizing a neural network.\n\ntypo:\n- In the 215th row, presnted -> presented", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "### **We thank the reviewer for the helpful reviews that will help strengthen our paper. Our replies are as follows:**\n\n---\n\n**Q1: In equation 1, only a rounding operation is applied to obtain quantized integers without a clip operation?**\n\n**A1: Thank you for reminding us that we omitted a clip operation in Eq. 1, and we have revised it.**\n\n---\n\n**Q2: The paper design texture filter manually. Is it possible to get texture filters with the training process?**\n\n**A2: This is entirely a promising point.** \n\n* With the manually designed texture feature filters, we are the first to introduce the idea of texture calibration and realize it in quantization for better performance. \n* The iterable filters take advantage of automatic design features to facilitate the adaptation of different datasets and tasks. They will be explored in subsequent work and hopefully improve performance.\n\n---\n\n**Q3: Calibration samples are obtained without a generator. Is it possible to generate calibration samples with another generator, or the synthetic sample generator by giving the texture feature energy distribution calibration loss?**\n\n**A3: These are two possible options. Considering the time cost, we choose to directly extract calibration samples from the model.**\n\n* For introducing another generator, training the generator increases the time and information transfer cost. \n\n* For applying calibration lost to the generator, results in slow iterations and homogeneous samples. So, these two options were not adopted.\n\n---\n\n**Q4: How expensive it is to generate both samples, compared to other works that generate synthetic samples only?**\n\n**A4: Generating calibration samples requires additional time, which is acceptable for offline PTQ. We generate calibration set (one calibration sample per class) on an NVIDIA GeForce RTX 3090 GPU.**\n\n* For images of size 3×32×32, the generation speed is about 10 seconds per image. For images of size 3×224×224, the generation speed is about 20 seconds per image.\n\n* Taking CIFAR10 as an example, generating the whole calibration set takes 10*10 seconds=100 seconds=1.67 minutes. Parallel processing to accelerate this process is possible.\n\n---\n\n**Q5: Qimera [11] executed several experiments with mixup and cutmix, similar with 'Mixup knowledge distillation module' described in 3.2.3, claiming that superposed latent embedding works better than mixup and cutmix. Can a comparison with those methods be provided?**\n\n[11] Choi et al. Qimera: Data-free Quantization with Synthetic Boundary Supporting Samples. In Conference on Neural Information Processing Systems. 2021.\n\n**A5: This is a very meaningful question. We will address your concerns with several experiments.**\n\n* First of all, we need to clarify that **the applications of “Mixup knowledge distillation module” and “Superposed latent embeddings/Mixup/Mixcut” are different.** “Superposed latent embeddings/Mixup/Mixcut methods” in Qimera [11] generate **samples with mixed labels to fine-tune the quantization model with cross-entropy loss**. Different from them, we apply the **mixed samples to knowledge distillation with KL divergence loss** of the pre-trained model (teacher model) and the quantized model (student model) (see Eq.13 in Section 3.3.3), **without using mixed labels to fine-tune** the quantized model with cross-entropy. \n\n* Why does superposed latent embedding (Qimera) work better than mixup and cutmix? We observed that traditional mixup and cutmix lead to inaccurate labels. To be detailed, the true label (the inference results of the pre-trained model) of the mixed image is inconsistent with the mixed label. Taking such mixed labels to fine-tune the quantized model with cross-entropy loss tends to be disastrously misleading. A simple experiment as below might be more straightforward. We randomly performed Mixup or Mixcut on 1000 synthetic images and their labels. Similarly, we warm up the generator with 50 epochs and use superposed latent embeddings to generate 1000 synthetic images. Then, we count the consistency of mixed labels and real labels. As shown in Table E, we found that only 34.4% percent of the Mixup or Mixcut samples were correctly labeled, while Qimera's got an advanced Acc. of 66.1%. However, it still can be seen that the labels produced by the above methods are not accurate enough, so we do not recommend using such mixed labels to fine-tune quantization models. Note that we do not use mixed labels to fine-tune the model and do not suffer from such problems.\n\n---\n\n#### **Tabel E\tComparisons with mix methods on correct label rate (4 bits MobIleNet-V2 on ImageNet)**\n|     Method    |     Correct   label    |     Incorrect   label    |     Correct   rate    |\n|---|---|---|---|\n|     Mixup   or Mixcut    |     344    |     656    |     34.4%    |\n|     Superposed   latent embeddings (Qimera) [11]   |     661    |     339    |     **66.1%   (Best)**    |\n\n---\n\n* Finally, we would like to compare the effect of superposed latent embeddings/Mixup/Mixcut in our framework. We conduct the comparison on 4 bits MobIleNet-V2 case on ImageNet. As shown in Table F, we find that the above three methods have similar effects. Our proposed “Mixup knowledge distillation module” is slightly ahead of the other two, which takes advantage of decoupling the generator to fuse the entire image, maximizing sample diversity.\n\n---\n\n#### **Tabel F\tComparisons with mix methods for KL divergence distillation (4 bits MobIleNet-V2 on ImageNet)**\n|     Method    |     Acc.   of quantized model    |     Acc.   of pre-trained model    |     Acc.   loss    |\n|---|---|---|---|\n|     No   augmentation    |     66.21    |     72.49    |     -6.28    |\n|     Mixup   knowledge distillation module (Ours)    |     **67.07  (Best)**    |     72.49    |     -5.42     |\n|     Mixcut                       |     67.01    |     72.49    |     -5.48    |\n|     Superposed   latent embeddings (Qimera)  [11]   |     66.89    |     72.49    |     -5.60    |\n\n---\n"}, {"review_id": "GTzEw8QzHz", "reviewer": "Reviewer_F97y", "summary": "This work proposes TexQ, which targets keeping the texture information of the synthetic samples of zero-shot quantization. The texture feature energy distribution calibration method is applied to the synthesized samples, and mixup knowledge distillation is introduced to improve the diversity of the synthetic samples. Extensive experiments of ResNet, MobileNet on CIFAR, and ImageNet datasets prove the effectiveness of this method.", "questions": "* Most previous work uses the term ''data-free quantization (DFQ)'' instead of \"zero-shot quantization (ZSQ).\" I want the author to make sure that these two terminologies are identical.\n* What is the actual (visual/physical/signal) meaning of the feature extracted using the filters $E_5, S_5, W_5, R_5$?\n* Can TexQ be transferred to language tasks without \"texture\" in the data?\n", "limitations": "The author includes a discussion of the problems to be solved in Section 5.2, which is great. One crucial limitation I would like to raise is that this work is built upon the concept of \"texture\" and is **only meaningful for visual samples**. The application to other tasks with different modality (language, speech, etc.) would be limited.", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "* The paper is well-organized and easy to follow. Fig.3 is an excellent visualization of the proposed system architecture.\n\n* To measure the texture feature distribution for the input sample of quantization is novel. The comparison (Fig. 4/5) of synthetic samples and natural images is insightful and may help future research on the ZSQ.\n\n* The experiment results are convincing and high accuracy (especially for 3-bit) demonstrates the effectiveness of TexQ.", "weaknesses": "* The introduction of the concept \"LAWS texture feature energy\" needs to be improved. The example given in Eq.5 is not straightforward. Visualization of features extracted using $E_5, S_5, W_5, R_5$ would be better. Why these \"texture\" feature is important to retain should also be included more in the discussion.\n* There are too many artifact weighting coefficients $\\alpha_i, i \\in [1,5]$ to balance different loss function. The author claims in Sec. 4.1 that they \"empirically\" select the value. An ablation study or sensitivity analysis on these parameters would be better to prove that the proposed loss is solid and that better performance does not come from a grid search of the parameters.\n* The method is only validated on CNNs. The experiment results on Vision Transformer would be a plus.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "### **Thank you for providing new ideas for straightforward visualization and interesting transferred language tasks. We would like to address the concerns below:**\n\n---\n\n**Q1: The introduction of the concept \"LAWS texture feature energy\" needs to be improved. The example given in Eq.5 is not straightforward. Visualization of features extracted using $E_5, S_5, W_5, R_5$ would be better. Why these \"texture\" feature is important to retain should also be included more in the discussion. What is the actual (visual/physical/signal) meaning of the feature extracted using the filters?**\n\n**A1: We agree to provide more details to introduce the concept of \"LAWS texture feature energy\"**\n\n* More background in the Introduction and Methods (Section 3.2.1) will be provided to introduce the concept of \"LAWS texture feature energy\", including the details of LAWS texture feature filters [8] and their application [9-10]. This helps future readers to understand our work.\n\n* Visualization is a good idea. Straightforward visualization of the texture features extracted will be provided in Figure 5 (line 127) after introducing the concept of \"LAWS texture feature energy\".\n\n* In addition, we will add the actual signal meaning and function of the filters in Section 3.2.1 (line 126). $E_5, S_5, W_5, R_5$ are series of texture feature filters mnemonics standing for Edge, Spot, Wave, and Ripple. The filtered feature map reflects the degree of matching between the texture and the filters. Complex texture feature distribution is composed of simple texture elements, so it is reasonable to introduce basic texture filters to characterize the texture feature distribution of images. These discussions will be supplemented in the camera-ready version.\n\n---\n\n**Q2: There are too many artifact weighting coefficients to balance different loss function. The author claims in Sec. 4.1 that they \"empirically\" select the value. An ablation study or sensitivity analysis on these parameters would be better to prove that the proposed loss is solid and that better performance does not come from a grid search of the parameters.**\n\n**A2: Thank you for this suggestion. We agree that the adopted hyperparameter settings are not globally optimal. We adopted the settings of relevant studies [12-14] to avoid time costly grid search.**\n* More importantly, we focus on verifying the texture feature distribution calibration method, and empirical settings are conducive to fair comparison with the same type of work. \n* Experiments show that our idea works even when we configure hyperparameters empirically, which is enough to verify our idea.\n\n---\n\n**Q3: Can TexQ be transferred to language tasks without \"texture\" in the data?**\n\n**A3: That's an interesting question.**\n\n* In computer vision, texture is an important feature of images. Is there any similar feature in the field of language such as speech? I think the answer is absolutely yes. \n\n* I agree with the constructive comment made by reviewer yCFw, that we can further introduce trainable filters to achieve automatic feature extraction. With such methods, our method holds promise for applications in other fields.\n\n---\n\n**Q4: The method is only validated on CNNs. The experiment results on Vision Transformer would be a plus.**\n\n**A4: Thank you for this suggestion, the ideas of our work can be transferred to other visual models.**\n\n* Unfortunately, the quantizer adopted in this paper does not involve the quantizer of ViT.\n* The emphasis of this paper is to put forward the idea of texture calibration and verify it. We take Vision Transformer into consideration in the subsequent work.\n\n---\n\n**Q5: Most previous work uses the term ''data-free quantization (DFQ)'' instead of \"zero-shot quantization (ZSQ).\" I want the author to make sure that these two terminologies are identical.**\n\n**A5: The terminologies ''data-free quantization (DFQ)' and 'zero-shot quantization (ZSQ)' are identical in the research community.** We will illustrate these terms in Related work (line 86) and modify the expression in the camera-ready version.\n\n---\n\n```\n[8] Randen, Trygve, and John Hakon Husoy. Filtering for texture classification: A comparative study. IEEE Transactions on pattern analysis and machine intelligence. 1999.\n[9] Gillett, Will D. Image Classification Using Laws' Texture Energy Measures. 1987.\n[10] Zhang, Yuwei, et al. Texture and shape biased two-stream networks for clothing classification and attribute recognition. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2020.\n[12] Zhong, Yunshan, et al. Fine-grained data distribution alignment for post-training quantization. European Conference on Computer Vision. Cham: Springer Nature Switzerland, 2022.\n[13] Xu, Shoukai, et al. Generative low-bitwidth data free quantization. Computer Vision–ECCV 2020: 16th European Conference, Glasgow, UK, August 23–28, 2020, Proceedings, Part XII 16. Springer International Publishing, 2020.\n[14] Zhong, Yunshan, et al. Intraq: Learning synthetic images with intra-class heterogeneity for zero-shot network quantization. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2022.\n```"}, {"review_id": "UbPtujmQ0o", "reviewer": "Reviewer_qhGS", "summary": "TexQ is a novel zero-shot quantization (ZSQ) method that addresses the limitations of conventional synthetic samples in retaining texture feature distributions. It achieves state-of-the-art results in ultra-low bit width quantization, with a significant accuracy increase compared to existing methods on ImageNet.", "questions": "The authors could refer to the Weaknesses. Additionally, I also have some open questions to discuss.\n\n1. The authors could discuss how to ensure the generalization of the method since the calibration is conducted on a specific dataset.\n2. Could the method be used in the Transformer structure?", "limitations": "N/A", "rating": 7, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "Strengths are shown below:\n\n1. This paper tried to exploit the important direction for inevitable privacy and security.\n2. The performance on the benchmark datasets is promising.\n3. The paper is well-organized.", "weaknesses": "1. Maybe the structures used are insufficient with ResNet-18 and MobileNet-V2. What about the most commonly used ResNet-50?\n2. Maybe the datasets verified are insufficient with Cifar and ImageNet. What about the others tasks, such as CoCo of detection.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "### **Thank you for your positive review and constructive comments. We have performed some of them and will include them in the camera-ready version.**\n\n---\n\n**Q1: Maybe the structures used are insufficient with ResNet-18 and MobileNet-V2. What about the most commonly used ResNet-50?**\n\n**A1: Thank you for your advice. We supplement the experiments on ResNet-50, and the results are shown in Table D.**\n\n* **We continue to show advanced performance on the ResNet50, such as we lead AdaDFQ with 7.64%/2.34% Top1 accuracy on 3/4 bits case**.\n* For our experiments, we follow the settings of Section 4.1 except that we raise the weight of L-BNS loss and BNS alignment loss to ensure the convergence of the model. \n\n---\n\n#### **Table D. Top 1 accuracy (%) results of ResNet50 on ImageNet. WBAB indicates the weights and activations are quantized to B-bit.**\n|     Methods    |     W4A4    |     W3A3    |\n|---|---|---|\n|     GDFQ(ECCV   2020)    |     54.16    |     0.31    |\n|     ZAQ   (CVPR 2021)    |     53.02    |     -    |\n|     ARC   (IJCAI 2021)    |     64.37    |     1.63    |\n|     Qimera   (NeurIPS 2021)    |     66.25    |     -    |\n|     ARC+AIT   (CVPR 2022)    |     68.27    |     -    |\n|     AdaSG   (AAAI 2023)    |     68.58    |     16.98    |\n|     AdaDFQ   (CVPR 2023)    |     68.38    |     17.63    |\n|     **TexQ   (Ours)**    |     **70.72**    |     **25.27**    |\n\n---\n\n**Q2: Maybe the datasets verified are insufficient with Cifar and ImageNet. What about the others tasks, such as CoCo of detection.**\n\n**A2: Generally, most zero-shot quantization works [12-16] in the research community are validated in CIFAR10/100 and ImageNet, for these datasets are persuasive and convincing.**\n* For our work, we are the first to propose the idea of texture calibration and validate it, which is the focus.\n* Expanding to downstream tasks will be a new research hotspot, which will also be the direction of our future exploration.\n\n---\n\n**Q3: The authors could discuss how to ensure the generalization of the method since the calibration is conducted on a specific dataset.**\n\n**A3: This is an open question worth exploring.**\n\n* In our work, we apply the same texture feature distribution calibration method (including hyperparameters) across different image sizes and scales of datasets. Advanced results show that our method is capable of generalization, even if these settings are not optimal for every dataset.\n* Further considering a specific dataset, the following two aspects can be explored. First, trainable texture feature filters can be used to extract specific features on a specific dataset. Second, adaptive method can be introduced to balance multiple losses.\n\n---\n\n**Q4: Could the method be used in the Transformer structure?**\n\n**A4: The calibration idea proposed can be transferred to other computer vision models including the transformer structure.**\n* However, currently CNN and Transformer require different quantizers, and the quantization framework we adopted does not support the transformer structure model.\n* More importantly, our main contribution is to propose the idea of texture calibration in zero-shot quantization and verify it. We will introduce the quantizer for the transformer structure in future work.\n\n---\n\n```\n[12] Zhong, Yunshan, et al. Fine-grained data distribution alignment for post-training quantization. European Conference on Computer Vision. Cham: Springer Nature Switzerland, 2022.\n[13] Xu, Shoukai, et al. Generative low-bitwidth data free quantization. Computer Vision–ECCV 2020: 16th European Conference, Glasgow, UK, August 23–28, 2020, Proceedings, Part XII 16. Springer International Publishing, 2020.\n[14] Zhong, Yunshan, et al. Intraq: Learning synthetic images with intra-class heterogeneity for zero-shot network quantization. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2022.\n[15] Qian, Biao, et al. Rethinking data-free quantization as a zero-sum game. arXiv preprint arXiv:2302.09572. 2023.\n[16] Qian, Biao, et al. Adaptive Data-Free Quantization. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2023.\n```"}, {"review_id": "tM2ssHZ1bJ", "reviewer": "Reviewer_h8LC", "summary": "This paper starts from an interesting viewpoint that the synthetic of the previous ZSQ method usually fails to model the similar text feature like real data. As a result, the authors suggest retaining the texture feature. At first, they synthesize calibration images with a LAWS texture feature energy preserve loss. Then, the calibration images are used to provide mean and variance centers for each class, which is then used to guide the generator to synthesize samples. At last, they proposed using a mix-up strategy to further augment the synthetic data.", "questions": "1, Line 193, what is \\bar(D)?\n2, It actually uses synthetic data from the generator and from direct optimization. It may an unfair comparison.\n", "limitations": "The authors do provide a discussion about the limitations.", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1, The viewpoint is interesting and persuasive. Also, the results do demonstrate the effectiveness of their method.\n2, Sec 5.1 provide many meaningful discussion, which makes this paper more convincing.\n", "weaknesses": "1, To be honest, the writing of this paper is not good enough and I get lost in many parts. \n\nFor example, Line 171, ‘Q always faces linear decisions when inferencing’ is very strange. I can't understand the meaning behind it.\n\nLine 166, where µ_l (\\bar(x)| \\bar(y) = k) and σ_l (\\bar(x)| \\bar(y) = k) should be the calibrating mean and variance center since calibration set C = {( \\bar(x), \\bar(y))} in Line 160.\n\n2, Why do the authors want to use a calibration center in Step2: Synthetic samples generation? The paper lacks some discussion.\n\n3, The principle behind Calibration set generation and Synthetic samples generation is not clear. Why do you still need Synthetic samples, even though you already have Calibration set. I know such a way could give a better performance. The authors should provide some ablation study when only using Calibration set.\n\n4, The role of Eq6. The K set only selects top-k texture elements that account for more than 80%. However, the images are randomly initialized from Gaussian noise. I am wondering if the distribution of the K set keeps the same for each synthetic image. For example, R5R5 is very fit for Gaussian noise and is selected for each image.\n", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "### **We would like to thank the reviewer for the thorough and thoughtful revision of the paper. In the following, we will address each point raised.**\nWe not only respond to or clarify the points but have also made changes accordingly to the main text to make them more clear to future readers.\n\n---\n\n**Q1: Line 193, what is $\\bar{D}$?**\n\n**A1:  $\\bar{D}$ denotes the synthetic sample set  $\\bar{D} =  \\\\{\\( \\bar{x},  \\bar{y}\\)\\\\} $. The definition is presented in Section 3.1.2 Data synthesis (line 117).**\n\n---\n\n**Q2: It actually uses synthetic data from the generator and from direct optimization. It may an unfair comparison.**\n\n**A2: Zero-shot quantization (ZSQ) requires strictly avoiding real data. In our work, both the synthetic dataset $\\bar{D}$ and the calibration dataset $C$ are synthesized, so it conforms to the fairness of ZSQ comparison.**\n\n---\n\n**Q3: Line 171, ‘Q always faces linear decisions when inferencing’ is very strange. I can't understand the meaning behind it.**\n\n**A3: We rewrite this paragraph and hope it is clearer.**\n\nLine 171: Our motives lie in the fact that quantized model Q always faces samples with soft labels when inferencing, we hope to synthesize samples with soft labels, too.\n\n---\n\n**Q4: Line 166, where $µ_l (\\bar{x}| \\bar{y} = k)$ and $σ_l (\\bar{x}| \\bar{y} = k)$ should be the calibrating mean and variance center since calibration set $C = \\{\\( \\bar{x}, \\bar{y}\\)\\}$ in Line 160.**\n\n**A4: We checked the expression and found no problem, but we would like to make this point more clear to future readers.**\n\n* In the synthetic sample generation stage, we used layered BNS alignment to constrain the generator to synthesize samples that fit the calibration centers. Therefore, Eq. 8 includes the calibrating center and BNS of synthetic samples. In other words, with this method, texture feature distribution knowledge is transferred from the calibrating center to the synthetic samples. \n* We will add superscript $^\\bar{D}$ to the variables involved in the synthetic samples to clarify the data source. \n\n---\n\n**Q5: Why do the authors want to use a calibration center in Step2: Synthetic samples generation? The paper lacks some discussion.**\n\n**A5: We will supplement the relevant details in Section 3.2.2 (line 155).**\n\n* The introduction of calibration centers is a strategy for information transfer, which is also done in FDDA[12] and ClusterQ[17].\n* The principle is that the batch normalized statistics (BNS) of the convolutional neural network are highly related to the class, so introducing a calibration center in Step2 means transferring the information of the calibration center extracted in Step 1 to the generator.\n\n---\n\n**Q6: The principle behind Calibration set generation and Synthetic samples generation is not clear. Why do you still need Synthetic samples, even though you already have Calibration set. I know such a way could give a better performance. The authors should provide some ablation study when only using Calibration set.**\n\n**A6: These are commonly used information transfer strategies, and we will supplement the detailed motivation in Section 3.3.2 (line 185) for easy understanding by readers:**\n\n* Distillation (optimization) [14] and generation (generator) [13] are two commonly used methods for synthesizing data. Distillation scheme directly optimizes Gaussian noise to synthesize samples, which takes a long time but less information transfer links, so the knowledge is more accurate. Generation scheme require training a generator. It is suitable for mass data generation, but the increase in information transfer links is not conducive to accurate knowledge transfer.\n\n* Our work combines the best of both schemes. We use the optimization method to synthesize accurate calibration centers for each class and introduce calibration centers into the generator to synthesize samples in batches, taking both accuracy and speed into account. \n\n* In addition, another possible scheme is to directly apply texture feature constraints to the generator. However, applying calibration lost to generator results in slow iterations and homogeneous samples. So, this option was not adopted.\n\nWe conducted ablation studies on calibration samples and synthetic samples. **The three sample synthesis schemes and their results are shown in Table G. The scheme adopted in this paper is the optimal solution.**\n\nDue to characters limit, ***Tabel G are displayed in the global response area.***\n\n---\n\n**Q7: The role of Eq6. The K set only selects top-k texture elements that account for more than 80%. However, the images are randomly initialized from Gaussian noise. I am wondering if the distribution of the K set keeps the same for each synthetic image. For example, R5R5 is very fit for Gaussian noise and is selected for each image.**\n\n**A7: The K sets are similar when Gaussian noise is initialized, but finally they become different, especially for different classes of images.**\n\n* Many studies [8-10] have shown that texture features are conducive to classifying images, so the final K sets are various from different classes of images.\n* R5R5 is very suitable for Gaussian noise, so it is selected by most images in the initial stage, and acts as a noise reduction function.\n\n```\n[8] Filtering for texture classification: A comparative study. IEEE Transactions on pattern analysis and machine intelligence. 1999.\n[9] Image Classification Using Laws' Texture Energy Measures. 1987.\n[10] Texture and shape biased two-stream networks for clothing classification and attribute recognition. CVPR. 2020.\n[12] Fine-grained data distribution alignment for post-training quantization. ECCV. 2022.\n[13] Generative low-bitwidth data free quantization. ECCV. 2020.\n[14] Intraq: Learning synthetic images with intra-class heterogeneity for zero-shot network quantization. CVPR. 2022.\n[17] ClusterQ: Semantic Feature Distribution Alignment for Data-Free Quantization. arXiv. 2022.\n```"}]

Author rebuttal:
## **[Global Response] Tables for supplementary experiments**

************************************************

### **Tabel A	Comparisons with MixMix and KW (4 bits MobIleNet-V2 on ImageNet)**
|     Method    |     Settings    |     Acc.   of quantized model    |     Acc.   of pre-trained model    |     Acc.   loss    |
|---|---|---|---|---|
|     Ours    |     1   model, all layers in 4 bits    |     **67.07  (Best)**    |     72.49    |     -5.42     |
|     MixMix   [1]    |     3   model, all layers in 4 bits    |     64.01   [1]    |     72.49       |     -8.48    |
|     KW   [3]    |     1   model, first & final layers in 8 bits    |     66.07   [3]    |     71.88       |     -5.81    |

[1] Mixmix: All you need for data-free compression are feature and data mixing. ICCV. 2021.

[3] The knowledge within: Methods for data-free model compression. CVPR. 2020.

---

### **Tabel B	Comparison with Genie on the same quantizer (4 bits MobIleNet-V2 on ImageNet)**
|     Synthetic   data    |     Acc.   of quantized model    |     Acc.   of pre-trained model    |     Acc.   loss    |
|---|---|---|---|
|     Ours    |     **67.07  (Best)**     |     72.49    |     -5.42   |
|     Genie   (CVPR 2023)  [2]    |     65.28    |     72.49    |     -7.21    |
|     AdaDFQ   (CVPR 2023)    |     65.41    |     72.49    |     -7.08    |

[2] Genie: Show Me the Data for Quantization. CVPR. 2023.

---

### **Tabel C	Comparisons on different synthetic image constraints (4 bits MobIleNet-V2 on ImageNet)**
|     Method    |     Settings    |     Acc.   of quantized model    |     Acc.   of pre-trained model    |     Acc.   loss    |
|---|---|---|---|---|
|     Our    |     Texture   calibration, Unrestricted tensor range    |     **67.07  (Best)**     |     72.49    |     -5.42    |
|     Our+clamp    |     Texture   calibration, Restricted tensor range of [-1, 1]    |     66.26    |     72.49    |     -6.23    |
|     Genie   [2]    |     Restricted   tensor range of [-1, 1]    |     65.28    |     72.49    |     -7.21    |

[2] Genie: Show Me the Data for Quantization. CVPR. 2023.

---

### **Table D. Top 1 accuracy (%) results of ResNet50 on ImageNet.**
|     Methods    |     W4A4    |     W3A3    |
|---|---|---|
|     GDFQ(ECCV   2020)    |     54.16    |     0.31    |
|     ZAQ   (CVPR 2021)    |     53.02    |     -    |
|     ARC   (IJCAI 2021)    |     64.37    |     1.63    |
|     Qimera   (NeurIPS 2021)    |     66.25    |     -    |
|     ARC+AIT   (CVPR 2022)    |     68.27    |     -    |
|     AdaSG   (AAAI 2023)    |     68.58    |     16.98    |
|     AdaDFQ   (CVPR 2023)    |     68.38    |     17.63    |
|     **TexQ   (Ours)**    |     **70.72**    |     **25.27**    |

---

### **Tabel E	Comparisons with mix methods on correct label rate (4 bits MobIleNet-V2 on ImageNet)**
|     Method    |     Correct   label    |     Incorrect   label    |     Correct   rate    |
|---|---|---|---|
|     Mixup   or Mixcut    |     344    |     656    |     34.4%    |
|     Superposed   latent embeddings (Qimera) [11]   |     661    |     339    |     **66.1%   (Best)**    |

[11] Qimera: Data-free Quantization with Synthetic Boundary Supporting Samples. NeurIPS. 2021.

---

### **Tabel F	Comparisons with mix methods on TexQ (4 bits MobIleNet-V2 on ImageNet)**
|     Method    |     Acc.   of quantized model    |     Acc.   of pre-trained model    |     Acc.   loss    |
|---|---|---|---|
|     No   augmentation    |     66.21    |     72.49    |     -6.28    |
|     Mixup   knowledge distillation module (Ours)    |     **67.07  (Best)**    |     72.49    |     -5.42     |
|     Mixcut                      |     67.01    |     72.49    |     -5.48    |
|     Superposed   latent embeddings (Qimera)  [11]   |     66.89    |     72.49    |     -5.60    |

[11] Qimera: Data-free Quantization with Synthetic Boundary Supporting Samples. NeurIPS. 2021.

---

### **Tabel G	Three possible sample synthesis schemes for TexQ (4 bits MobIleNet-V2 on ImageNet)**
|     Method    |     Acc.   of quantized model    |     Acc.   of pre-trained model    |     Acc.   loss    |
|---|---|---|---|
|     Calibration   samples + Synthetic samples    |     **67.07  (Best)**    |     72.49    |     -5.42     |
|     Only   synthetic samples    |     65.42    |     72.49    |     -7.07    |
|     Only   calibration samples    |     66.04    |     72.49    |     -6.45    |


Meta-review: The paper titled "TexQ: Zero-shot Network Quantization with Texture Feature Distribution Calibration" proposes a novel approach to zero-shot quantization (ZSQ) by addressing the challenge of retaining detailed texture feature distributions in synthetic samples. The authors introduce the concept of texture feature energy distribution calibration to guide the synthesis of calibration images, and they employ a mixup knowledge distillation module to enhance the diversity of synthetic samples for fine-tuning. The paper showcases strong performance in ultra-low bit width quantization on benchmark datasets such as CIFAR10/100 and ImageNet.

Reviewer zKQV acknowledges the paper's contributions and highlights its identification of the need for new features when generating synthetic data for quantization. The strengths include the novel approach to texture feature distribution calibration and the use of mixup for knowledge distillation. However, the reviewer raises concerns regarding the lack of comparisons with related works, as well as the empirical nature of the paper without extensive intuitive or mathematical explanations. The reviewer also comments on the quality of generated images and requests more evaluation on various models to demonstrate the superiority of the proposed method. In their rebuttal, the authors address each concern raised by the reviewer and other reviewers, providing detailed explanations and additional experimental results. They emphasize the distinction between post-training quantization (PTQ) and zero-shot quantization (ZSQ) methods, highlighting the different optimization goals and resulting incompatibility in sample synthesis. The authors compare their approach with MixMix, Genie, and KW, discussing how the unique nature of their proposed method affects these comparisons. They provide results on various models and quantizers to demonstrate their method's performance. The reviewer acknowledges the authors' efforts in addressing concerns and understanding the distinction between PTQ and ZSQ. While maintaining their concerns about outdated quantizers, the reviewer raises their rating and recognizes the progress and importance of the proposed texture feature calibration approach. In the later stages, the reviewer is willing to increase the score to borderline accept but reiterates their earlier concerns about using outdated quantizers for ZSQ.

Reviewer yCFw acknowledges the paper's strong motivation and clear presentation. The introduction of texture features in ZSQ is highlighted as a significant contribution, along with the effective demonstration of the proposed method through experiments. The reviewer raises concerns about the cost of generating both calibration and synthetic samples, prompting the authors to provide insights into the time and computational requirements. The reviewer also suggests comparing the proposed mixup knowledge distillation module with other methods like superposed latent embeddings from Qimera (which was also requested in Reviewer zKQV's questions). In response, the authors differentiate the applications of these techniques and provide a thorough comparison of their proposed method with superposed latent embeddings, Mixup, and Mixcut, addressing label accuracy and performance. The reviewer also inquires about the effectiveness of using only calibration samples compared to synthetic samples. In their rebuttal, the authors provide an insightful analysis, explaining that calibration samples offer greater accuracy due to shorter information transfer links and more obvious class information. This explanation clarifies the observed performance difference between the two types of samples. Finally, the reviewer appreciates the authors' responses, and after receiving clarifications, raises their rating.

Reviewer F97y raises several concerns, including the need for improved clarity in introducing the concept of "LAWS texture feature energy." In their rebuttal, the authors agree to provide more background and visualization to clarify the concept. They also address the reviewer's query about the significance of these texture features and their importance in retaining texture information. The authors provide additional explanations and promise to enhance the discussion around this aspect. The reviewer suggests that the paper could benefit from conducting an ablation study or sensitivity analysis on the weighting coefficients used to balance different loss functions. In response, the authors acknowledge the suggestion and explain their empirical parameter settings. They also justify their focus on verifying the texture feature distribution calibration method and its compatibility with similar studies. Regarding the terminology "data-free quantization (DFQ)" vs. "zero-shot quantization (ZSQ)," the authors confirm their equivalence and agree to clarify these terms in the paper's related work section. In the follow-up comments, the reviewer acknowledges that some concerns have been well-addressed, particularly the clarification of terminology and the inclusion of insights on transferring the method to other modalities. They also raise specific points related to visualization and parameter analysis. The authors respond by providing visualization material for the LAWS texture features and demonstrating the influence of trade-off parameters through sensitivity analysis (Though ACs are not certain that sharing the material with the official comment to ACs channel is the right way to do this). Overall, the reviewer finds that some of their concerns have been effectively addressed and acknowledges the authors' responses. 

Reviewer qhGS suggests considering more widely used architectures, such as ResNet-50, in experiments, and expanding validation to other tasks like object detection on datasets like COCO. Additionally, the reviewer raises questions regarding the generalization of the proposed method and its applicability to Transformer structures. In the authors' rebuttal, they include ResNet-50 in the revised version, showcasing competitive results. Regarding the Transformer structure, they indicate plans for introducing quantization for it in future work. The reviewer increases their score to 7, expressing support for accepting the paper.

Finally, reviewer h8LC points out specific confusing statements, inconsistencies, and unclear explanations in the text. They also raise questions about the role of the calibration center in synthetic sample generation and the need for synthetic samples when a calibration set is available. Additionally, they inquire about the distribution of texture elements in synthetic images and the fairness of comparison between synthetic data from the generator and direct optimization. In their rebuttal, the authors address each point raised by the reviewer and provide explanations and revisions to enhance the paper's clarity. In the final comment, reviewer expresses willingness to raise their rating.

In general, the authors' rebuttal was effective in persuading the reviewers to support acceptance. The ACs align with the reviewers' assessments and recommend acceptance.
Decision: Accept (poster)