Understanding the Generalization of Blind Image Quality Assessment: A Theoretical Perspective on Multi-level Quality Features

Thank you for your affirmation and the valuable comments that help us improve our work. The following is a careful response and explanation about the weaknesses and questions. And we have submitted an updated PDF version of our improved paper.

For Weakness 1

Thank you for your thoughtful reminder. Although we have provided explanations for $b$, $M$, $\delta$, and $L_\phi$ in Lines 254, 248, 249, 231, 232, 259, respectively in the original pdf version, it may not be clear enough. We have made improvements in Lines 230-261 in the updated PDF version. To further enhance the clarity of our paper, we have explicitly defined these symbols in the text preceding the equations. Additionally, we have conducted a thorough review of the paper's notation to ensure that every symbol is clearly explained, thereby improving the overall readability and clarity of the manuscript.

For the meaning of $b$, $M$, $\delta$, and $L \phi$, specifically:

• $b$ is a constant independent of the other variables in Eq. (7), derived from the proof of Theorem 1.
• $M$ represents the maximum value of the input image pixels.
• $L_\phi$ is the Lipschitz constant of the activation function.
• $\delta$ is a variable from Probability Theory that characterizes the degree of uniformity for the inequality in Eq. (8).

For Weakness 2

This is a misunderstanding. In fact, according to [1], the generalization bound is upper-bounded by the Rademacher complexities (RA term) and quantifies the difference between the expected loss and the empirical loss.

In other words, the generalization bound refers to the gap between the test error and the training error, expressed as $err_P(f) - err_S(f)$, as shown below:

$\operatorname{err}_P(f)- \operatorname{err}_S(f)\leq \mathcal{O} \left(\frac{\left(p L _\phi A\right)^{L}}{n^{\frac{1}{2}}} \right)+c \sqrt{\frac{\log (1 / \delta)}{2 n}}$

Therefore, there is no issue of an indeterminate generalization bound caused by an increase in the RA term with larger L, while the $err_S(f)$ term decreases. Thus, Conclusion (1) in Theorem 1 holds true: With an increasing depth L, the upper bound of the RA term will increase, leading to a looser generalization bound. This indicates that relying solely on high-level quality perception features can negatively impact the generalization ability of BIQA models.

In the updated PDF version, we have further emphasized this point in Lines 229 and 258 Section 4, clarifying that the generalization bound refers to $err_P(f) - err_S(f)$, not generalization bound refers to $err_P(f)-err_S(f)$, not $err_P(f)$. This reduces potential misunderstandings and further enhances the clarity of our paper.

For Weakness 3 and Question 1

Thank you for your valuable advice. In fact, as stated in Lines 318–321, based on the theoretical results and Conclusion (3) in Theorem 2, we have concluded that the generalization bound is linearly and positively correlated with the Lipschitz constant of the BIQA loss function. This suggests that the choice of loss function significantly impacts the generalization capability of the BIQA model, offering new insights into the success of existing methods like NIMA and Norm-in-Norm, as mentioned in Lines 409–411 in the original pdf version.

However, calculating the Lipschitz constant for the loss functions used in NIMA and Norm-in-Norm is quite complex, which requires more time for in-depth exploration. This paper primarily focuses on theoretically exploring the impact of multi-level quality features on the generalization bound of BIQA models, while a comprehensive theoretical analysis of how different loss functions influence the generalization bound is another valuable topic for further investigation but is secondary to the primary scope of this work.

We will continue to investigate this valuable issue raised by the reviewer regarding the theoretical impact of the loss functions used in NIMA and Norm-in-Norm, then we will explore this valuable topic about the theoretical influence of loss function on BIQA generalization more thoroughly in future researches and works.

For Weakness 4

Thank you for your valuable advice. Although the network settings and loss functions may not be IQA-specific, the theoretical analysis and contributions in this paper have fully considered the task characteristics of the IQA domain. This is one of the core differences of this paper, distinguishing it from existing theoretical research, and it mainly includes the following two aspects:

• Focus on Regression Tasks in IQA: As stated in Lines 158–161 in the original pdf version, most existing theoretical studies on deep neural networks focus on fully connected networks. Although some recent works have explored the generalization of CNNs, they are primarily applicable to classification tasks rather than regression tasks. However, the IQA task studied in this paper is a classic regression problem, making prior theoretical results for classification tasks unsuitable for IQA.

• Consideration of IQA-Specific Characteristics: As discussed in Section 6 and noted in Lines 64–67 and Lines 15–19 in the original pdf version, this paper thoroughly considers the unique characteristics of IQA tasks: (1) quality perception information predominantly resides in low-level image features, and (2) effective representation learning of multi-level image features and distortion information is critical for the generalization of Blind IQA (BIQA) methods. In contrast, existing theoretical studies on general deep neural networks often overlook the role of low-level image features.

To illustrate this more intuitively, we conducted an experiment on another regression task, i.e. on the UTK-Face dataset [2], where the task is to predict age from input facial images. Using ResNet-50 as the backbone, 80% of the data was used for training, and 20% for testing. The experimental setup followed Table 3, and the recorded MAE （Mean Absolute Error） results for $B$, $B+S_1$, $B+S_1+S_2$,$B+S_1+S_2+S_3$ as follows:

It can be observed that the three suggestions proposed in this paper perform poorly in the age prediction task, as this task primarily relies on high-level features. This indirectly confirms that the contributions of this paper are more relevant to IQA tasks, which differ significantly from other tasks. We have further emphasized this distinction in the discussion of Related Work in Section 2.2 (Generalization Bound in Deep Learning). We have also added the corresponding discussion and analysis in the Appendix H in Lines 1246-1280 in the updated PDF version.

[1] Kakade S M, Sridharan K, Tewari A. On the complexity of linear prediction: Risk bounds, margin bounds, and regularization[J]. Advances in neural information processing systems, 2008, 21.

[2] Zhang Z, Song Y, Qi H. Age progression/regression by conditional adversarial autoencoder[C]//Proceedings of the IEEE conference on computer vision and pattern recognition. 2017: 5810-5818.

For Weakness 4

Thank you for your reminder. We thoroughly reviewed the notation and proof process throughout our paper. In Lines 896-976 in the updated PDF version, we have corrected a few typographical errors and provided additional, more detailed steps in the proof of Theorem 2 to enhance the clarity and readability of the theoretical analysis.

For (1) and (2), we have provided more detailed derivations in the main text to help readers better understand how Equation (45) (in the original PDF version) is derived and how Equation (46) (in the original PDF version) is obtained by substituting Equations (44) and (45) (in the original PDF version) into Lemma 2.

Specifically, based on the front part of the proof for Theorem 2, from Eq. (39), we can derive:

$\frac{1}{\lambda}\log\\{2^L \mathbb{E} \exp \lambda Z\\} \leq M(\sqrt{2 \log (2) L}+1) \sqrt{\sum _{i=1}^{n} \eta _i^2 \left\|\|x _i\right\|\|^2}$

According to [1], the chi-squre divergence between training and test distribution $D\left(P_{\text{test}} \|\| P_{\text{train}}\right)$ can be computed by $D\left(P_{\text{test}} \|\| P_{\text{train}}\right)=\int \frac{P_{\text{test}}^2\left(x_j\right)}{P_{\text{train}}\left(x_j\right)}-1$. Note that $\eta_i = P_{\text{test}}(x_i) / P_{\text{train}}(x_i)$ defined in Lemma 3, we have:

$\frac{1}{n} \sum _{i=1}^{n} \eta _i^2 \left\|\|x _i\right\|\|^2$

$= \frac{1}{n} \sum _{i=1}^{n} \frac{P _{\text{test}}^2(x_i)}{P _{\text{train}}^2(x _i)} \left\|\|x _i\right\|\|^2$

$\approx \lim _{n \rightarrow +\infty} \frac{1}{n} \sum _{i=1}^{n} \frac{P _{\text{test}}^2(x_i)}{P _{\text{train}}^2(x _i)} \left\|\|x _i\right\|\|^2$

$= \mathbf{E} _{x _j \sim P _{\text{train}}}\left[\frac{P _{\text{test}}^2\left(x _j\right)}{P _{\text{train}}^2\left(x _j\right)}\left\|\|x _j\right\|\|^2\right].$

Therefore, by the Law of Large Number [2], we can obtain:

$\frac{1}{n} \sum_{i=1}^{n} \eta_i^2 \left\|\|x_i\right\|\|^2 \leq D\left(P_{\text {test}} \|\| P_{\text {train}}\right)+1+o\left(\frac{1}{\sqrt{n}}\right).$

Then, through substituting Eq. (49) into Eq. (47) and Eq. (38), we can obtain $R_{n, \boldsymbol{\eta}}\left(\mathcal{F}_A^L\right)$ for BIQA model as follows:

$R _{n, \boldsymbol{\eta}}\left(\mathcal{F} _A^L\right) \leq \frac{1}{n} \frac{1}{\lambda} \log \\{ 2^L \mathbb{E} \exp (\lambda Z) \\}$

$\leq \frac{1}{\sqrt{n}} M(\sqrt{2 \log (2) L}+1) \sqrt{\sum _{i=1}^{n} \eta _i^2 \left\|\|x _i\right\|\|^2}$

$= M(\sqrt{2 \log (2) L}+1) \sqrt{\frac{1}{n}\sum _{i=1}^{n} \eta_i^2 \left\|\|x _i\right\|\|^2}$

$\leq M(\sqrt{2 \log (2) L}+1) \sqrt{D\left(P _{\text {test}} \|\| P _{\text {train}}\right)+1+o\left(\frac{1}{\sqrt{n}}\right)}$

$\leq \mathcal{O}\left( \sqrt{L} M \cdot \sqrt{D\left(P _{\text{test}} \|\| P _{\text{train}}\right)+1}\right)M(\sqrt{2 \log (2) L}+1)$

Finally, we can substitute $R_{n, \boldsymbol{\eta}}\left(\mathcal{F}_A^L\right)$ into Lemma 2 and obtain the result in Theorem 2 as follows:

$\operatorname{err}_P(f) \leq \operatorname{err}_S(f) +\mathcal{O}\left(\frac{L _{\ell} \sqrt{L} M \cdot \sqrt{D\left(P _{\text{test}} \|\| P _{\text{train}}\right)+1}}{\sqrt{n}}\right) + c\sqrt{\frac{\log (1 / \delta)}{2n}}$

For (3), thank you for pointing this out. Yes, the definition of $Z$ was missing $\epsilon_i$ in the original PDF version. We have now corrected it to $Z = M \left\|\|\sum_{i=1}^n \epsilon_i \eta x_i\right\|\|$

[1] Bell R P, Everett D H, Longuet-Higgins H C. Kinetics of the base-catalysed bromination of diethyl malonate[J]. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1946, 186(1007): 443-453.

[2] Durrett R, Durrett R. Probability: theory and examples[M]. Cambridge university press, 2019.

Thank you for the valuable comments that help us improve our work. The following is a careful response and explanation about the weaknesses. And we have submitted an updated PDF version of our improved paper.

For Weakness 1

Thank you for your valuable feedback. Although the theoretical analysis in this paper builds, to some extent, on previous theoretical research, we would like to clarify that our approach is distinct from existing theoretical frameworks, offering new insights and methods for IQA framework design.

On the one hand, the core differences, adaptations, and contributions of this paper compared to existing theoretical research are as follows:

• Focus on Regression Tasks: As stated in Lines 158-161 in the original pdf version, most existing theoretical studies on general deep neural networks concentrate on fully connected networks. While some works have explored the generalization of CNNs, these are primarily applicable to classification tasks, not regression tasks. However, IQA is a classic regression problem, and prior results on classification tasks are not directly applicable.
• Consideration of IQA-Specific Characteristics: As discussed in Section 6 and mentioned in Lines 64-67 and Lines 15-19 in the original pdf version, our analysis explicitly considers the unique aspects of IQA tasks, namely: (1) Quality perception information predominantly resides in low-level image features. (2) Effective representation learning for multi-level image features and distortion information is critical to the generalization of Blind IQA (BIQA) methods. In contrast, existing theoretical research on deep neural networks often neglects the importance of low-level image features.

On the other hand, our theoretical results present new insights and methods for IQA tasks. The contributions of this paper to practical BIQA model design and related research are comprehensively discussed in Lines 093-101 and Section 6 in the original pdf version. Key contributions include:

• Revealing the Conflict Between Representation and Generalization in BIQA Models: We demonstrate that generalization ability tends to decrease while representation power increases as the level of image features rises. Consequently, as the level of quality perception features increases, the test error of BIQA networks may first decrease and then increase. This observation is validated in Figure 1 (c-d) in the Section 7 experiments.
• Theoretical Explanation for Existing IQA Models: As outlined in Section 6.2, we provide theoretical explanations for the success of existing representative DL-based IQA models (e.g., CONTRIQUE, LIQA, MUSIQ, Hyper-IQA, Stair-IQA, NIMA, Norm-in-Norm). These insights are valuable for BIQA algorithm design. Notably, this is the first work to summarize these experiences from a theoretical perspective, laying a foundation for future BIQA algorithm development.
• Providing Exemplary Suggestions Related to Proposed Theorems: As discussed in Section 6.3, our proposed theorems not only support existing works but also offer actionable insights for further exploration. The three proposed suggestions are typical examples. Extensive experiments validate the effectiveness and generality of these suggestions, demonstrating the correctness of the proposed theorems and their practical value for BIQA model design.

To our best knowledge, this paper is the first theoretical analysis in the IQA field, and we believe it can mark a solid starting point from the theoretical perspective. In our future works, we will conduct deeper investigations into the generalization theory of more complex IQA models and provide even more valuable theoretical insights.

For Weakness 2

Yes, the conclusions drawn from the theoretical analysis in this paper effectively explain the role of multi-level feature fusion within a single network. In fact, as stated in Lines 176-177 in original PDF version, the BIQA networks examined in this paper consist of $L-1$ hidden layers for quality perception feature extraction and an output layer for MOS prediction. In other words, the depth of BIQA networks determines the level of image quality perception features. Therefore, our investigation and theoretical analysis for the role of multi-level image features are based on the depth of the quality feature extractor. This approach enhances the rigor of the theoretical derivation, as the depth of BIQA networks can be explicitly represented.

Based on the revised paper and the authors' response, I have decided to lower my rating for the following reasons:

1. There are quite a few existing works (e.g. [1], [2]) studying generalization error bounds for regression tasks, which contradicts the authors' claimed core contribution and their stated key differences from existing work. Furthermore, these relevant works have not been reviewed in the related work.
2. The authors' contribution to the theoretical derivations is limited, and the reliability of Theorem 2 is questionable:
   1. Eq. 7 in Theorem 1 of this paper originates from Theorem 2 in [3] (which is not properly cited). Theorem 1 merely substitutes the upper bound of Rademacher complexity derived in [3] into Lemma 2 (the generalization error bound based on Rademacher complexity from [4]), with authors arbitrarily setting VC dimension d=3HW without further explanation.
   2. The proof of Theorem 2 raises reliability concerns. On page 18, lines 944-947 (and similarly in "Comment: For Weakness 4"), the authors state: "According to (Bell et al., 1946), the chi-square divergence between training and test distribution D(Ptest||Ptrain) can be computed by..." Notably, [5] (Bell et al. 1946) is a chemistry-related paper, and it is implausible that it could be used to derive the chi-square divergence.
   3. Theorem 3 is almost identical to Theorem 3 in [3]. The only difference lies in the derivation process where the original uses "According to (Zell 1999), since Si is defined by K-1 sign conditions (inequalities or equalities) on Pfaffian functions," while this paper states "According to (Zell, 1999) and Definition 4, since Si is defined by 2 sign conditions (inequalities or equalities) on Pfaffian functions."
3. The authors attempt to confuse the concepts of model depth (fundamentally a matter of model complexity) and hierarchical features to support their arguments. These theorems essentially describe the bias-variance trade-off, which aligns with their observed phenomena: models with fewer layers have lower complexity and thus underfit the training data, while models with excessive layers lead to overfitting, performing well on training data but poorly on test data. However, this is clearly insufficient to directly justify that a large network using hierarchical features has characteristics of both large and small networks when training, as it fundamentally remains a large network. Therefore, the presented theory fails to provide a rigorous demonstration for the effectiveness of hierarchical features.
4. This paper makes no methodological contributions, and its guidance merely reflects consensus in the field.

[1] Jakubovitz D, Giryes R, Rodrigues M R D. Generalization error in deep learning[C]//Compressed Sensing and Its Applications: Third International MATHEON Conference 2017. Springer International Publishing, 2019: 153-193.

[2] Amjad J, Lyu Z, Rodrigues M R D. Regression with deep neural networks: generalization error guarantees, learning algorithms, and regularizers[C]//2021 29th European Signal Processing Conference (EUSIPCO). IEEE, 2021: 1481-1485.

[3] Sun S, Chen W, Wang L, et al. On the depth of deep neural networks: A theoretical view[C]//Proceedings of the AAAI Conference on Artificial Intelligence. 2016, 30(1).

[4] Bartlett P L, Mendelson S. Rademacher and Gaussian complexities: Risk bounds and structural results[J]. Journal of Machine Learning Research, 2002, 3(Nov): 463-482.

[5] Bell R P, Everett D H, Longuet-Higgins H C. Kinetics of the base-catalysed bromination of diethyl malonate[J]. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1946, 186(1007): 443-453.

For the new Concern 2

Thank you for your reminder. We first provide an overall response, and then offer detailed replies to each specific point individually.

For the overall response: we acknowledge that our Theorems 1 and 3 are indeed inspired by existing research (as cited in our paper as Sun et al., 2016 in Lines 176 and 337). However, there are significant differences between our work and the issues and objectives explored in the cited papers. Sun et al. (2016) focused on classification tasks, while our work is dedicated to exploring the generalization of Image Quality Assessment (IQA) tasks and the theoretical interpretation of existing IQA model design principles. To achieve more precise citations, we have provided a more detailed citation of related works in the updated PDF version in anonymous link in Lines 247 and 873, especially in front of Theorem 1. Furthermore, Theorem 2 in our paper is entirely the result of our independent innovation, which is reasonable and rigorous. It not only reduces the exponential dependence of the generalization bound on $L$ in Theorem 1 to a linear dependence, but also effectively proposes a generalization bound related to the distribution difference between the training set and the test set. In our view, Theorem 2 makes an important contribution to the theoretical derivations and results.

For the point-by-point replies, for point (1), in our paper, prior to deriving the theoretical result Eq. 7 in Theorem 1, we first defined a CNN architecture tailored for the IQA task (as outlined in Eqs. 2-5). This differs from the architectures presented in the cited (Sun et al., 2016), resulting in differences in the theoretical conclusions regarding the Rademacher complexity compared to the cited work. Ultimately, based on the Rademacher complexity stated in Eq. 7 in our paper, we derived the generalization bound for the IQA task.

Additionally, our proposed explanation for setting the VC dimension d=3HW in the generalization bound is provided in Lines 194-196 and Eq. 5, where $x$ represents the input image and 3×H×W denotes the dimensions of the input image.

Moreover, we have given more meticulous consideration to the characteristics of regression networks in the field of Image Quality Assessment (IQA) by applying second-order pooling to quality feature extraction (as stated in the updated PDF version in anonymous link in Lines 877-881). This approach is recognized as an effective means of enhancing the performance of IQA models. Although we drew inspiration from the ideas presented in (Sun et al., 2016), the specifics of our proof differ from theirs.

In addition, the derivation of the Theorem 2 in (Sun et al., 2016) only considers a part of the classification network. And if the entire classification network is considered, Eq. 13 in (Sun et al., 2016) does not hold. By contrast, there is no such limitation in Theorem 1 designed for BIQA regression model in our paper (as stated in the updated PDF version in anonymous link in Lines 873-876). Therefore, overall, although we are inspired by the proof framework from (Sun et al., 2016), our focus is on the IQA task. The investigated problems and the defined networks in our paper differ from those in (Sun et al., 2016), leading to distinct proof details. Furthermore, our proof is more rigorous, as it fully considers the structure of the regression network for IQA. Based on our theoretical results and analysis, we ultimately draw conclusions regarding the theoretical impact of low-level features on the performance of IQA models. To further highlight the differences from the proof conclusions presented in (Sun et al., 2016), we have refined the proof of Theorem 1 in the updated PDF version in anonymous link in Lines 857-965, emphasizing the distinctions from other works and providing more specific theoretical results and explanations.

For point (2), thank you for your reminder. We did not misquote, but it was indeed our oversight that led to a citation that is not precise enough. Specifically, the cited (Bell et al. 1946) are titled as "Kinetics of the base-catalysed bromination of diethyl malonate" is actually a journal book, and our intention was to cite the article at https://royalsocietypublishing.org/doi/epdf/10.1098/rspa.1946.0056, which is purely mathematical in nature and provides the definition of the chi-square divergence in Eq. 26. This paper is one part of "Kinetics of the base-catalysed bromination of diethyl malonate" and titled as "An invariant form for the prior probability inestimation problems". We have made the necessary correction in the updated PDF version in anonymous link in Line 1049. Therefore, the proof of our Theorem 2 is rigorous and reliable.

Thank you for your meticulous review and patient communication with us. Regarding the current concerns that still persist, we have provided an updated PDF version. So sorry, due to time constraints, we can only upload the new updated PDF version in the anonymous link：https://anonymous.4open.science/r/tmp-pdf-A6FE/2025_ICLR_IQA_update_2%20(1).pdf, and we will make more detailed and comprehensive updates in the camera-ready version subsequently.

For the new Concern 1

This was an oversight on our part, and we have added the two articles on studying generalization error bounds for regression tasks to the related work section of our paper in the new updated PDF version in anonymous link in Lines 157-161. However, we would like to clarify that the core contribution of this paper and its key differences from existing work do not lie in the global generalization error bounds for regression tasks. As stated in Lines 159-161, we innovatively introduce a generalization bound specifically for regression networks in Image Quality Assessment (IQA) tasks. Our theoretical analysis fully takes into account the unique characteristics of IQA tasks, thereby effectively bridging the theoretical gap in the field of IQA. The unique characteristics of IQA tasks include: (1) the scale of training datasets is small due to high annotation costs; and (2) quality-aware features are closely related to low-level features, making IQA a low-level task. Therefore, the focus of this paper is on the role of high-level and low-level features in IQA networks, studying the generalization of IQA tasks, and providing a theoretical explanation for the design principles of existing IQA models.

Thank you for your affirmation and the valuable comments that help us improve our work. The following is a careful response and explanation about the weaknesses and questions. And we have submitted an updated PDF version of our improved paper.

For Weakness 1 and Question 1

The contributions of this paper to practical BIQA model design and related research are comprehensively discussed in Lines 093–101 and Section 6 in the original pdf version, with the main points summarized as follows:

• Revealing the Conflict Between Strong Representation and Generalization in BIQA Models: Specifically, as the level of image features increases, generalization ability tends to decrease while representation power improves. Consequently, as the level of quality perception features rises, the test error of BIQA networks may first decrease and then increase. This conclusion is demonstrated in Figure 1(c–d) in Section 7 of the Experiments.
• Providing a Theoretical Explanation for Existing IQA Models: As outlined in Section 6.2, the proposed theorems offer a theoretical explanation for the success of representative deep learning-based IQA models, such as CONTRIQUE, LIQA, MUSIQ, Hyper-IQA, Stair-IQA, and NIMA, among others. These insights provide valuable guidance for BIQA algorithm design. Notably, this paper is the first to summarize these findings from a theoretical perspective, laying a solid foundation for future BIQA algorithm development.
• Providing Exemplary Suggestions Based on the Proposed Theorems: As stated in Section 6.3, the proposed theorems not only provide theoretical support for existing works but also offer meaningful insights for further exploration. The three suggestions proposed in this paper serve as typical examples. Through a series of experiments, we validated the effectiveness and generalizability of these suggestions, demonstrating the correctness of the theorems and their practical value in BIQA model design.

In the updated PDF version, we further refined the explanation of the summarized contributions (listed in Lines 101–117), explicitly highlighting that our theoretical findings can assist BIQA model design from a feature-level perspective and explain the success of existing methods. This emphasizes the paper's contributions to practical BIQA model design and related research. Additionally, we improved the presentation of Section 6 to better underscore the practical value of the theoretical results for BIQA model development.

For Weakness 2 and Question 2

The core differences and and contributions of this paper, distinguishing it from existing research, lie in the following two aspects:

• Focus on Regression Tasks in IQA: As stated in Lines 158–161 in the original pdf version, most existing theoretical studies on deep neural networks focus on BP neural networks. Although some recent works have explored the generalization of CNNs, they are primarily applicable to classification tasks rather than regression tasks. However, the IQA task studied in this paper is a classic regression problem, making prior theoretical results for classification tasks unsuitable for IQA.

• Consideration of IQA-Specific Characteristics: As discussed in Section 6 and noted in Lines 64–67 and Lines 15–19 in the original pdf version, this paper thoroughly considers the unique characteristics of IQA tasks: (1) quality perception information predominantly resides in low-level image features, and (2) effective representation learning of multi-level image features and distortion information is critical for the generalization of Blind IQA (BIQA) methods. In contrast, existing theoretical studies on general deep neural networks often overlook the role of low-level image features.

To illustrate this more intuitively, we conducted an experiment on the UTK-Face dataset [1], where the task is to predict age from input facial images. Using ResNet-50 as the backbone, 80% of the data was used for training, and 20% for testing. The experimental setup followed Table 3, and the recorded MAE results for $B$, $B+S_1$, $B+S_1+S_2$,$B+S_1+S_2+S_3$ as follows:

It can be observed that the three suggestions proposed in this paper perform poorly in the age prediction task, as this task primarily relies on high-level features. This indirectly confirms that the contributions of this paper are more relevant to IQA tasks, which differ significantly from other tasks. We have further emphasized this distinction in the discussion of Related Work in Section 2.2 (Generalization Bound in Deep Learning) in the updated PDF version.

Thank you for acknowledging our work. Since StairIQA has publicly available code, we conducted experiments on StairIQA model using KADID10k, CLIVE and CID2013 datasets, training on KADID10k and testing on CLIVE and CID2013 respectively. We recorded the results for $B$, $B+S_2$, and $B+S_2+S_3$ with the same experimental settings as Table 4.

For the KADID-10k (train)/CLIVE (test) setup, the experimental results are as follows:

For the KADID-10k (train)/CID2013 (test) setup, the experimental results are as follows:

In our aforementioned experiments, the reason why we did not adopt the $B+S_1$ strategy is that StairIQA has already incorporated $S_1$, i.e., it has already implemented a multi-level feature fusion approach. As can be seen from the tables above, $B+S_2$ and $B+S_2+S_3$ perform better than $B$, which validates the effectiveness of the suggestions proposed in this paper and the correctness of our theoretical results.

Furthermore, according to our research, the RichIQA work has not been published yet and there is no publicly available code, so it is unrealistic to reproduce it and conduct experiments in a short period of time. Therefore, we will try our best to include the reproduced RichIQA results in the camera-ready submission.

Lastly, given that the reviewer believes that most of the concerns have been addressed, we kindly request the reviewer to consider further increasing the score if possible.

Thank you for the valuable comments that help us improve our work. The following is a careful response and explanation about the weaknesses and questions. And we have submitted an updated PDF version of our improved paper.

Responses to Weaknesses

For Weakness 1

Thank you for your valuable reminder.

Regarding the first point. We have added experimental results for $\mu=0$ and $v=0$ to Tables 1 and 2, respectively, in the updated PDF version of the paper. The experimental settings remain consistent with those of Table 1 (with fixed $v=0.01$) and Table 2 (with fixed $\mu=10$).

The current Table 1 has been updated to:

The current Table 2 has been updated to:

From the updated Tables 1 and 2, it can be observed that setting $\mu=0$ or $v=0$ generally reduces the model's performance. This provides evidence, to some extent, of the effectiveness of the Consistency Regularizer and Parameter Regularizer in Eq. (15).

In fact, $\mu=0$ and $v=0$ correspond to not adopting Suggestion (2) and Suggestion (3), respectively. The experimental effects of these suggestions have already been thoroughly discussed in Tables 3 and 4. Specifically:

• When $\mu=0$, it implies not using the Consistency Regularizer (the second term in Eq. (15)) in the loss function, which corresponds to not adopting Suggestion (2) during training.
• When $v=0$, it implies not using the Parameter Regularizer (the third term in Eq. (15)) in the loss function, which corresponds to not adopting Suggestion (3) during training.

Regarding the second point. We use the KADID-10k (train)/CID2013 (test) database pair for cross-dataset experiments because CID2013 is one of the representative authentically distorted datasets, while KADID-10k is one of the representative synthetically distorted datasets. This setup effectively evaluates the generalization ability of BIQA methods.

Additionally, to further validate the experiments comprehensively, we also use the KADID-10k (train)/CLIVE (test) and KADID-10k (train)/KonIQ-10k (test) database pairs for cross-dataset experiments, following the same experimental settings as in Table 4.

For the KADID-10k (train)/CLIVE (test) setup, the experimental results are as follows:

For the KADID-10k (train)/KonIQ-10k (test) setup, the experimental results are as follows:

From the above results, it can be seen that, overall, the three exemplary suggestions proposed in this paper are effective. This is consistent with the conclusions drawn from Table 4, demonstrating the practical value of the theorems proposed in this paper.