GAQAT: Gradient-Adaptive Quantization-Aware Training for Domain Generalization

W1

In the main text, Figure 3 should be referred before Figure 4.

Thank you for your suggestion, it has been updated in the latest version.

W2

The gradient disorder is measured with two sequences according to Equation 4. However, in Line 254, the author says 'the gradient disorder of the g_{task} decreases significantly as training progresses.' How do measure the gradient disorder of the g_{task} alone?

Gradient disorder measures the inconsistency in directions between adjacent gradients within the same gradient sequence (applicable to any gradient sequence, see lines 211-235). In our experiments, it is computed every KK steps (see lines 294-295). For example, given $K=3 \ G={−1,2,3,−4} S_1 = \{-1, 2, 3\}, \quad S_2 = \{2, 3, -4\},\text{sgn}(S_1) = \{-1, 1, 1\}, \quad \text{sgn}(S_2) = \{1, 1, -1\},\text{sgn}(S_1) \neq \text{sgn}(S_2) = 2.Thus, the gradient disorder is:\delta = \frac{1}{3} \cdot 2 = \frac{2}{3}.$

W3

Line 259 - 263. Why lower layers with lower gradient disorder are more likely to exhibit the phenomenon of two gradients in suboptimal equilibrium state? How the Figure 2 and Figure 4 prove this? What is the suboptimal equilibrium state?

Gradients with similar magnitudes but opposite directions define what we term as the "opposite equilibrium state." We have clarified this in the latest version and reordered the figures for better comprehension. Specifically, layers with lower gradient disorder (illustrated in the bottom-right images of Figure 3) show this phenomenon clearly in Figure 2.

W4

Line 259 - 263. Why lower layers with lower gradient disorder are more likely to exhibit the phenomenon of two gradients in suboptimal equilibrium state? How the Figure 2 and Figure 4 prove this? What is the suboptimal equilibrium state?

It demonstrates that sub-optimal equilibrium state leads to suboptimal convergence in other layers, causing abnormal gradients. To address this, we froze layers with task gradient disorder below a certain threshold. Figure 4 shows this reduced abnormal gradients in the unfrozen layers, while the gradients in the frozen layers fluctuated and were further refined through continued training.

W5

Line 297, 'Continuously freezing the g_{task} without unfreezing'? How can you freeze g_{task} while unfreezing it?

"Unfreezing" refers to the process where previously frozen layers are re-activated under certain conditions, allowing g_task to rejoin training. "Not unfreezing" means the frozen layers remain inactive, with g_task excluded from training once frozen.

E1

Why only 4/4 and 3/3 bit-width?

For 5-bit and 8-bit quantization, we observed similar gradient conflict phenomena. Results on the cartoon domain show improvements even without fine-tuned hyperparameter search: 5-bit accuracy increased from 76.05%/54.64% to 80.59%/59.22%, and 8-bit from 77.42%/56.34% to 80.74%/56.45%. Due to time and resource constraints, we will provide complete results with more refined hyperparameter search in the final version. The newly added Figure 6 visualizes the loss curves for the four PACS domains under 4-bit quantization. As shown, the proposed method achieves significantly smoother surfaces, further confirming its effectiveness.

Additionally, a classic study on freezing also explored 3-bit and 4-bit quantization settings [1]

[1] Nagel M, Fournarakis M, Bondarenko Y, et al. Overcoming oscillations in quantization-aware training[C]//International Conference on Machine Learning. PMLR, 2022: 16318-16330.

E2

Maybe the author should add some experiments that quantized the trained model with PTQ methods.

QAT has shown strong performance in non-large-scale models, which is why we focused on it. We believe that PTQ is a promising future direction, and PTQ could be explored in future work, though it is not the focus of this paper.

E3

Does the quantized model is initialized from the pre-trained full-precision model?

Our experiments are based on a model pre-trained on the DG source domain dataset (lines 309-315). Specifically, we used the MoCoV2-pretrained ResNet50, as proposed in [1] , and fine-tuned it using ERM on the source domain data from the DG dataset. This approach aligns with current standard DG practices, where a pretrained model is fine-tuned on a DG dataset for better performance, as outlined in previous works like [1] [2] [3]. Based on this well-performing full-precision DG model, we proceeded with quantization.

[1] Yu, Han, et al. "Rethinking the evaluation protocol of domain generalization." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024.

[2] Gulrajani, Ishaan, and David Lopez-Paz. "In search of lost domain generalization." arXiv preprint arXiv:2007.01434 (2020).

[3] Cha, Junbum, et al. "Swad: Domain generalization by seeking flat minima." Advances in Neural Information Processing Systems 34 (2021): 22405-22418.

W1

I think that the paper require a better examination of the domain generalization under different quantization datatypes, group sizes, gradient approximation before it get can a general conclusion and try to solve it.. I think it is a must to be at a level expected from an ICLR paper. Showing results only for INT quantization with learnable scale is not enough in my opinion.

Our setup is based on the latest and most commonly used configurations in the relevant fields. For example, in terms of the model, we use ResNet50, which is widely adopted in both DG and QAT research. The initialization of the model follows the methods recommended in recent papers. For the QAT method, we choose LSQ, which is commonly used in QAT. The quantization data type is selected as INT, which is hardware-friendly and widely used. We choose tensor-wise quantization granularity to balance precision and latency, and use the widely adopted STE scheme for gradient approximation. These are common configurations used in many papers[1-4]. Moreover, our method is orthogonal to most of the basic settings, so we believe our current setup meets general requirements. Additional experimental setups will be explored as future work.

[1] Esser S K, McKinstry J L, Bablani D, et al. Learned step size quantization[J]. arXiv preprint arXiv:1902.08153, 2019.

[2] Lee J, Kim D, Ham B. Network quantization with element-wise gradient scaling. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2021: 6448–6457.

[3] Liu S Y, Liu Z, Cheng K T. Oscillation-free quantization for low-bit vision transformers[C]//International Conference on Machine Learning. PMLR, 2023: 21813-21824.

[4] Tang, Chen, et al. "Retraining-free model quantization via one-shot weight-coupling learning." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024.

Q1

Do you tried to use scaling factor that is not learnable and only is measured. It is a well used methods, not only for INT quantization also for FP quantization. It is interesting if in that cases we still see the gap between both losses - which is the main motivations for the paper.

Using scaling factor that is not learnable is relatively inferior, as discussed in [1] and [2]. Learning the step size allows the quantizer to adapt dynamically to the model’s state transitions, enabling finer-grained optimization. Additionally, balancing step size updates with weight updates ensures better convergence and overall performance [1]. Therefore, we opted for a more general and effective quantization method as the basis for our study.

[1] Esser S K, McKinstry J L, Bablani D, et al. Learned step size quantization[J]. arXiv preprint arXiv:1902.08153, 2019.

[2] Lee J, Kim D, Ham B. Network quantization with element-wise gradient scaling. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2021: 6448–6457.

Q2

Interesting to see how to proposed methods work for other quantization method, such as FP. For example the MXFP4 datatype is a good candidate. Moreover, what about other gradients approximation that are not STE, like PWL or MAD (https://arxiv.org/pdf/2206.06501)

The INT quantization method with STE, broadly adopted in both hardware implementations and research studies [1-5], was chosen for its practicality. Newer formats may face compatibility issues, limiting deployment benefits [6]. Furthermore, our approach is orthogonal to quantization type and granularity.

We believe that exploring additional quantization methods and broader experiments could provide more comprehensive validation. However, our main focus is on identifying the conflicts between QAT and DG and validating our proposed solution, as demonstrated in the paper. Future work will expand these explorations to enhance the generality and performance of our method.

[1] Esser S K, McKinstry J L, Bablani D, et al. Learned step size quantization[J]. arXiv preprint arXiv:1902.08153, 2019.

[2] Lee J, Kim D, Ham B. Network quantization with element-wise gradient scaling. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2021: 6448–6457.

[3] Liu, Shih-Yang, Zechun Liu, and Kwang-Ting Cheng. "Oscillation-free quantization for low-bit vision transformers." International Conference on Machine Learning. PMLR, 2023.

[4] Tang, Chen, et al. "Retraining-free model quantization via one-shot weight-coupling learning." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024.

[5] Wang, Kuan, et al. "Haq: Hardware-aware automated quantization with mixed precision." Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2019.

[6] https://images.nvidia.com/content/Solutions/data-center/a100/pdf/nvidia-a100-datasheet-us-partner-1758950-r4-zhCN.pdf

Q3

I would like to see also experiments in language models.

Since most existing DG methods use ResNet50 as the baseline (e.g., [1], [2], [3]), we align our experiments with this choice to ensure consistency with the state of the art. We recognize that language models are a promising direction for future research, this does not undermine the significance of our work. Language models could be explored in future work, though it is not the focus of this paper.

[1] Huang, Zeyi, et al. "Self-challenging improves cross-domain generalization." Computer vision–ECCV 2020: 16th European conference, Glasgow, UK, August 23–28, 2020, proceedings, part II 16. Springer International Publishing, 2020.

[2] Cha J, Chun S, Lee K, et al. Swad: Domain generalization by seeking flat minima[J]. Advances in Neural Information Processing Systems, 2021, 34: 22405-22418.

[3] Wang P, Zhang Z, Lei Z, et al. Sharpness-aware gradient matching for domain generalization[C]//Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2023: 3769-3778.

Thank you very much for your thorough and insightful review of our paper. We greatly appreciate your time, effort, and the valuable suggestions you have provided.

To the best of our knowledge, no existing quantization work simultaneously addresses a wide range of data types and gradient approximation methods. Most studies primarily focus on integer formats paired with Straight-Through Estimator approximations [1–5]. If the reviewer is aware of works that explore all data types and multiple gradient approximation methods, we would greatly appreciate it if you could point them out.

Additionally, as discussed in the surveys by [13] and [14], the current definition of the out-of-distribution problem, along with the widely used setting with ResNet50 and datasets like PACS and DomainNet, aligns with our framework. Furthermore, the DomainBed benchmark [6], as well as previous and recent works [7–9, 10–12], have not incorporated experiments with language models. Therefore, we believe that requiring experiments with language models is beyond the reasonable scope of our work.

[1] Esser S K, McKinstry J L, Bablani D, et al. Learned step size quantization. arXiv preprint arXiv:1902.08153, 2019.

[2] Lee J, Kim D, Ham B. Network quantization with element-wise gradient scaling. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2021: 6448–6457.

[3] Liu, Shih-Yang, Zechun Liu, and Kwang-Ting Cheng. Oscillation-free quantization for low-bit vision transformers. International Conference on Machine Learning, PMLR, 2023.

[4] Tang, Chen, et al. Retraining-free model quantization via one-shot weight-coupling learning. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2024.

[5] Wang, Kuan, et al. HAQ: Hardware-aware automated quantization with mixed precision. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2019.

[6] In Search of Lost Domain Generalization, Gulrajani et al., ICLR 2021.

[7] Ensemble of Averages: Improving Model Selection and Boosting Performance in Domain Generalization, Arpit et al., NeurIPS 2022.

[8] SWAD: Domain generalization by seeking flat minima, Cha et al., NeurIPS 2021.

[9] Diverse weight averaging for out-of-distribution generalization, Rame et al., NeurIPS 2022.

[10] Cross-contrasting feature perturbation for domain generalization, Li et al., ICCV 2023.

[11] Yu, Han, et al. Rethinking the evaluation protocol of domain generalization. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2024.

[12] Wang P, Zhang Z, Lei Z, et al. Sharpness-aware gradient matching for domain generalization. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2023: 3769–3778.

[13] Zhou, Kaiyang, et al. "Domain generalization: A survey." IEEE Transactions on Pattern Analysis and Machine Intelligence 45.4 (2022): 4396-4415.

[14] Wang, Jindong, et al. "Generalizing to unseen domains: A survey on domain generalization." IEEE Transactions on Knowledge and Data Engineering 35.8 (2022): 8052-8072.

W1

Applicability of Quantization to ResNet-50 in DG Scenarios: I find it challenging to fully appreciate the motivation for applying quantization to ResNet-50 in the context of Domain Generalization, especially with a focus on deployment to resource-constrained devices. ... It appears this choice may stem from the use of benchmarks typically associated with DG research, but for the edge-device assumption, studying alternative, more compact models seems essential.

ResNet50 is widely used in most DG research, as shown in recent studies [1-3]. Moreover ResNet50 is also a common baseline in QAT research, reinforcing its relevance to our study [5-7]. Therefore We chose ResNet50 as the standard baseline model to ensure consistency and comparability with them.

We appreciate your suggestion. However, the primary focus of our study is to address the unique challenges arising from the interplay between QAT and DG and to propose effective solutions to these conflicts. As such, architecture-related exploration can be a direction for future research.

[1] Huang, Zeyi, et al. "Self-challenging improves cross-domain generalization." Computer vision–ECCV 2020: 16th European conference, Glasgow, UK, August 23–28, 2020, proceedings, part II 16. Springer International Publishing, 2020.

[2] Cha J, Chun S, Lee K, et al. Swad: Domain generalization by seeking flat minima[J]. Advances in Neural Information Processing Systems, 2021, 34: 22405-22418.

[3] Wang P, Zhang Z, Lei Z, et al. Sharpness-aware gradient matching for domain generalization[C]//Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2023: 3769-3778.

[5] Esser S K, McKinstry J L, Bablani D, et al. Learned step size quantization[J]. arXiv preprint arXiv:1902.08153, 2019.

[6] Lee J, Kim D, Ham B. Network quantization with element-wise gradient scaling. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2021: 6448–6457.

[7] Liu S Y, Liu Z, Cheng K T. Oscillation-free quantization for low-bit vision transformers[C]//International Conference on Machine Learning. PMLR, 2023: 21813-21824.

W2

This insight may not be limited solely to DG + QAT settings but could have implications in broader contexts. I would be interested in seeing if this theoretical framework extends to general quantization-aware training (QAT) or even Vision Transformers, for instance. This paper could potentially expand its contributions beyond a localized scope, making the findings more universally relevant.

Thanks for your suggestion. Our framework can be extended to a broader range of research areas, which further emphasizes the exploratory nature of our work. This expansion will be pursued in future research.

Our work distinguishes itself by identifying and addressing the conflict between gradient scales in combining QAT and DG, a challenge not explicitly explored before. The newly added Figure 6 visualizes the loss curves for the four PACS domains under 4-bit quantization. As shown, the proposed method achieves significantly smoother surfaces, further confirming its effectiveness. By tackling this issue, we aim to inspire further advancements, including domain-specific methods or the introduction of additional DG objectives, as highlighted in the Conclusion and Future Work, or general quantization-aware training and even Vision Transformers as you say.

Sorry to disturb you during the Thanksgiving holiday.

In order to explain our work more clearly, we would like to summarize the responses over the past few days and outline the reviewers' views on the strengths and weaknesses of our paper. We hope this will help you gain a clearer understanding of our work.

Several reviewers have explicitly pointed out that the contribution of our paper is significant. Currently, the reviewers' recognition of our strengths mainly focuses on: "The combination of DG and QAT is important and has not been fully explored, and our work provides valuable insights from the perspective of gradient conflicts."

Regarding the comments from several reviewers on the insufficiency of the experimental section, we have conducted preliminary 5-bit and 8-bit experiments and added smoothness visualization experiments in the paper to demonstrate the effectiveness of our method. We commit to including the complete results of these experiments in the final version. In addition, we will revise the textual part to make it easier to understand.

Next, let me explain the concerns you raised regarding the experimental setup.

As for the experimental setup, Reviewer 2JwQ questioned whether our QAT experimental setup requires more data types, quantization granularity, and gradient approximation methods. We believe this request is unreasonable, and we have provided evidence to show that the current quantization setup is both general and reasonable, with no objections from other reviewers. Reviewer L5zt questioned whether our training process was correct, but our response, supported by citations from recent papers and experiments, demonstrates that the current training process is fully reasonable and even superior. No other reviewer has questioned the use of ResNet50 as the baseline model, considering it a general baseline model for DG. So, we believe our experimental setup is reasonable, and if you have any questions, feel free to keep in touch.

Regarding your second concern, we believe our method is centered on the DG-SAM perspective, and both our observations and approach are highly relevant to DG. The response to Reviewer zrms further supports this point. While we agree with your suggestion that our approach could be extended to broader domains, we see this as a potential direction for future research. However, this does not diminish the significance of our current work. On the contrary, our research provides valuable insights that can inspire further exploration, as you may have recognized in the ideas with potential for further investigation. This highlights the value of our work.

I hope this explanation helps clarify our work. If any points remain unclear, please don't hesitate to reach out for further discussion. We sincerely hope you will reconsider our paper.

Dear reviewer, As the discussion period nears its end, we kindly hope to receive your feedback today. We have carefully highlighted all revisions in blue and would greatly appreciate your kind consideration before finalizing your recommendation.

We greatly value your input and hope the updates meet your expectations.

W1

Incorporating QAT from scratch is not a good idea. QAT is generally performed on a pretrained model and literature shows that it can improve results significantly. You can significantly improve results if you perform quantization after some iterations.

Our experiments are based on a model pre-trained on the DG source domain dataset (lines 309-315). Specifically, we used the MoCoV2-pretrained ResNet50, as proposed in [1] , and fine-tuned it using ERM on the source domain data from the DG dataset. This approach aligns with current standard DG practices, where a pretrained model is fine-tuned on a DG dataset for better performance, as outlined in previous works like [1] [2] [3]. Based on this well-performing full-precision DG model, we proceeded with quantization. So, our experiments are based on a model pre-trained on the DG source domain dataset, not from scratch.

[1] Yu, Han, et al. "Rethinking the evaluation protocol of domain generalization." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024.

[2] Gulrajani, Ishaan, and David Lopez-Paz. "In search of lost domain generalization." arXiv preprint arXiv:2007.01434 (2020).

[3] Cha, Junbum, et al. "Swad: Domain generalization by seeking flat minima." Advances in Neural Information Processing Systems 34 (2021): 22405-22418.

W2

The approach does not show any significant improvement in comparison to baseline methods. On DomainNet dataset, there is no difference between all three (Yours, LSQ, and LSQ +SAGM). On PACS you have a difference of less than 2% between LSQ and your method and you reported a difference of 4.5% in the abstract.

Our baseline is QAT with the introduction of a smoothness objective. We observed significant conflicts when directly incorporating this objective. We identified and addressed these conflicts, making our baseline LSQ+SAGM. Compared to this, we achieved a 4.5% improvement, validating the effectiveness of our method. Additionally, compared to LSQ, we observe an average 2.4% improvement on PACS and a 1.4% increase on DomainNet at 4-bit. It is important to note that LSQ shows minimal performance loss on IID datasets, even in low-bit settings (3-bit and 4-bit), which further highlights the significant improvement our method offers over baseline methods.

W3

It's a norm in the literature[1,2,3,4,5] to show results on all DomainBed[1] datasets with the mean and standard error over multiple runs. I would recommend authors to add those results as the experiments are currently insufficient.

We observed that our method is relatively robust. Tables 5 and 6 show that the method is not sensitive to step size and threshold within a reasonable range. The 1.4% and 1.1% improvements on DomainNet are reliable. Due to time and resource constraints, we did not conduct multiple rounds of repeated experiments. We will include the mean results from repeated experiments in final version.

Q1：

Why in Table 2 and Table 4, "ours" result for 4 bits are different?

Lines 396-398 indicate that in Table 4, we fixed the freeze steps at 350 and set the threshold at 0.3, which differs from the settings in Table 2.

Q2:

Have you looked at the experiments with higher bit-precision? Does gradient conflict problem exist with higher bit-precision as well e.g 6,7 bit?

For 5-bit and 8-bit quantization, we observed similar gradient conflict phenomena. Results on the cartoon domain show improvements even without fine-tuned hyperparameter search: 5-bit accuracy increased from 76.05%/54.64% to 80.59%/59.22%, and 8-bit from 77.42%/56.34% to 80.74%/56.45%. We will provide complete results with more refined hyperparameter search in the final version.

Q3:

I would recommend to explore the generalization aspect of the QAT as well. I can clearly see that combining QAT with SAGM does not help, especially in the results for 3 and 4 bits on PACS dataset.

We explore QAT generalization from a smoothness perspective, and while other approaches may exist, this does not undermine the significance of our work. Our study offers valuable insights into quantization factors and gradient conflicts, inspiring future research. Reviewers ZRMS, EFHM, and MCAP also found that identifying and resolving this conflict is highly insightful.

Q4:

Having an empirical demonstration of flat minima like SWAD[1] would be good as there is no guarantee that your proposed approach will result in a flatter minima as compared to LSQ+SAGM.

Thank you for your suggestion. The newly added Figure 6 visualizes the loss curves for the four PACS domains under 4-bit quantization. As shown, the proposed method achieves significantly smoother surfaces, further confirming its effectiveness.

Minor recommendation

Please swap the colors in Table 1...

Thank you for your suggestion, it has been updated in the latest version.

We hope that our response have provided clarity and effectively addressed your concerns. We would greatly appreciate it if you could acknowledge this. If there are any remaining questions or unresolved concerns, we would be more than happy to provide further clarification. Thank you sincerely for your time and valuable feedback—it is greatly appreciated.

Dear reviewer, As the discussion period nears its end, we kindly hope to receive your feedback today. We have carefully highlighted all revisions in blue and would greatly appreciate your kind consideration before finalizing your recommendation.

We greatly value your input and hope the updates meet your expectations.

W1

Though objective disalignment (gradient inconsistency) between QAT and main task is observed in DG, the method proposed (Line 296-303) is not coupled with DG: it does not used any properties from DG and it can be applied to other problems that are involved with QAT (such as image classification, LLM with QAT). The inconsistency (method proposed is not coupled with the scene where motivation is discovered) harm the contribution. Author can either improve the method using DG's related parts or prove the method (and observation) is universal in QAT (for example conducting more experiments on other fields).

The conflict between task gradients and smooth gradients is unique under QAT-DG scenario because smooth gradients are associated with DG and task gradients are associated with QAT. Table 1 shows the suboptimal convergence of quantization factors, and Figure 2 visualizes the conflict between the two gradients. Figure 3 highlights that while smooth gradient disorder remains stable, task gradient disorder decreases. We clarify that introducing DG objectives directly into QAT leads to conflicts due to the distinct characteristics of QAT and DG. Identifying these these conflicts and propose solutions based on observations relevant to both QAT and DG, which is one of our contributions.

W2

author should explain how step K and threshold \tao are discovered and prove that these parameters are insensitive.

In our experiments, we empirically set the parameters by observing the trend of task gradient disorder in standard QAT. The step size was selected based on multiples of epochs. Tables 5 and 6 show that the method is not sensitive to step size and threshold within a reasonable range.

Q1

Grident disorderd is formulated as the dicrepancy between two gradient sequence in Eq.2, how is it applied to a solo g_task or \delta? It is calcualted between evaluation between successive steps?

Gradient disorder is a measure of the inconsistency in the directions of adjacent gradients in the same gradient sequence (applicable to any gradient sequence, as described in lines 211-235). In the experiment, we calculate it every K steps (see lines 294-295). For example, when K=3, G = {-1, 2, 3, -4}, then S1 = {-1, 2, 3}, S2 = {2, 3, -4}, $sgn(S1) = {-1, 1,1}, sgn(S2) = {1,1,-1},$ $(sgn(S1)\neq sgn(S2))=2$, $\delta = 1/3 * 2 =2/3$

Q2

How the update rule (Line 296-303) is determined? In other words, it is possilbe to use gtask (if disorder of gtask is under certain value, scaling factor in quantizer is not updated). How about simply alternatively update of QAT and DG every K steps, which should be listed as a baseline.

Our update rule is based on three key observations:

1. Figure 3 shows that task gradient disorder decreases over time for some layers (becoming more consistent), while smooth gradients do not exhibit a clear trend. Excessive consistency in task gradients can negatively affect smooth gradient training.
2. Lines 249-256 indicate that layers with low task gradient disorder are more likely to reach a suboptimal state where both gradients are in opposite directions but with similar magnitudes.
3. Lines 266-269 and Figure 4 validate that freezing layers with low task gradient disorder effectively reduces anomalous gradients in unfrozen layers.

Table 4 shows that performance decreases after freezing gradients, further validating the effectiveness of our freezing rule. Regarding the alternating updates and no updates you mentioned, we conducted experiments on DomainNet with 4-bit quantization.

Results:

1. Freezing both gradients below the threshold:

   For DomainNet’s three domains with 4-bit, freezing both gradients below the threshold yielded the following results, showing a performance drop compared to directly introducing the SAGM smoothness objective:

   Experiment	Origin (val/test_a,test_b)	Freezing both (val/test_a,test_b)
   Domain 01	65.77/（60.73, 15.64）	64.91 /（60.16, 15.20）
   Domain 23	61.21/（46.67, 16.29）	61.05 /（46.52, 15.90）
   Domain 45	56.77/（52.22, 48.45）	56.59 /（51.92, 48.40）

2. Alternating updates between DG and QAT:

   For Real and Sketch domains with 4-bit, alternating updates every 300 and 3000 steps gave the following results, showing a performance drop compared to directly introducing the SAGM smoothness target:

   Steps	val	max_all_test_list
   origin	56.77	（52.22, 48.45）
   300	54.78	（49.92, 46.48）
   3000	55.01	（50.22, 46.54）

The above shows that alternating updates or freezing without further updates cause performance drop. Complete experiments will be included in the final version.

Thank you very much for your thorough and insightful review of our paper. We sincerely appreciate the time and effort you dedicated to reviewing our work, as well as the valuable suggestions you have shared.

We would like to provide further clarifications in the hope of helping you better understand W1.

1. DG is not an isolated task but is closely tied to specific research domains

   Domain Generalization aims to address the issue of distributional mismatch between training and test domains. This problem is prevalent in both CV and NLP. DG is not an isolated task; rather, it is explored in the context of specific research areas. For example, the current focus is on DG issues within the CV domain [1-9]. Actually, our DG-QAT belongs to CV-QAT.

2. Smoothness optimization is a class of methods within DG

   In DG, there are various methods, and the sharpness-aware methods have recently gained considerable attention [3, 7]. From an optimization perspective, smoothness enhances generalization, forming a class of DG methods that explore smoother loss surfaces. For instance, the SAGM method improves generalization by optimizing smoothness and successfully trains high-performing models with full precision. Therefore, smoothness is intrinsically related to DG, and our method addresses the conflict caused by introducing a smoothness factor into QAT. Our goal is to preserve the smoothness of quantized models. Thus, from a motivational standpoint, our method is closely connected to DG.

3. Visualization confirms our method's association with smoothness

   In the latest version of our paper, we have included comparison plots showing the loss surface with and without our method. The results indicate that our method significantly improves smoothness, which is a key strategy in DG. Therefore, the visual results further demonstrate that our method is closely related to smoothness optimization, and by extension, to DG.

4. Task gradient disorder and the unique freezing strategy for DG-QAT

   Our experiments show that as training progresses, task gradient disorder decreases, and freezing layers with lower task gradient disorder reduces gradient conflicts, thereby improving smoothness. This phenomenon is unique to DG-QAT, rather than gradient conflicts being inherently unique.

   Scaling factors are specific to QAT and do not appear in full-precision training, so we focus on QAT scenarios. Using proof by contradiction, if the reduction in task gradient disorder and the smoothness gains from freezing gradients based on disorder metrics were not unique to DG-QAT, we would expect similar effects in IID-QAT.

   We tested this on the PACS dataset with four domains (training and validation on the same domain using LSQ), but found that task gradient disorder remained high (around 0.5) by the end of training . Freezing strategies showed no significant improvement, with validation curves mostly unchanged or negative, except for a slight increase in the Sketch and Art domains at a threshold of 0.32 (with freeze steps fixed at 150, and r∈[0.28,0.32,0.35,0.37,0.4], due to high initial task gradient disorder). However, no significant difference in smoothness was observed in the loss surface of the frozen models .

   These results confirm that task gradient disorder and the freezing strategy are unique to DG-QAT, reinforcing the strong connection between our method and DG-QAT.

5. Observations and contributions Our method is based on the observation of task gradient disorder and the use of a freezing strategy to enhance DG-QAT performance. The choice of freezing metric and the decision to freeze task gradients stem directly from these observations, making them an integral part of our approach.

Based on the above four objective observations and the subjective conclusions, we firmly believe that our method is strongly related to DG.

Once again, we sincerely appreciate your valuable feedback and the time you have dedicated to reviewing our paper. We hope the five points outlined above help clarify why our method is strongly connected to DG. If there are any unclear points, please feel free to reach out for further discussion.

[1] In Search of Lost Domain Generalization, Gulrajani et al., ICLR 2021.

[2] Ensemble of Averages: Improving Model Selection and Boosting Performance in Domain Generalization, Arpit et al., NeurIPS 2022.

[3] SWAD: Domain generalization by seeking flat minima, Cha et al., NeurIPS 2021.

[4] Diverse weight averaging for out-of-distribution generalization, Rame et al., NeurIPS 2022.

[5] Cross-contrasting feature perturbation for domain generalization, Li et al., ICCV 2023.

We hope that our response have provided clarity and effectively addressed your concerns. We would greatly appreciate it if you could acknowledge this. If there are any remaining questions or unresolved concerns, we would be more than happy to provide further clarification. Thank you sincerely for your time and valuable feedback—it is greatly appreciated.

We sincerely appreciate the time and effort you have dedicated to reviewing our work and would like to provide further clarifications.

To clarify, gradient disorder refers to directional inconsistency within a gradient sequence. For example:

• Task gradient disorder, derived from task loss, measures inconsistency within the task gradient sequence.
• Smooth gradient disorder, related to DG, measures inconsistency within the smooth gradient sequence.

Smooth gradient disorder exists only in DG tasks because it arises from the DG-related smoothness loss. Task gradient disorder exists in both DG and non-DG tasks. We believe that what you mentioned—“provide any evidence that gradient disorder is missing in other domains”—means validating that the gradient disorder phenomena described in our paper are unique to DG. Specifically, we aim to verify that our observations regarding gradient disorder are only suitable for DG scenarios, and our method is only effective in DG scenarios.

To address this, we conducted additional experiments to substantiate our claim, employing a proof by contradiction. Specifically, we compared DG with its opposite scenario, independent and identically distributed (IID) tasks—what you referred to as tasks involving other domains. The goal was to demonstrate that these phenomena are absent in IID scenarios.

We tested our approach on the PACS dataset with four domains, using LSQ for training and validation on the same domain(IID). Task gradient disorder remained high (~0.5) by the end of training. Freezing strategies showed little to no improvement in validation performance, except for minor gains in the Sketch and Art domains at a threshold of 0.32 (freeze steps fixed at 150, r∈[0.28,0.32,0.35,0.37,0.4]). However, no significant changes in loss surface smoothness were observed for models with frozen layers.

The following two observations in IID tasks strongly support the connection between our findings and DG:

1. In IID tasks, task gradient disorder does not decrease during training, unlike in DG scenarios.
2. Freezing task gradients with lower disorder scales in IID tasks does not improve smoothness , contrary to what is observed in DG scenarios.

These results confirm that the observations and methods presented in our paper are not applicable to IID tasks. Using proof by contradiction, we argue that if our methods were unrelated to DG, similar phenomena and outcomes would have been observed in IID settings. However, our key observations (e.g., the decrease in task gradient disorder during training) and the results of our methods (e.g., improved smoothness and DG performance) were not evident in IID tasks.

Thus, we conclude that both our observations and methods are strongly and uniquely associated with DG.

I hope this explanation helps clarify our work. If any points remain unclear, please don't hesitate to reach out for further discussion. We sincerely hope you will reconsider our paper.

We sincerely thank you for your thoughtful feedback and for recognizing the value of our work. It is truly inspiring to hear that you appreciate our contributions and lean strongly toward acceptance. We are grateful for your encouragement and hope that our research will inspire further exploration in this area.

W1 & Q1

The experiments section seems a bit weak and might need a clearer explanation.

I would be curious to see 2 ends of the quantization results. 1/2 bit and 8 bit quantized models using the same method compared to DG-SAM + LSQ.

Due to the significant I.I.D performance drop observed with 2-bit quantization in our experiments, exploring DG performance under such extreme settings seemed less meaningful, so we did not pursue further experiments. For 5-bit and 8-bit quantization, we observed similar gradient conflict phenomena. Results on the cartoon domain show improvements even without fine-tuned hyperparameter search: 5-bit accuracy increased from 76.05%/54.64% to 80.59%/59.22%, and 8-bit from 77.42%/56.34% to 80.74%/56.45%. We will provide complete results with more refined hyperparameter search in the final version. Additionally, the newly added Figure 6 visualizes the loss curves for the four PACS domains under 4-bit quantization. As shown, the proposed method achieves significantly smoother surfaces, further confirming its effectiveness.