Handling Label Noise via Instance-Level Difficulty Modeling and Dynamic Optimization

Overall Response:

We sincerely thank the reviewer for their insightful feedback and detailed comments. We have carefully studied your questions and, based on your suggestions, have conducted additional analysis and experiments. We are confident that incorporating these discussions and new results will significantly strengthen the final manuscript.

Question 1: In the first stage of this framework, the paper assumes that "prior knowledge, i.e., coarse distribution of wrong event, is obtained". However, the prior knowledge cannot be easily obtained in reality.

Response:

Thanks for your concerns! We apologize for the confusing terminology on "prior knowledge". We would like to clarify that this "prior knowledge" is not assumed or required beforehand, but is generated internally during Stage 1 of our framework. It specifically refers to the initial wrong event statistics gathered during Stage 1, which are then used to initialize the dynamic optimization in Stage 2. Our method does not require any pre-existing knowledge of the dataset-specific characteristics. The results on real world noisy datasets such as CIFAR-100N, Webvision and Clothing1M also show the practical applicability of our method in reality. We will add a more precise description to "prior knowledge" in the revision manuscript to avoid misunderstanding.

Question 2: The performance improvement may be from different components/terms of the loss function. Ablation Study is missing.

Response:

We completely agree that a thorough ablation study is essential for understanding the source of performance improvements. We included these studies in our original submission and appreciate the opportunity to highlight their findings here. The performance gains from IDO stem from two main contributions:

First, Comprehensive Loss Function: As you noted, our three-part loss function models clean, noisy, and difficult samples respectively. Our ablation study in Table 5 demonstrates that each component— $L_{C}$, $L_{N}$, and $L_{SIM}$ —contributes positively to the final performance, and removing any of them leads to a drop in accuracy.

Second, Superiority of the wrong event Metric: Our proposed wrong event metric provides more accurate and stable information for noise modeling than other metrics. The ablation study in Table 4 compares wrong event against Single Loss [1], EMA Loss [2], Forgetting Event (FE) [3] , and First k-epoch Learning (FkL) [4]. The results show that wrong event consistently outperforms these other metrics across different training stages.

We will ensure these key ablation results are more prominently signposted in the revised manuscript.

Question 3: In Figure 2, the authors mentioned "Since wrong events are monotonically increasing based on historical statistics instead of current model prediction, when model overfits the dataset, wrong event values for all samples do not change, rather than converging to zero as loss values typically do.". It is not clear about what the "wrong event values" is. Why, when wrong events are monotonically increasing, wrong event values do not change?

Response:

Thank you for this question. We agree the original phrasing in the Figure 2 caption was a bit confusing and appreciate the chance to clarify. Specifically, the wrong event value of a sample is the number of disagreement between the prediction and the given label during training. At each epoch, the wrong event value of a sample either stays the same (if the prediction matches the given label) or increments by one (if they differ), so the wrong event values are monotonically increasing. As the model overfits, almost memorizing all the given labels, the wrong event value of each sample nearly stabilizes (stops increasing), unlike the loss which converges to zero. This attribute preserves the discriminative power of wrong event distribution at overfitting phase.

We will revise the caption in Figure 2 to make this explanation clearer.

Question 4: The authors didn't compare the results with "Noise attention learning: Enhancing noise robustness by gradient scaling, NeurIPS 2022".

Response:

Thanks for providing related works! We agree that comparing with more recent works is important. We include InstanceGM [5] and NAL [6] as our two more baselines in 3 new experiments on CIFAR-100.

The results show that while InstanceGM is strong in its target setting (instance noise), it underperforms in symmetric and asymmetric noise because InstanceGM is too cautious in judging noise which leads to insufficient label correction. NAL performs well but is slightly behind IDO, particularly in the most challenging instance-dependent scenario. IDO demonstrates consistently state-of-the-art performance across all three settings. We will include a more comprehensive comparison with InstanceGM and NAL in our revised manuscript.

Once again, we thank you for your valuable and insightful feedback, which has significantly improved our work. We sincerely hope that our analysis and experiments can address your confusion and questions, providing a clearer understanding of our work. If you have any questions about our paper, please feel free to point out and we will try to address it as soon as possible. We would like to express our sincere gratitude for your valuable comments again. Thanks and looking forward to your reply!

[1] DivideMix: Learning with Noisy Labels as Semi-supervised Learning. ICLR'20

[2] Robust Curriculum Learning: from clean label detection to noisy label self-correction. ICLR'21.

[3] An Empirical Study of Example Forgetting During Deep Neural Network Learning. ICLR'19.

[4] Late Stopping: Avoiding Confidently Learning from Mislabeled Examples. ICCV'23.

[5] Noise attention learning: Enhancing noise robustness by gradient scaling. NeurIPS'22.

[6] Instance-dependent noisy label learning via graphical modelling.CVPR'23.

Dear Reviewer HFBm,

Greetings from the authors!

To begin with, we sincerely appreciate your acknowledgement of the following aspects of our work:

• Strong generalization performance while being computationally efficient and scalable

• Avoid the extensive hyperparameter tuning required by prior methods

• Provide clear theoretical rationale and empirical validation for the stability of the proposed metric.

Regarding the prior knowledge, reasons for performance improvements, explaining caption and including more baselines, we have conducted multiple experiments and included these experiments and analysis in the revised paper. We will include them in the final version and provide the link to code repository upon acceptance.

If you have any question for our paper, please feel free to point out and we will try to address it as soon as possible. We would like to express our sincere gratitude for your insightful comments again. Looking forward to your reply! Thanks!

Dear reviewer HFBm,

Thank you for your thoughtful efforts in reviewing our work! As the discussion period nears its end, we kindly hope you can take a moment to review our rebuttal. Looking forward to your feedback!

Best Wishes!

NeurIPS Authors

Dear Review HFBm,

Hope this message finds you well. As the discussion period is nearing its end with less than one day remaining, we kindly appreciate your service and wonder if our response has addressed your review feedback. If there are any additional points or feedback you'd like us to consider, please let us know. Your insights are invaluable to us, and we're eager to address any remaining issues to improve our work.

Thank you for your time and effort in reviewing our paper.

NeurIPS Authors

Overall Response:

We sincerely thank you for your critical and insightful review. Your insightful questions have helped us to further strengthen the paper. We have conducted several new experiments based on your suggestions and are confident that incorporating these results and discussions will significantly improve the final manuscript. Below, we address each of your points in detail.

Question 1: The paper is mainly a pure-observation based approach with limited justification for what is proposed in the paper, and in particular the wrong event.

Response:

Thank you for the incisive and critical feedback. We fully acknowledge that wrong event is a mainly empirical, observation-driven metric and totally agree with the reviewer that a rigorous theoretical analysis provides the most comprehensive understanding of a method. We view this as a valuable direction for our future work.

Nevertheless, we respectfully argue that in deep learning, providing extensive, consistent evidence for a novel metric and framework's superiority constitutes a significant contribution in its own right. Empirical, observation-driven research approach is a characteristic shared by many successful methods in Learning with Noisy Labels (LNL). The small loss hypothesis [1] as you mentioned and the memorization effect hypothesis [2] are mainly proposed with an empirical, observation-driven research approach. The metrics used to model noise such as loss[3], ema-loss[4], forgetting event(FE)[5], fluctuation event[6], first k-epoch learning(fkl)[7] and label wave[8] are also mainly proposed with an empirical, observation-driven research approach.

In our original manuscript, our validation in the manuscript goes far beyond simple observation. We demonstrate the superiority of wrong event not only through state-of-the-art accuracy on six diverse benchmarks (Tables 1, 2) but also through direct, multi-faceted comparisons against other metrics:

Noise Modeling Ability (Table 4): We show wrong event achieves superior final accuracy, demonstrating its robust modeling capability across all training phases (early, middle and late stages).

Stability and Robustness (Fig. 7): We analyze the change range of normalized metrics, proving that wrong event is significantly more stable than loss.

Clean Sample Selection (Fig. 2,5,6,8, Tables 9-12): We provide a comprehensive comparison against loss using visualizations of histograms and AUC-ROC curves and calculations of precision, recall, F1-score, and AUC. These results confirm the superior selection ability of wrong event across different training strategies (from-scratch and pre-trained) and throughout all training phases (early, middle and late stages).

We believe our method, backed by this extensive evidence, offers valuable insights to the community. We will explicitly state the lack of a formal convergence proof as a limitation in the revised manuscript, highlighting it as a promising avenue for future theoretical research.

We believe that our method can offer insights for the community on this field, and we will included the limitation of lacking rigorous theoretical analysis such as full theoretical proof of convergence in the revised paper, leaving a promising future work.

Question 2: It is unclear whether the metric is effective in identifying label noise, because such a metric largely depends on the model used to estimate it. Then, if the model is bias, the metric is also bias, rendering its ineffectiveness.

Response:

This is an excellent point, and we acknowledge your valid concern regarding the interplay between the metric and potential model bias. We designed our experimental protocol specifically to test this.

Our method was validated on six diverse synthetic and real-world benchmarks (CIFAR-10/100, Tiny-ImageNet, CIFAR-100N, Clothing1M and WebVision), across various noise types (symmetric, asymmetric, instance-dependent and real world noise), architectures (ResNet18/50, ViT, ConvNeXt) and training strategy (from-scratch / pretrained). IDO consistently outperforms state-of-the-art methods in these varied settings, demonstrating the generalizability and robustness of our approach.

More directly, our analyses in Figures 4, 8 and Tables 9-12 demonstrate the metric's resilience to model state and bias:

Robustness to Model State: wrong event maintains its discriminative power in early, middle, and late training stages, regardless of whether the model is underfitting or has begun overfitting (i.e., become biased by) the noisy labels.

Robustness to Model Initialization: The metric performs effectively in both randomly initialized and powerful pre-trained settings, showing it is not dependent on a strong initial model.

Extensive experiments demonstrate the consistent efficacy of wrong event across diverse settings, particularly its robustness to various models. This comprehensive evidence demonstrates that wrong event is not fragilely dependent on a perfectly unbiased model but is a robust metric across a wide spectrum of practical conditions. We hope this fully addresses your concern.

Question 3: The claim of the theoretical analysis at line 132 and in the Appendix C2: $\frac{w_i^{T+1}-w_i^{T}}{w_i^T}\in[0,\frac{1}{T}]$ is incorrect. The left hand side term should be in $[0,+\infty]$ . A slightly similar concern on the loss. Since the loss is positive, $\frac{l_i^{T+1}-l_i^{T}}{l_i^T}\in[-\infty,+\infty]$.

Response:

We sincerely apologize for this error and are very grateful for your sharp attention to detail. This was an oversight on our part. We have thoroughly re-examined this point and provide a corrected, more rigorous analysis below.

The change rate of loss is indeed $\frac{l_i^{T+1}-l_i^{T}}{l_i^T}\in[-\infty,+\infty]$ in every epoch $T$ with unbounded limits and frequently unpredictable mutations. A usually seen phenomenon named forgetting event [5] (last epoch right, this epoch wrong) can cause the probability of given label to plummet from a high probability (e.g. ~0.9) to a small probability (e.g. ~0.1), causing the loss to skyrocket and the relative change to become enormous. This can happen randomly and repeatedly for all the samples.

However, for wrong event, the change rate needs more discussion. Firstly, we have $w_i^{T+1}=w_i^T+\delta_i^{T+1},\delta_i^{T+1}\in\{0,1\} \text{ and } w_i^T\in [0,\dots,T]$, meaning the wrong event value is monotonically increasing. The change rate is $\frac{\delta_i^{T+1}}{w_i^T}$. We analyze this in two distinct cases:

The "0 to 1" Transition: You are correct to identify the unique case where the metric's stability might be questioned. When a sample is misclassified for the very first time, $w_i^T$ transitions from 0 to 1. At this point, the relative change $\frac{1}{0}$ is undefined. This is a singular, one-time event for any given sample, marking its initial entry into the set of "ever-misclassified" samples.

All Subsequent Changes ($w_i^T \geq 1$): For every subsequent misclassification, the denominator $w_i^T$ is at least 1. The relative change is $\frac{\delta_i^{T+1}}{w_i^T}$. This value is strictly bounded within the range [0,1] far smaller than the change rate of loss. More importantly, as the model continues to misclassify a sample, $w_i$ increases, causing the maximum possible relative change ($\frac{1}{w_i^T}$) to decrease. The metric is therefore self-stabilizing.

This analysis provides a strong theoretical basis for the empirical stability we observed in Figure 7. The relative change of wrong event is well-behaved, bounded, and self-stabilizing after a single initial event. Conversely, the relative change of loss is unbounded and perpetually susceptible to explosive volatility. This fundamental difference in their rate of change is why wrong event serves as a far more reliable and stable signal for modeling sample characteristics in noisy environments.

We thank you again for pushing us to analyze our metric's stability more deeply. We will completely revise this section in the manuscript to reflect this rigorous and correct analysis.

Once again, we thank you for your valuable and insightful feedback, which has significantly improved our work. We sincerely hope that our analysis and experiments can address your confusion and questions, providing a clearer understanding of our work. If you have any questions about our paper, please feel free to point out and we will try to address it as soon as possible. Thanks and looking forward to your reply!

[1] Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels. NIPS'18

[2] A closer look at memorization in deep networks. ICML'17

[3] DivideMix: Learning with Noisy Labels as Semi-supervised Learning. ICLR'20

[4] Robust Curriculum Learning: from clean label detection to noisy label self-correction. ICLR'21

[5] An Empirical Study of Example Forgetting During Deep Neural Network Learning. ICLR'19

[6] Self-filtering: A noise-aware sample selection for label noise with confidence penalization. ECCV'22.

[7] Late Stopping: Avoiding Confidently Learning from Mislabeled Examples. ICCV'23

Overall Response:

We sincerely thank you for your detailed and constructive feedback. Your insightful questions have helped us to further strengthen the paper. We have conducted several new experiments based on your suggestions and are confident that incorporating these results and discussions will significantly improve the final manuscript. Below, we address each of your points in detail.

Question 1: On the evidence for the claim that "wrong event can clearly separate noisy and clean data at all training stages."

Response:

We appreciate your question regarding this core claim. Fig.2,5,6,8 (visualizations of histogram and AUC-ROC curves) and Tab.9,10,11,12 (calculations of precision, recall, F-score and AUC) show that wrong event can clearly separate noisy and clean data at all training stages with pretrained or randomly initialized models. For the extremely early training stage, i.e., one epoch, Tab.4 shows that wrong event can achieve the accuracy of 80.2% same as loss.

Question 2: On the comparison of variance between Loss and Wrong Event, and their different units.

Response:

Yes, we are comparing the relative variance. The loss $l$ and wrong event $w$ are not in the same range. We normalize the two metrics and track the range of value changes during training. As shown in Fig. 7, the experimental results show that the range of loss has no clear upper bound, confirming its instability, and the range of wrong event converges as training progresses, demonstrating superior stability. Furthermore, due to loss mutations, the mean change of loss is also larger than that of wrong event.

Question 3: On providing evidence for "outcomes frequently flipping between similar classes" for hard samples.

Response:

Thanks for this question! This characteristic of hard samples is widely recognized in the field and has been demonstrated in several prior works. Previous papers [1][2][3][4][5][10] have shown that the hard sample predictions frequently flipping between similar classes by visualizing the learned representations using t-SNE 2D embeddings, giving the confusion matrix of prediction and labels or giving the statistic information about softmax outputs of certain samples, such as chiffon/shirt, windbreaker/jacket, 1/7, deer/horse, whale/dolphin and etc. In our single-label classification task, although these classes may be semantically related, the sample officially belongs to only one correct class. Therefore, such "flipping" is still considered a misclassification. We will add these citations to the manuscript to support this point.

Question 4: On demonstrating the process of "the clean and noisy distribution gradually separate."

Response:

Thank you for the valuable question. We can empirically illustrate the process as follows. At initialization, wrong event value for all samples is 0. During early training, the model learns correct patterns, its predictions for clean samples tend to match the given labels, so their wrong event values grow slowly or not at all. Conversely, for noisy samples, the model's prediction based on true features mismatches the given noisy label, causing their wrong event values to increase steadily. This differential growth progressively separates the distributions of clean and noisy samples, making it easier to distinguish which distribution a sample is from. Even if the model later memorizes the entire dataset, the wrong event values are "frozen" at their current, separated states, thus preserving the established distinguishability.

Question 5: On the correction that $L_{SIM}$ is squared error, not MSE.

Response:

We really appreciate your attention to detail. $L_{SIM}$ is indeed the per-sample squared error, not MSE. We will correct it in the manuscript.

Question 6: On issues with figures and grammar.

Response:

Thanks for your attention to detail. For Fig.2, we will clarify that the horizontal axis represents the "Value of Wrong Event / Loss," move the y-axis of subplot (d) back to the left, and confirm that the figure reports the median, not the mean. For Fig.4, we will replace the line chart with a more appropriate format and clarify the y-axis as accuracy(%). We will correct all the issues with figures and grammar in the final manuscript.

Question 7: On including error bars (std) for experimental results.

Response:

Thanks for your concerns! Reporting statistical significance is crucial for demonstrating robustness. We show some error bars in the CIFAR-100 experiment as follows

We will include the error bars (std) for all experiments in the revised manuscript to report the statistical significance and robustness of our 5-run experiments.

Question 8: On discussing the weaknesses/limitations of our work in the main paper.

Response:

Thanks for suggestions! We run 6 new experiments under a wider range of noise levels in the three noise types to verify IDO's robustness and potential weakness. For Sym. noise, 80% is added. For Asym. noise, 20% and 45% are added. For Inst. noise, 20% and 60%. Besides, a noise-free (0 %) baseline is included. All the experiments use ResNet-50 to train on CIFAR-100 following the implements in the paper.

The results show that IDO performs well and robustly within a noise range that far exceeds the 8 %–38.5 % observed in real-world datasets [6]. Degradation only appears under extremely high noise ratios—rare in practice—because, as discussed in line 670, the highly imbalanced wrong event distribution prevents BMM and model from converging. We will move the "Limitations" section from the appendix to the main paper.

Question 9: What is the meaning of f() and noise rate in the paper?

Response:

Thanks for pointing it out! We apologize for the confusing terminology on f(). f() is the softmax probability of model output. We will explicitly define the output of the function f(⋅) in different contexts (predicted class $\text{argmax } f()$ vs. softmax probabilities $f()$) to remove all ambiguity in Equations (1), (10), and (11). Noise rate $r$ is a given number in each task.

Question 10: On clarifying whether the main contribution is the Wrong Event metric or the IDO framework.

Response:

Thank you for the question that helped us clarify our core contribution. We regard the two components as an inseparable and mutually reinforcing system that together forms our main contribution. Current frameworks suffer from high computational costs, heavy hyperparameter tuning and corase-grained optimization, which our lightweight, hyperparameter-free IDO framework is designed to address. The dynamic loss coefficients of IDO relies on robust noise modeling, but existing metrics loss[7], EMA-loss[8], FE[9], FKL[10] have known limitations (Line 76, 296, 584). We therefore introduce wrong event, which supplies accurate noise-modeling information at no extra computational cost. While wrong event could in principle be plugged into other frameworks and IDO could adopt alternative metrics, the two components are designed to complement each other and achieve optimal performance when used jointly.

Question 11: On the question of why the method uses 10/15 epochs vs. 100 epochs shown in figures.

Response:

Thank you for this detailed observation. The difference in epoch numbers stems from the model initialization settings: Fig.2 show 100 epochs for randomly initialized ResNet-18 models, and method uses 10 or 15 epochs for pretrained ResNet-50 models. For randomly initialized models, the visualizations of histogram and AUC-ROC curves are in Fig.2,5,6,8, and calculations of precision, recall, F1-score and AUC are in Tab.9,11. For pretrain models, visualizations are in Fig.8, and calculations are in Tab.10,12. The results confirm that the core intuition behind our framework is effective in both scenarios.

Once again, we thank you for your valuable and insightful feedback, which has significantly improved our work. We sincerely hope that our analysis and experiments can address your confusion and questions, providing a clearer understanding of our work. If you have any questions about our paper, please feel free to point out and we will try to address it as soon as possible. Thanks and looking forward to your reply!

[1] Symmetric Cross Entropy for Robust Learning With Noisy Labels. ICCV'19

[2] Beyond Class-Conditional Assumption: A Primary Attempt to Combat Instance-Dependent Label Noise. AAAI'21

[3] Learning from Massive Noisy Labeled Data for Image Classification. CVPR'15

[4] Beyond Synthetic Noise: Deep Learning on Controlled Noisy Labels. ICML'20

[5] Tripartite: Tackle Noisy Labels by a More Precise Partition. arXiv'22

[6] Learning from noisy labels with deep neural networks: A survey. CoRR'20

[7] DivideMix: Learning with Noisy Labels as Semi-supervised Learning. ICLR'20

[8] Robust Curriculum Learning: from clean label detection to noisy label self-correction. ICLR'21

[9] An Empirical Study of Example Forgetting During Deep Neural Network Learning. ICLR'19

[10] Late Stopping: Avoiding Confidently Learning from Mislabeled Examples. ICCV'23

Dear Reviewer 2oRY,

Greetings from the authors!

To begin with, we sincerely appreciate your acknowledgement of the following aspects of our work:

• Idea of IDO is well-motivated and technically sound.

• Comprehensive outperformance of existing methods on all datasets and noise rates.

Regarding the evidence for some claims, the generalization of intuition and other concerns, we have conducted multiple experiments and included these experiments and analysis in the revised paper. We will include them in the final version and provide the link to code repository upon acceptance.

If you have any question for our paper, please feel free to point out and we will try to address it as soon as possible. We would like to express our sincere gratitude for your insightful comments again. Looking forward to your reply! Thanks!

Dear reviewer 2oRY,

Thank you for your thoughtful efforts in reviewing our work! As the discussion period nears its end, we kindly hope you can take a moment to review our rebuttal. Looking forward to your feedback!

Best Wishes!

NeurIPS Authors

Overall Response:

We sincerely thank you for your detailed and constructive feedback. Your insightful questions have helped us to further strengthen the paper. We have conducted several new experiments based on your suggestions and are confident that incorporating these results and discussions will significantly improve the final manuscript. Below, we address each of your points in detail.

Question 1: The paper does not sufficiently discuss potential failure cases, such as performance under a wider range of noise levels, especially in instance-dependent noise settings and high noise ratio settings. More experiments help to evaluate the robustness and practical applicability of the method.

Response:

Thank you for this excellent suggestion. To thoroughly evaluate IDO's robustness and practical applicability, we agree that testing on a wider range of noise levels is crucial. We have conducted 6 new experiments on CIFAR-100 using the pretrained ResNet-50 with more noise levels. For symmetric noise, a high noise ratio of 80% is added. For asymmetric noise, 20% and 45% are added. For instance-dependent noise, 20% and 60% are added. Besides, a noise-free (0%) baseline is included. The results summarized below.

These results demonstrate that IDO maintains a significant performance advantage across a wide spectrum of noise types and levels, including the challenging 45% asymmetric noise and 60% instance-dependent noise scenario. This confirms the robustness of our approach, even under conditions far more extreme than the 8%–38.5% noise typically found in real-world datasets [1]. Impressively, IDO also achieves the best performance in the noise-free (0%) setting, showing it does not degrade performance on clean data.

As we discussed in our limitations (line 670), performance degradation is only observed at an extremely high noise ratio of 80%, which is expected due to the severe imbalance in the wrong event distribution that affects the BMM and model convergence. We believe these new results comprehensively address the concern about robustness and practical applicability.

Question 2: Although obtaining prior knowledge in Stage 1 is crucial—particularly in capturing the label wave number—, there is a lack of detailed analysis on its impact and sensitivity.

Response:

We appreciate the reviewer's focus on the criticality of Stage 1. We agree that its impact and sensitivity are vital for the framework. In our original manuscript (Table 4), we investigate how the duration of Stage 1 could influence capturing the label wave number and then influence the final performance.

For the reviewer's convenience, we summarize that Table 4 shows our method's final performance remains consistently high, regardless of whether Stage 1 fits noise—across early (1/2 epochs), middle (4 epochs), or late (8 epochs) training stage—demonstrating robustness throughout. This demonstrates that our framework, especially obtaining the prior knowledge, is not sensitive to the exact stopping point of Stage 1. This robustness is also supported by the original Label Wave paper [2] with experiments on various noise settings and datasets, which established its stability.

To make this point clearer for the reader, we will add a dedicated paragraph in the final manuscript to explicitly discuss the sensitivity and impact of Stage 1, referencing these findings.

Question 3: How does the method perform when class boundaries are highly entangled?

Response:

This is a very insightful question. Highly entangled class boundaries are precisely the challenge posed by asymmetric, instance-dependent, and real-world noise. Our framework handles this through two parts: 1. The wrong event metric helps identify these hard examples, which tend to have fluctuating predictions and thus cluster in the middle of the wrong event distribution. 2. The difficulty coefficient $ϵ(w)$ and consistency loss $L_{SIM}$ then dynamically up-weights the consistency loss $L_{SIM}$ for these specific samples.

This forces the model to learn more robust and consistent representations for samples near the decision boundary, effectively disentangling them. As demonstrated in our new experiments for Question 1, IDO's superior performance under 45% asymmetric and 60% instance-dependent noise directly demonstrates its effectiveness in handling such entangled boundaries.

Question 4: The similarity loss seems to have a larger effect in more challenging noise settings. Does this imply that the method relies more heavily on consistency learning under difficult conditions? What happens if the difficulty score is fixed to a high value—i.e., treating all samples as difficult? Is it desirable for easy samples to receive a low weight for similarity loss? A deeper analysis of the behavior of the difficulty-based weighting would be helpful.

Response:

We appreciate the reviewer's sharp observation and agree that this is a crucial aspect of our method. Your intuition is correct: IDO relies more heavily on consistency learning under difficult conditions. To analyze the behavior of the difficulty-based weighting, we conducted 4 new experiments comparing our dynamic weight $ϵ(w)$ against several fixed-weighting methods.

The result shows that dynamic weighting > fixed weighting > drop the loss term, and the performance shows no clear correlation with fixed value of difficulty coefficients. This supports our core hypothesis, much like the principle behind Focal Loss [3]: $F(p)=-(1-p)^γlog(p)$, showing that a weighting term to expand the loss of difficult data is really necessary and better than treating all samples the same. We consider that for easy data, cross-entropy loss serves as a more direct and effective learning signal than consistency loss while consistency loss $L_{SIM}$ serves as a effective learning signal for difficult data. Dropping and fixing the difficulty coefficient $ϵ$ both decrease the performance.

Question 5: Including more baselines, such as InstanceGM [4], would provide a more comprehensive comparison and help contextualize the proposed method’s performance more clearly.

Response:

Thanks for providing related works! We agree that comparing with more recent works is important. We include InstanceGM [4] and NAL [5] as our two more baselines in 3 new experiments on CIFAR-100.

The results show that while InstanceGM is strong in its target setting (instance noise), it underperforms in symmetric and asymmetric noise because InstanceGM is too cautious in judging noise which leads to insufficient label correction. NAL performs well but is slightly behind IDO, particularly in the most challenging instance-dependent scenario. IDO demonstrates consistently state-of-the-art performance across all three settings. We will include a more comprehensive comparison with InstanceGM and NAL in our revised manuscript.

Once again, we thank you for your valuable and insightful feedback, which has significantly improved our work. We sincerely hope that our analysis and experiments can address your confusion and questions, providing a clearer understanding of our work. If you have any questions about our paper, please feel free to point out and we will try to address it as soon as possible. We would like to express our sincere gratitude for your valuable comments again. Thanks and looking forward to your reply!

[1] Learning from noisy labels with deep neural networks: A survey. CoRR'20.

[2] Early stopping against label noise without validation data. ICLR'20.

[3] Focal Loss for Dense Object Detection. ICCV'17.

[4] Instance-dependent noisy label learning via graphical modelling.CVPR'23.

[5] Noise attention learning: Enhancing noise robustness by gradient scaling. NeurIPS'22.

Dear Reviewer hZpr,

Greetings from the authors!

To begin with, we sincerely appreciate your acknowledgement of the following aspects of our work:

• Idea of IDO is well-motivated and empirically sound.

• Clearly written with thorough explanations, visualizations, and ablation studies.

• Thoughtfully designed to reduce reliance on hyperparameter tuning.

Regarding the potential failure cases, difficulty-based weighting, more baselines and other concerns, we have conducted multiple experiments and included these experiments and analysis in the revised paper. We will include them in the final version and provide the link to code repository upon acceptance.

If you have any question for our paper, please feel free to point out and we will try to address it as soon as possible. We would like to express our sincere gratitude for your insightful comments again. Looking forward to your reply! Thanks!