Enhancing Sample Selection Against Label Noise by Cutting Mislabeled Easy Examples

Dear Reviewer Dz13 and Area Chair,

We sincerely thank you for your valuable time in reviewing our manuscript. We have carefully studied all your questions and will address each point below.

On the Paper's Core Contribution and Baseline Comparisons

We would like to respectfully clarify a key point regarding the baseline comparisons. The reviewer noted that our work was missing comparisons to Late Stopping [1] and Me-Momentum [2] (Weakness 3). We would like to respectfully point out that both of these methods were included as core baselines in our main experimental results (Tables 2, 3). The results demonstrate that our proposed method significantly outperforms them across all tests.

This point is directly related to our core contribution, which we also wish to clarify. The reviewer suggested that our motivation (that early-learned noisy samples are particularly harmful) has been discussed by Late Stopping [1] and Me-Momentum [2] (Weakness 1). We respectfully argue that these paper are not discuss this motivation.

Specifically, methods like Late Stopping [1] and Me-Momentum [2] are built on a core assumption: that models learn simple, clean samples first, and therefore, examples learned early in training are trustworthy. Our paper's central contribution is to demonstrate, through empirical analysis, that this assumption is risky and can even be detrimental. Our novelty is three-fold:

• 1. We are the first to systematically identify and define the concept of Mislabeled Easy Examples (MEEs): We show that while these samples are "easily learned" early in training, they cause disproportionate harm to the model's generalization ability (as shown in Fig. 1 and Fig. 2).
• 2. We propose a counter-intuitive solution (Early Cutting): Based on our insights into MEEs, our novel Early Cutting method introduces a counter-intuitive calibration mechanism. It uses a later-stage, overfitted model to correct and purify the confident set selected during the early stage.
• 3. We provide a precise identification tool: To enable Early Cutting, we designed the combined criteria of high loss, high confidence, and low gradient norm. This is not a simple heuristic but a standard specifically engineered to pinpoint MEEs within a late-stage model.

Our work is not an incremental improvement on existing methods but rather a significant revision to a mainstream methodology in learning with noisy labels, for which we provide a solution. We would like to revise the Introduction and Related Work sections to more clearly emphasize this critical distinction and our contribution.

2. Justification for Using Gradient Norm to Identify MEEs (Response to Weaknesses 2, 4)

You raised an excellent question regarding why a low gradient norm can reliably help filter out MEEs.

• Theoretical Motivation : When a model "memorizes" an incorrect pattern, it gives a wrong but high-confidence prediction for a sample (e.g., predicting an image of a plane labeled "ship" as "ship" with 99% probability). For this sample, the loss (relative to its incorrect label $y_i$) will be very high. But, for a small gradient norm indicates that the loss is insensitive to small perturbations in $\mathbf{x}_i$, suggesting a strong (but potentially incorrect) association between the input features and the predicted label. MEEs tend to have low gradient norms because the model has confidently mislearned them, making the loss stable even under input perturbations. (Section 3, line 202-206)

• Empirical Validation : To validate that the gradient norm is a crucial component, we provided empirical evidence in our ablation study (Appendix B.9, line 623). We showed that removing the gradient norm criterion from our selection process leads to a significant drop in final model performance.

3. Details on MixMatch

Thank you for pointing this out; this indeed requires clarification. In our current implementation, the confident set (labeled data) and un-confident set (unlabeled data) are determined once and remain fixed during the subsequent MixMatch training. We will add this explicit detail to Section 4.3 of the paper.

4. Performance at Low Noise Rates

We thank you for this interesting question about whether our experimental findings generalize to scenes with extremely low noise rates. Following your constructive suggestion, we have conducted additional experiments to test our hypothesis in very low noise rate.

To do this, we constructed two separate low-noise training sets for both CIFAR-10 and CIFAR-100. Each set contains the full clean dataset plus 2,000 mislabeled samples (~6% noise rate, which is much lower than the common low noise setting, 20% noise rate, in learning with noise labels). The difference lies in which mislabeled samples were chosen, based on their learning-time ranking from our original, higher-noise experiments (as detailed in Section 2). All other experimental settings were kept identical to those used for Figure 2. The results, shown in the table below, confirm that even at this very low noise rate, the mislabeled samples learned earliest by the model are significantly more harmful to final generalization performance:

5. Discussion of Trade-offs and Limitations (Response to Limitations)

You've raised an important point about the risk of our method removing a small number of clean samples (i.e., false positives). We agree this trade-off exists in any sample selection method. The critical question is whether the benefit of removing harmful mislabeled examples outweighs the cost of losing these false positives.

Our Early Cutting method is designed to mitigate this risk through its strict, multi-part criterion. By engineering the method to require that a sample simultaneously meets three conditions (high loss, high confidence, and low gradient norm), we reduce the likelihood of removing hard clean samples. For instance, a challenging clean sample, such as from a long-tail class, might exhibit high loss. However, the model's confidence in its prediction would be low, and its gradient norm would be high, because a merely difficult sample does not confuse the model in the same way. Therefore, difficult long-tail samples typically do not fit our criteria for removal. Our experimental results confirm that this multi-part constraint significantly improves selection precision, ensuring the net effect is a substantial gain in performance.

Despite these design choices, we agree with your sentiment that this trade-off becomes more critical in scenarios with extremely sparse data. We will add a Section 6: Limitations to the paper to discuss this trade-off, acknowledging that the method may require adjustments or further research for such specific use cases.

Thank you once again for your thoughtful feedback.

Best regards,

The Authors

Reference:

[1] Late Stopping: Avoiding Confidently Learning from Mislabeled Examples, ICCV 2023.

[2] Me-Momentum: Extracting Hard Confident Examples from Noisily Labeled Data, ICCV 2021.

Dear Reviewer bRY1 and Area Chair,

We sincerely appreciate the valuable suggestions, which have been instrumental in improving the quality of our manuscript. We agree with all the points you raised and have revised the paper accordingly. Below, we detail the specific changes made:

On the Confusion of Notation:

We thank you for pointing out the confusion with the overloading of the symbols. We have carefully revised the notation throughout the manuscript to ensure clarity. We now use $\mathbf{E}$ to denote the number of training epochs.

On Missing Citations:

We appreciate your reminder to include citations for foundational methods. We have now added the appropriate references for SGD [1], AdamW [2], Weight Decay [3], and SGD with momentum [4]. These citations can be found in Section 4.2 (Datasets and implementation) and in Appendix B (Detailed Settings).

On Clarification of a Hyperparameter:

Thank you for pointing out the omission of the specific value for the "Early Cutting Rate" hyperparameter in the main paper. We have now specified in Section 3 (line 209) that the Early Cutting Rate was set to 1.5. In line with our treatment of other hyperparameters, we have also included a sensitivity analysis for the Early Cutting Rate in Section 4.3 and a corresponding ablation study in Appendix B.9.

Thank you once again for your consideration of our work and for your constructive guidance. We are confident that these revisions have enhanced the readability of our paper.

Best regards,

Authors

References:

[1] A stochastic approximation method, The annals of mathematical statistics, 1951.

[2] Decoupled Weight Decay Regularization, ICLR 2019.

[3] A Simple Weight Decay Can Improve Generalization, NeurIPS 1991.

[4] Learning representations by back-propagating errors, Nature, 1986.

Dear Reviewer 5oqq and Area Chair,

Thank you for your detailed and constructive feedback. We appreciate your recognition of our work's motivation, that it is "valuable to distinguish the varying negative impacts of mislabeled examples on model performance", and your assessment that this is an "important and often overlooked issue in sample selection strategies for learning with label noise".

You have raised specific, valuable points regarding the paper's clarity and methodological details. In the following, we address your concerns and detail the significant revisions we have undertaken based on your suggestions.

1. On Improving Clarity (in response to Weaknesses 2, 4 & Questions 1, 2)

1.1. Clarification of Figure 1 (in response to Q1)

We thank you for your questions regarding the clarity of Figure 1 and offer the following clarifications:

• Q1.A (Experimental Setup): The experimental setup for Figure 1(a) is detailed in Section 2.1 (in the context of Figure 2). This experiment demonstrates the unique harm of MEEs by comparing the performance degradation when adding an equal number of MEEs versus Mislabeled Hard Examples to a clean dataset. In the revised manuscript, we have added an explicit reference to Section 2.1 when Figure 1 is first mentioned and have enhanced the figure caption with a concise summary of the setup.
• Q1.B (Definition): The phrase "mislabeled samples which are correctly predicted by the model" refers to instances where a sample is inherently mislabeled, yet the model has learned to classify it according to its given (incorrect) noisy label.
• Q1.C (Early in Training): The sentence immediately following the one you quoted explains this. We define the process of the model first learning these initial four thousand mislabeled samples as occurring "early in the training process".
• Q1.D (Disproportionate Impact): The "disproportionate" impact is precisely what is illustrated in Figure 1(a). A training set contaminated with Mislabeled Easy Examples yields a model with significantly worse performance than one contaminated with the same number of Mislabeled Hard Examples, demonstrating that the negative impact of noisy labels is not uniform.

1.2. Definition of Key Concepts (in response to Q2)

Regarding the definition of "class centers" (Q2), we specified in both our analysis in Section 2.2 and the caption of Figure 4 that a "center" is the mean embedding vector of all samples belonging to that class, and distance is measured using the Euclidean distance. We also note that when this concept was first introduced in the introduction, we had already included a reference pointing to the detailed description via "(see Section 2.2)".

1.3. Notation and Prose (in response to W3, W5)

We have conducted a thorough pass of the manuscript to unify all notation (e.g., consistently using $K$ for the number of classes), streamline the prose, and remove redundant descriptions.

We respectfully point out that while we strive for precision, our goal in the Section 1 Introduction is to provide a clear and concise overview of the phenomena we observe. For this reason, certain granular details are necessarily elaborated upon in their respective, dedicated sections.

2. On Clarifying Methodological Details (in response to Weaknesses 1, 3, 5 & Questions 3, 4)

2.1. On the Methodology (in response to Q3.A)

You suggested that the calculation of the conditional probability $p_i^{(k)}$ requires the true label $y$. There may have been a misunderstanding here, which we are happy to clarify:

1. The term $p_i^{(k)}$ is a direct output of the model's forward pass and requires no label information. In the expression $Pr(y=k|x_i;\theta^t)$, the symbol $y$ represents a random variable for the class label, and $y=k$ denotes the event that this random variable takes the value of class $k$.
2. The calculation of the loss $L_i$, the predicted label $\hat{y}_i$, and the confidence $c_i$ do not depend on the unknown true label. They use either the given (noisy) label $y_i$ (during backpropagation) or the model's own probabilistic output $p_i$.

While we believe our notation is standard, we have revised this section (lines 184-190) in the manuscript to use more explicit notation (e.g., using $Y$ to denote the random variable) to prevent any possible ambiguity.

2.2. On the Instance-Independent Noise Assumption (in response to Q4)

We wish to clarify that our method does not depend on the instance-independent label noise assumption. The discussion of this assumption in Appendix A (Equation 7) is part of a standard protocol for describing how synthetic noisy datasets are generated; it describes the data generation process, not a prerequisite for our methodology. In Section 3, our method operates directly on the observed dataset $\mathcal{D}^s$ with its given (noisy) labels $y_i$, irrespective of how the label noise was generated. Crucially, as shown in Tables 2-5, we have already validated our method's performance under various noise types, including synthetic symmetric, synthetic instance-dependent, and real-world label noise.

2.3. On Ensuring the Set $\mathcal{S}$ is Non-Empty (in response to Q3.B)

We agree with your suggestion that the definition should ensure the set $\mathcal{S}$ is non-empty. We have incorporated a formal discussion of the constraints on the thresholds into the manuscript and updated Algorithm 1 accordingly. We would also like to humbly point out that in practice, our use of percentile-based thresholds effectively prevents the sets $\mathcal{S}$ or $\mathcal{S}'$ from being empty.

2.4. On Threshold Design (in response to Q3.B)

You noted that using fixed percentile thresholds might be "overly simple". Our rationale for this design choice was to prioritize generality, robustness, and ease of use, thereby avoiding complex hyperparameters that require fine-tuning for each dataset. Our sensitivity analysis (Figure 5) demonstrates that the method's performance is highly stable across a wide range of threshold values, which empirically validates the robustness of this design.

2.5. On the Empirical Nature of the Work (in response to W1)

We acknowledge that our work is primarily an empirically-driven study. We believe its main contributions are nonetheless significant: (1) identifying and defining a novel and impactful problem (the disproportionate harm of MEEs); (2) proposing a novel, effective, and practical solution (Early Cutting); and (3) validating this solution with extensive experiments on large-scale benchmarks, including full ImageNet-1k. We are confident that such empirical contributions hold significant value, particularly in an application-driven field like machine learning.

We hope that these clarifications and our accompanying revisions will address your concerns and significantly improve your opinion of our paper. Thank you once again for your tremendous effort and valuable feedback.

Sincerely,

The Authors

The reviewer thanks the authors for their efforts in addressing the comments and criticisms on the initial submission. While the rebuttal clarifies several points, key concerns remain, as outlined below.\ %------------------------------------------------------------------- Regarding 1.1. Clarification of Figure 1 (in response to Q1)"**\\ While the authors responded with: ‘Q1.C (Early in Training): The sentence immediately following the one you quoted explains this. We define the process of the model first learning these initial four thousand mislabeled samples as occurring "early in the training process",’ this response does not fully address the original question: ‘C. The phrase "early in the training process" needs clarification. How early is considered "early"? Does this vary across training algorithms or settings?'\\ %------------------------------------------------------------------- **Regarding 1.2. Definition of Key Concepts (in response to Q2)"\ The authors clarified that, in their analyses, a 'center' refers to the mean embedding vector of all samples belonging to a class, and that distance is measured using the Euclidean metric, with a reference provided. Accompanying questions arise: why was Euclidean distance chosen over other metrics to reflect the closeness of MEEs to these centers? Would using a different distance metric alter the conclusions? Are there any experiments available to demonstrate the sensitivity (or robustness) of the results to this choice?\ %------------------------------------------------------------------- **Regarding 2.1. On the Methodology (in response to Q3.A)"**\\ Thank you for clarifying that $y_i$ represents 'the given (noisy) label'. However, this explanation appears to conflict with the notation used in Appendix A, where the 'observed noisy labels' are denoted by $\tilde{y}_i$ and the true label is denoted by $y_i$ (or $y$), which also aligns with standard practice in the label noise literature. Please clarify this inconsistency.\\ In addition, the descriptions in Appendix A do not align well with Lines 183–189 in the main text, due to inconsistent notation and the imposition of equation (7), which implicitly assumes instance-independent label noise.\\ %------------------------------------------------------------------- **Regarding 2.3. On Ensuring the Set {\cal S** is Non-Empty (in response to Q3.B)"}\ The reviewer thanks the authors for their response: 'We agree with your suggestion that the definition should ensure the set is non-empty. We have incorporated a formal discussion of the constraints on the thresholds into the manuscript and updated Algorithm 1 accordingly. We would also like to humbly point out that, in practice, our use of percentile-based thresholds effectively prevents the sets from being empty.'\ However, as a revised version of the manuscript does not appear to be available, and the authors have not provided details on how the critical comments under '[3.] Lines 190–213' in the initial report have been addressed, the reviewer currently has no basis for assessing whether the revisions are acceptable.\ %------------------------------------------------------------------- Regarding 2.4. On Threshold Design (in response to Q3.B)"**\\ The authors' response on this point does not fully address the initial concern that ‘this treatment of the threshold values $\delta$ and $\tau$ appears overly simplistic and does not adequately account for the diversity and complexity of real-world data.’ While the authors mention that their design choice uses fixed rates, this choice does not seem to be directly linked to the threshold values $\delta$ and $\tau$ in the imposed constraints.\\ Furthermore, although you state that ‘Our sensitivity analysis (Figure 5) demonstrates that the method's performance is highly stable across a wide range of threshold values, which empirically validates the robustness of this design,’ this claim is not entirely convincing. A typical concern is that numerical studies alone cannot capture the full range of data characteristics encountered in real-world applications. Even if Figure 5 illustrates the intended message, it does not necessarily justify the generality of the proposed approach. \\ %------------------------------------------------------------------- **Regarding 2.5. On the Empirical Nature of the Work (in response to W1)"\ The reviewer appreciates the authors’ acknowledgement that their work is primarily an empirically driven study. It would be informative to include a theoretical guarantee to enhance the rigor and generality of the proposed method. What are the main challenges preventing the establishment of such a guarantee?

Dear Reviewer 5oqq,

Thank you for your time and for acknowledging our response.

We are glad we have clarify your initial key concerns. In particular, we believe the foundational misunderstandings regarding our method's core mechanics (e.g., that our method does not require clean labels, nor does it rely on the instance-independent noise assumption) have been fully resolved. Following your suggestions in the second round of discussion, we also addressed more detailed points, such as the specific strategy to ensure the set $\mathcal{S}$ is non-empty and the rationale for our choice of distance metric.

We understand that your subsequent questions, such as the discussion on theoretical guarantees, are constructive suggestions aimed at further improving the work. We believe that with the above-mentioned fundamental issues clarified, the initial concerns that led to the very low scores for this work in Quality (1), Clarity (1), and Significance (1), and the resulting reject recommendation, have been substantially mitigated.

Thank you again for your time and continued effort. Your comments have certainly helped us to significantly improve the readability of our paper.

Sincerely,

Authors

Dear Reviewer Sv4t and Area Chair,

Thank you for your thoughtful and constructive feedback on our manuscript. We have carefully revised the manuscript based on your suggestions and have detailed our revisions below.

1. On the Justification and Definition of Mislabeled Easy Examples (MEEs)

Thank you for your feedback. We agree that the high-level notion that not all mislabeled examples are equally harmful can be intuitive. However, we would like to clarify that our core contribution is not merely to restate this intuition. Rather, our goal is to systematically quantify this phenomenon, providing it with a solid empirical and conceptual foundation.

Based on quantitative experiments in Section 2, we extend this high-level notion to uncover a more specific and counter-intuitive finding: the mislabeled examples learned earliest by the model, which we define as Mislabeled Easy Examples (MEEs), are particularly harmful to generalization.

This key insight stands in direct opposition to a prevailing assumption in the Learning with Noisy Labels field: that early-learned examples are reliable and trustworthy, an assumption that forms the basis of several mainstream methods. Therefore, a detailed analysis in Section 2 is necessary to reveal this potential blind spot in current methodologies and to provide the fundamental motivation for our proposed Early Cutting strategy.

To address your valid concerns about clarity and conciseness, we have undertaken the following significant revisions:

• Streamlined Analysis: We have streamlined the presentation of Section 2 to be more direct. We now focus on the most critical evidence supporting our core, counter-intuitive claim (e.g., Figures 1 and 2) and have significantly reduced the descriptive text.
• Formal Definition of MEEs: In response to your request for a more rigorous formulation, we have introduced a precise operational definition in Section 3. Specifically, we have added a clear Definition 1 box, which is directly linked to and cross-referenced with Algorithm 1. As noted below, Algorithm 1 has been moved to the main text.

With these revisions, we aim to make our core conceptual contribution clearer, while conserving space in the main body for the methodological improvements described next.

2. On the Clarity and Placement of the Methodology

We fully agree with your assessment that core algorithmic details should not be relegated to the appendix. We have made the following revisions:

• By streamlining Section 2, we have freed up space in the main body. This has allowed us to move key algorithmic details from Appendix B directly into Section 3. We have also included the pseudocode for Algorithm 1 in the main body to provide a clear, step-by-step description of our final method.
• In the revised Section 3, we now explicitly state the objectives of our proposed Early Cutting method and explain how the recalibration step is designed to identify and eliminate the MEEs identified in Section 2.

These changes make the methodology section more self-contained and ensure that readers can understand our core technical contribution without referring to the appendix.

3. On the Missing Limitations Section

We have added a Section 6: Limitations in the revised manuscript. In this section, we acknowledge the computational overhead of the training process and discuss potential fairness and performance concerns related to the method's application on datasets with class imbalance.

Thank you once again for your valuable feedback.

Best regards,

Authors

2.2. On the Performance Degradation in Figure 2 (in response to Weakness 4)

This is a very keen and insightful observation. Analyzing this phenomenon helps to more deeply understand how different types of noisy samples affect learning dynamics.

You correctly noted that the model trained with "Mislabeled Hard Examples" (MHEs) (Clean + (16000:20000]) shows a more drastic performance drop after an initial peak. The mechanism is as follows:

• In the early training phase, the model struggles to fit the MHEs because their features are so dissonant with their incorrect labels. It therefore learns primarily from the 30,000 clean samples, building a relatively pure and high-quality simple pattern. This leads to higher initial test accuracy.
• However, as training progresses, the memorization effect of deep networks begins to dominate. The model starts to forcibly memorize the MHEs it previously ignored. This process severely corrupts the well-established representations, causing a sharp decline in generalization performance.

In contrast, the model trained with MEEs is polluted with incorrect patterns from the very beginning. Its starting point is worse, and while its performance also degrades, it does not exhibit the same "fall from a great height".

We extended the training CIFAR-100 with different label noise to 200 epochs and obtain ed the following results:

These extended results confirm our core thesis: although the learning dynamics differ, the final outcome is consistent. Whether at the early stopping point or the end of training, the dataset containing MEEs inflicts more severe and lasting damage on the model's final performance.

3. On Practical Details and Reproducibility (in response to Weakness 2)

To clarify: the "early stopping epoch" and the "later training stage" (which are the same point in time for our method) are determined using a held-out, noisy validation set (10% of the training data, as stated in the main text). This is a standard practice in the LNL field. We monitor the model's accuracy on this validation set and select the epoch just before accuracy begins to degrade due to overfitting. This method for determination is applied consistently across all datasets.

4. On the Effectiveness on the Clothing1M Dataset (in response to Questions)

Our manuscript did not include experiments on Clothing1M because we prioritized CIFAR-N and WebVision as our primary real-world noise benchmarks, complemented by full ImageNet-1k to show scalability.

We would like to humbly note that Clothing1M was not our first choice for evaluation because we found that its validation set also contains significant label noise from machine annotation. This can limit its utility for evaluating SOTA LNL algorithms, as the performance gap between vanilla CE and advanced methods is often less than 5%. We believe that CIFAR-N, with its human-curated noise, currently offers a more stable and reliable benchmark for real-world noise.

Despite these reasons, we agree with your suggestion that Clothing1M can serve as a further validation point for our method's effectiveness. Given the time constraints in emergency reviewing, we commit to adding an experiment on Clothing1M, in the revised manuscript to address your question.

Thank you once again for your valuable and detailed feedback.

Best regards,

Authors

Dear Reviewer XCQx and Area Chair,

We sincerely thank you for providing such a detailed and constructive emergency review of our paper. We have comprehensively revised our manuscript based on your feedback.

1. On the "Counter-intuitive" Dynamics of MEEs (in response to Weakness 1)

You have raised an insightful question: why would an MEE, which is "easy" (low loss) in the early stages, exhibit "high loss" and "high confidence" later in training?

This seemingly counterintuitive behavior is at the core of our Early Cutting method (detailed in section2.2 and section3) and can be explained by the dynamic evolution of the model's representation power as training progresses.

• Early Stage (Learning Simple Patterns): At the beginning of training, a deep model prioritizes learning the most salient and easily distinguishable patterns. A typical MEE (e.g., an image of a ship on a vast blue ocean, mislabeled as airplane) possesses superficial features (like a large blue background resembling the sky) that align well with its incorrect label. Consequently, the early-stage model quickly learns to classify this sample as "airplane," resulting in a low loss, and the sample is thus considered "easy".

• Later Stage (Learning Semantic Representations): As training continues, the model is exposed to thousands of true examples of both "airplanes" and "ships". Its feature extractor becomes far more powerful, learning to understand deeper semantic concepts like object contours, textures, and structures. While the model's overall generalization may start to degrade due to the noisy labels, its fundamental representation power continues to strengthen (than model in the early-stage).

• The Shift: When this more mature, later-stage model re-encounters the same MEE, its powerful classifier now confidently predicts the correct label, "ship". However, the sample's given label is still "airplane". The loss is computed by comparing the model's high-confidence prediction ("ship") against the given incorrect label ("airplane"), which naturally results in a high loss value.

To make this dynamic process more intuitive, and in line with your suggestion, we will add a new set of t-SNE visualizations in the appendix to illustrate the feature space evolution at different training stages.

2. Clarifications on Experimental Settings and Baseline Results

2.1. On the Performance Discrepancy of the CSGN Baseline (in response to Weakness 3)

You correctly observed a performance gap for the CSGN baseline. This was an intentional result of our experimental design aimed at ensuring fair comparisons. To clarify: the higher accuracy reported in the original CSGN paper is the result of their algorithmic pipeline, which includes different backbones (e.g., PreAct ResNet, Inception-ResNet-v2) and advanced modules like semi-supervised learning. In our main experiments (Tables 2-5), we re-implemented all baselines under a unified supervised learning framework. This includes using the same backbone, hyperparameters, and components for all methods to ensure an apples-to-apples comparison. This design ensures that any reported performance differences are attributable to the core noise-handling strategy itself.

Dear Reviewer 99k4 and Area Chair,

We sincerely thank you for your prompt and constructive emergency review, which provides valuable guidance for further improving our manuscript. We have formulated a detailed plan for revisions and supplementary experiments based on your questions and suggestions, which we outline below.

1. On Evaluating with Instance-Dependent Noise on ImageNet (in response to Q1)

First, we would like to humbly note the practical reason we did not initially include an experiment with instance-dependent noise on the full ImageNet-1k dataset (only include Symmetric label noise). Standard protocols [1, 2] for generating this noise type on ImageNet-1k require hundreds/thousands of gigabytes of memory; our attempts failed even after allocating 512GB of virtual memory (swap).

However, we fully agree with your point that demonstrating performance under large-scale corruption scenarios is important. While we included the large-scale, real-world WebVision experiment as an evaluation, your suggestion to use a subset of ImageNet is excellent. Given the time constraints of the rebuttal period, we commit to supplementing our paper with this experiment on a large subset of ImageNet (should be much larger than Tiny ImageNet) to validate our method’s effectiveness under these conditions.

2. On the Choice of Thresholds (in response to Q2)

Our initial thresholds were determined empirically on a held-out validation set, which is standard practice in machine learning. However, we wish to emphasize that the success of our method is not contingent on these precise values. As shown in the sensitivity analysis in Figure 5, the method’s performance remains highly stable across a wide range of threshold values. This demonstrates the robustness of our combined criteria and explains why a single, fixed set of thresholds can be effective across multiple different datasets and noise settings. We will add this clarification to Section 3 of the revised manuscript.

3. On the Number of Experimental Trials (in response to Q3)

For all experiments reporting mean±std, the results are the average and standard deviation over three trials with different random seeds. We have now explicitly added this information to our experimental setup section in the revised paper.

4. Addressing Weaknesses and Planned Revisions

We agree entirely with the weaknesses you identified and have already addressed them in our revised manuscript:

• Language Issues: Thank you for pointing out the blemishes in our writing. We have conducted a thorough proofread of the entire manuscript to correct the issues you mentioned and other grammatical errors.
• Limitations Section: We have added a new Section 6: Limitations. In this section, we discuss potential failure modes of the method, potential performance and fairness concerns on long-tailed or extremely sparse datasets, and the computational and memory overhead involved.
• Figure Readability: We greatly appreciate your feedback on figure readability. Acknowledging the nine-page limit requires making certain trade-offs. Following your excellent suggestion, we have moved the CIFAR-100 results from Figures 2 and 3 to the appendix. This allowing improvement of the clarity of the main-text figures and frees up space, which we have used to enhance the rigor and completeness of the methodology in Section 3.

Thank you once again for your valuable suggestions for our work.

Best regards,

Authors

Reference:

[1] Part-dependent label noise: Towards instance-dependent label noise, NeurIPS 2020.

[2] Estimating Instance-dependent Bayes-label Transition Matrix using a Deep Neural Network, ICML 2022.

Dear Reviewer Q7UE and Area Chair,

We sincerely thank you for providing such a prompt, detailed, and constructive emergency review for our paper. We deeply appreciate the time and expertise you have dedicated to our work.

We have comprehensively revised our manuscript based on your feedback. Below, we provide a point-by-point response to each of your questions and concerns.

1. Strengthening the Core Concept

1.1. Quantitative Analysis of MEE Harm with Influence Functions (in response to Q1)

Following your excellent suggestion, we have conducted a new quantitative analysis using influence functions to more directly measure the harm caused by MEEs. Specifically, we use influence functions to calculate the impact score of different training samples on a clean, held-out validation set.

This analysis parallels the experiment in Figure 2, comparing three sample categories: (1) MEEs (the first 4,000 mislabeled samples learned during training); (2) Clean Easy Examples (the first 4,000 clean samples learned); and (3) Mislabeled Hard Examples (the last 4,000 mislabeled samples learned). We used the pytorch_influence_functions library on CIFAR-10 with 40% instance-dependent noise. The results are as follows:

These results provide direct, quantitative proof of our claim: while all mislabeled examples are harmful (positive influence scores), the average harm of MEEs is over 60% greater than that of Mislabeled Hard Examples (4.96 vs. 3.01). This demonstrates at a microscopic level that MEEs are far more detrimental to the model. In contrast, the negative influence score of Clean Easy Examples (-2.22) confirms their beneficial impact.

The full version of this new analysis will be added to the appendix, and we will reference it in Section 2 to further substantiate our claims about the unique harm of MEEs.

1.2. Theoretical Grounding of the Gradient Criterion (in response to Q3)

Thank you for pushing us to better situate our gradient criterion within the literature. We have now added citations and discussion in the Related Work and Methodology (Section 3) sections, connecting our work to Variance of Gradients (VoG) [1], Input-output Jacobian Norm [2], and Sharpness-Aware Minimization (SAM) [3]. In brief:

VoG uses temporal variance over training to identify "hard-to-memorize" samples. We use local input sensitivity at a later training stage to identify samples that are "easily and stably mislearned". The two criteria focus on different dimensions (time vs. input space) and training phases, making them complementary. When the model is highly confident in a wrong class, the loss gradient w.r.t. the input, $\|\nabla_x \ell\|$, is dominated by the input-output Jacobian norm. A small $\|\nabla_x \ell\|$ thus indicates that the model's incorrect prediction is insensitive to perturbations in the input neighborhood (a "bad" flat minimum). SAM seeks "good" flat minima in the parameter space to improve generalization. Our criterion measures sample-wise flatness in the input space to identify stability in incorrect predictions. The two concepts are therefore complementary.

We have also further clarified that the "low input gradient norm" is not a standalone filter but a refinement step. It is only applied to the subset of early-learned samples that already meet the "high loss + confident-and-wrong" criteria, allowing us to distinguish stably mis-memorized MEEs from truly clean but hard examples.

2. Exploring Generality

2.1. Applying Early Cutting to Loss-Based Methods (in response to Q4)

To demonstrate that Early Cutting is a general principle, we applied it to a confident set selected by the classic "small-loss trick". On CIFAR-10 with 40% instance-dependent noise, we first selected ~60% of the training data using the small-loss criterion. We then compared the final test accuracy after retraining on this set, with and without an additional Early Cutting step.

The results show that Early Cutting successfully improves the performance of a loss-based selection method, confirming its modularity. Regarding Co-teaching, we humbly discuss a direct application is inappropriate, as our method's core idea, using a "less reliable" later-stage model to clean up a "more reliable" early-learned set, does not align with the dual-network, peer-teaching dynamic of Co-teaching.

2.2. Exploring Applicability Across Domains and Tasks (in response to Q2)

We have added a new appendix section (B.11) to discuss the potential translation of our concepts to other domains, as you suggested. We provide some conceptual examples, in brief: In NLP, an MEE could be a text with strong, misleading keywords. For instance, a sarcastic positive review like "Wow, I can't believe how awful the service was" being mislabeled as "Positive". A model might quickly learn this incorrect association due to "Wow" and "can't believe". The Early Cutting criteria could be adapted by using the gradient norm of input word embeddings. In regression, an MEE could be a data point where a feature has a strong local linear relationship with the target value, but this relationship is globally spurious. The model would fit this pattern early on. Our criteria (high loss, high confidence in a different value range, and stable gradients) could be conceptually adapted.

3. Methodological Details

3.1. Precision Analysis of MEE Removal (in response to Q5)

Thank you for this question. The data is included in the last row of Table 1 (Additional Samples Filtered...). To make this clearer, we present the absolute numbers of "truly mislabeled" vs. "clean but removed (false positives)" for the samples filtered by Early Cutting:

3.2. Further Rationale on Thresholds and the "Later Stage" (in response to Q6 & Weakness 6)

On Percentile Thresholds: Our initial percentile values were determined empirically on a held-out validation set, which is standard practice. However, our core argument is that the method's success is not contingent on these exact values. As the sensitivity analysis in Figure 5 shows, performance is highly stable across a wide range of thresholds.

We agree that the optimal thresholds may correlate with the noise rate, this is a good idea for optimal performance. Given the time constraints in emergency reviewing, we commit to adding an experiment exploring this relationship in the appendix. We note, however, that our fixed thresholds already achieve strong performance across all reported noise rates, although it may not be the best.

On Determining the "Later Stage": You raised a point about identifying the early stopping epoch without a clean validation set. We wish to clarify that this is a solvable problem. As detailed in a research [4], the early stopping point in LNL can be accurately determined by monitoring training dynamics on the noisy validation set or by observing changes in the model's "fitting performance" on training set, thus making our approach practical in real-world scenarios.

4. Revisions to Presentation and Limitations

Finally, we will adopt all of your presentation suggestions and add a comprehensive Limitations section.

• Limitations Section: We have freed up space by streamlining Section 2 and have now included a detailed Limitations section in the main paper. It discusses: (1) scope being limited to visual classification, (2) the empirical nature of the MEE harm justification, (3) computational overhead, and (4) potential risks in extreme noise or imbalanced data scenarios.
• Presentation: We will more explicitly link the ViT results in the main text. We will also replace the red/green colors in Figure 4a with a colorblind-friendly palette (#5cb6ea and #e5a11c). We believe that improving the accessibility of every paper is important for promoting fairness and inclusion in the community. We have previously reviewed grayscale images to make the color palette of line graphs friendly to everyone. However, we overlooked the dot graphs such as Figure 4a that you pointed out. We thank you for this thoughtful suggestion.

Once again, we extend our sincerest gratitude for your constructive and prompt review.

Best regards,

Authors

Reference:

[1] Estimating Example Difficulty using Variance of Gradients, CVPR 2022.

[2] Sensitivity and Generalization in Neural Networks, ICLR 2018.

[3] Sharpness-aware minimization for efficiently improving generalization, ICLR 2021.

[4] Early Stopping Against Label Noise Without Validation Data, ICLR 2024.