CSOT: Curriculum and Structure-Aware Optimal Transport for Learning with Noisy Labels

Learning with noisy labels (LNL) poses a significant challenge in training a well-generalized model while avoiding overfitting to corrupted labels. Recent advances have achieved impressive performance by identifying clean labels and correcting corrupted labels for training. However, the current approaches rely heavily on the model's predictions and evaluate each sample independently without considering either the global and local structure of the sample distribution. These limitations typically result in a suboptimal solution for the identification and correction processes, which eventually leads to models overfitting to incorrect labels. In this paper, we propose a novel optimal transport (OT) formulation, called Curriculum and Structure-aware Optimal Transport (CSOT). CSOT concurrently considers the inter- and intra-distribution structure of the samples to construct a robust denoising and relabeling allocator. During the training process, the allocator incrementally assigns reliable labels to a fraction of the samples with the highest confidence. These labels have both global discriminability and local coherence. Notably, CSOT is a new OT formulation with a nonconvex objective function and curriculum constraints, so it is not directly compatible with classical OT solvers. Here, we develop a lightspeed computational method that involves a scaling iteration within a generalized conditional gradient framework to solve CSOT efficiently. Extensive experiments demonstrate the superiority of our method over the current state-of-the-arts in LNL. Code is available at https://github.com/changwxx/CSOT-for-LNL.

Paper

References (87)

Scroll for more · 38 remaining

Similar papers

Peer review

Reviewer 7s926/10 · confidence 5/52023-07-02

Summary

The paper studies the problem of noisy label learning. The paper adopts an optimal transport approach to generate pseudo labels for noisy samples. Particularly, the paper builds on the existing method and adds additional regularization terms to enforce the consistency between sample classes and learned representations. The paper also extends the sinkhorn algorithm to solve the proposed OT objective efficiently. Empirically, the proposed method has improved performance over baselines on widely used datasets with various noisy ratios.

Strengths

1. The paper extends the existing optimal transport approach to include the consistency between the sample representations and predictions/labels. It is a novel objective and a solid idea intuitively. 2. The paper extends the sinkhorn algorithm to solve the proposed new OT objective efficiently. 3. The proposed method has strong empirical performance, especially for high noise ratios. 4. As a pseudo-labeling step, the proposed method can potentially work with other noisy label learning objectives.

Weaknesses

1. The proposed method is a regularization of the existing optimal transport pseudo-labeling method. The novelty is thus limited. 2. The introduced regularization uses the same weight kappa for the two terms, while the two terms could have quite different behaviors/values. 3. It is not clear to me how does the method perform or should be modified in the case where the class distribution is imbalanced. 4. The OT objective is not directly related to the training objective but serves as a sieving step. It would be great if a more comprehensive training objective can be formalized to include the OT based selection.

Questions

1. Please address the weaknesses 2 3 and 4. 2. What's an explanation for the experimental results that the given method does better in top-1 ACC but worse in top-5 for the imagenet and webvision datasets? 3. The global relationship modeled by OT depends on the batch size. How does the batch size affect the empirical performance? How does the number of total classes in the training set affect the choice of the ideal batch size for the OT step?

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

5: You are absolutely certain about your assessment. You are very familiar with the related work and checked the math/other details carefully.

Soundness

3 good

Presentation

4 excellent

Contribution

3 good

Limitations

Yes.

Reviewer Zh5c5/10 · confidence 3/52023-07-05

Summary

This paper introduces a novel formulation of Optimal Transport (OT), named Curriculum and Structure-Aware Optimal Transport, for generating pseudo labels by considering both inter- and intra-distribution structures of samples. Moreover, to efficiently estimate the distribution's structure, the authors adopt a curriculum paradigm to progressively train the proposed denoising and relabeling allocator. Additionally, they present a computation method for the proposed CSOT that ensures faster processing speeds, reducing computational overhead. Experimentally, this paper achieved SOTA performance on various benchmarks.

Strengths

1.Estimating the intra- and inter-structure coherence of samples is a convincing and reliable method for improving relabeling accuracy. The proposed prediction-level and label-level consistency constraints seem also interesting and plausible. 2.The combination of the proposed OT and curriculum learning for solving INL is also smooth and makes sense.

Weaknesses

1.The effectiveness for alignment of global and local structures between samples and classes is not fully convincing. The ablation results for OT in Table 3 seem weak. The comparison between row (a) with 78.07 and row (b) with 78.65 suggests that the performance improvement brought by the proposed prediction-level and label-level constraints is limited. Moreover, the introduction of two additional constraints adds complexity to the optimization. Similarly, row (e), CSOT w/o Ω^{L}, achieves the best performance, indicating that the benefits brought by the prediction-level and label-level constraints are unstable. 2.As the part that readers are most concerned about, the section 4.3, the loss function needs to be able to reflect the integrity of the method and the specific combination with its own innovation points. I can’t see the innovation of this article in the loss function here, and each loss term is an existing work. The work in this paper seems to be only used to build a dataset $\mathcal{D}_{\text{clean}}$ and $\mathcal{D}_{\text{corrupted}}$ for training? This structure and method of writing can greatly weaken the contribution of this paper. Besides, I would like to suggest the authors provide an overall alghrothim to show the whole training process, where the proposed methods would have been used during each training epoch and the training objectives are not the key point in this paper. 3.Considering the complexity of the proposed algorithm, and its marginal improvement over previous methods on two real datasets in Table 2, especially compared to NCE. The effectiveness of this work is questionable. Additional experiments are suggested, especially on Clothing1M. Besides, some related works[1] should be discussed which are published recently. [1] OT-Filter: An Optimal Transport Filter for Learning with Noisy Labels (CVPR 2023) 4.The results of row (g) in Table 3 are not sufficient to show that the performance improvement is brought about by the method in this paper. For example, we need a more detailed ablation study to explain the role of NCE loss and the role of CSOT. 5.The structure of the article is confusing, which weakens the contribution of this article. Secondly, the introduction of some tool concepts is quite abrupt. For example, the proposal of Eq. (3) and (6) gives people a new form of OT formulation and will give specific solutions later. This expectation is affected by the entropy regularization in the following text, whose introduction is abrupt. This results in the final Eq. (16) which does not look significantly different from the original sinkhorn algorithm. It is recommended to introduce sinkhorn from the beginning and to emphasize that there are new constraints based on it. 6.The characters in the figures in the experimental part are too small, which affects reading. At the same time, why are there two figures, and their labels are figure 2? Moreover, Fig. 4 is quoted in the description of the text, but there is no figure 4 in fact.

Questions

1.For more precision, I would like to suggest providing a more detailed description of Equation (6). What does the left constraint in Equation (6) signify? Why should $Q\mathbb{1}_{C}$ not exceed $\frac{1}{B}\mathbb{1}_{B}$? Furthermore, it seems that $\frac{m}{c}\mathbb{1}_{C}$ is not a simplex. Could you please explain the rationale behind this relationship and provide additional descriptions or citations to support it? Additionally, the introduction of curriculum into SOT appears to be too direct and lacks smoothness. 2.The identification of selected samples in Equation (7) is confusing. What does "topK(W,⌊mB⌋)" mean? Based on my understanding, it implies that a sample pair (x_i, y_i) will be considered clean if it belongs to the top k convincing samples in the current training batch. I would suggest adding a description for the round-down symbol ⌊ and ⌋ to clarify its purpose.

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

2 fair

Contribution

3 good

Limitations

The authors describe its limitations.

Authorsrebuttal2023-08-18

Thanks for your valuable comments and suggestions. We greatly appreciate your time and effort in reviewing our work. We have carefully considered each of your concerns and have made the necessary revisions to address them. We sincerely hope that our responses have adequately addressed the concerns raised in your review. Please feel free to let us know if you have any further questions. We are dedicated to further clarifying and addressing any remaining issues to the best of our ability.

Reviewer ZdDn6/10 · confidence 4/52023-07-05

Summary

This paper introduces CSOT, an approach to address the challenge of noisy labels in machine learning models. CSOT incorporates optimal transport formulation to assign reliable labels during training, considering the structure of the sample distribution. The authors also propose an efficient computational method for solving CSOT. Experimental results demonstrate the superior performance of CSOT compared to existing methods for learning with noisy labels.

Strengths

- The paper is strongly motivated by theoretical analysis, particularly optimal transport analysis. - The writing style is clear and easy to follow. - CSOT exhibits superior performance when compared to previous algorithms.

Weaknesses

- The paper lacks a comparison with a baseline algorithm called UNICON [1], which has shown good performance in highly noisy scenarios (e.g., 0.9 noisy ratio). It would be valuable for the authors to include a performance comparison with UNICON. - The authors do not analyze the case of instance-wise noisy labels, which is a prevalent type of noisy label model. Including an analysis of this case would be beneficial. - The paper does not investigate the sensitivity of hyperparameters, which are required to run the algorithm. It would be valuable for the authors to perform a hyperparameter sensitivity analysis. - To enable a comprehensive comparison, the authors should report both the best and last performances of the model, as models trained on noisy labels tend to memorize the noisy labels. [1] UNICON: Combating Label Noise Through Uniform Selection and Contrastive Learning Minor) The legend size in Figure 2 is too small to read.

Questions

-

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

3 good

Presentation

2 fair

Contribution

3 good

Limitations

The limitations of this paper are summarized in the "Question" and "Weakness" sections ------ (Raise score from 5 to 6 after rebuttal)

Reviewer gpRK7/10 · confidence 5/52023-07-05

Summary

This paper proposes a novel optimal transport formulation, called Curriculum and Structure-aware Optimal Transport (CSOT) for learning with noisy labels. CSOT considers both the inter- and intra-distribution structure of the samples to construct a robust denoising and relabeling allocator. It’s worthing noting that Notably, CSOT is a new OT formulation with a nonconvex objective function and curriculum constraints. The authors developed a lightspeed computational method that involves a scaling iteration within a generalized conditional gradient framework to solve CSOT efficiently.

Strengths

1. Novel Approach: The paper proposes a novel optimal transport (OT) formulation called Curriculum and Structure-aware Optimal Transport (CSOT) to address the challenge of learning with noisy labels. I believe this paper introduces a new perspective and potentially brings fresh insights to the field. 2. Consideration of Global and Local Structure: Unlike current approaches that evaluate each sample independently, CSOT concurrently considers the inter- and intra-distribution structure of the samples. This consideration of both global and local structure helps construct a more robust denoising and relabeling allocator, potentially leading to improved performance. 3. Incremental Assignment of Reliable Labels: CSOT incrementally assigns reliable labels to a fraction of the samples with the highest confidence during the training process. This approach ensures that the assigned labels have both global discriminability and local coherence, which could contribute to better generalization and reduced overfitting. 4. This paper provides a very detailed derivation for the lightspeed computational method.

Weaknesses

Researchers or practitioners interested in using CSOT may need to invest additional effort in adapting or developing specialized solvers.

Questions

1. How does CSOT incorporate the global and local structure of the sample distribution? Could you provide more details on the methodology used to capture this information? 2. Can you explain in more detail the nonconvex objective function of CSOT? How does the nonconvexity affect the optimization process, and how does the proposed method handle this challenge? 3. What is the iteration number required by the generalized conditional gradient? 4. Are there any specific scenarios or types of noisy labels where CSOT may not perform as well?

Rating

7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.

Confidence

5: You are absolutely certain about your assessment. You are very familiar with the related work and checked the math/other details carefully.

Soundness

4 excellent

Presentation

3 good

Contribution

4 excellent

Limitations

CSOT is described as having a nonconvex objective function. Nonconvex optimization problems can be challenging to solve, and they may have multiple local optima, making it difficult to guarantee finding the global optimum. This could potentially impact the reliability and efficiency of the proposed method.

Reviewer qnim5/10 · confidence 3/52023-07-12

Summary

This paper proposes a new noisy label learning approach based on Optimal Transport (OT) and Pseudo-Labeling (PL). Specifically, the authors extent OT-based PL with the consideration of the intrinsic coherence structure of sample distribution. Consequently, this paper proposes a novel optimal transport formulation, namely Curriculum and Structure-aware Optimal Transport (CSOT), which constructs a robust denoising and relabeling allocator that mitigates error accumulation. Experiments on both controlled and real noisy label datasets show the effectiveness of the proposed method.

Strengths

1. The paper proposes a method named Curriculum and Structure-aware Optimal Transport (CSOT) to address the problem of noisy label learning, and the application of OT-based pseudo-labeling in tackling noisy label learning problem has not been thoroughly investigated. 2. The experimental results on different datasets in this paper validate the effectiveness of the proposed method. Additionally, several ablation experiments are conducted to demonstrate the effectiveness of each module in the method.

Weaknesses

1. In terms of methodological novelty, OT-based PL has been previously applied to other problems, and this paper only applies it to the specific problem namely noisy label learning rather than introducing it for the first time. Additionally, employing curriculum learning to address the issue of pseudo-labeling is a common strategy in the field of weakly supervised learning. 2. The utilization of SOT is a key contribution of this paper. However, the current motivation behind this aspect, as presented in Figure 1, is not sufficiently clear. The authors are encouraged to provide additional descriptions in this section to enhance the clarity and understanding of the motivation. 3. Since the differences between the proposed method and the comparison methods in several cases is too small, it is hard to provide a clear comparison without the present of standard deviations. Additionally, the backbone and other parameter settings of the SOTA methods are not clearly listed, thus, further evidence is needed to establish the fairness of the comparisons.

Questions

Please refer to Weaknesses

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

N/A.

Reviewer ZdDn2023-08-17

Official Comments and decision.

Thank you for your detail responses. I have read the responses from the authors to the questions I raised (including other reviewers' comments and responses). I would like to raise the score from 5 to 6.

Reviewer 7s922023-08-19

Thanks for the authors' reply. I keep my score unchanged.

Reviewer Zh5c2023-08-22

Response to Rebuttal

Thanks for the authors' reply. I increase my score to 5.

Reviewer qnim2023-08-22

Thanks for the responses

Thank you for your responses. Your explanation has clarified some of the previous concerns. However, I still believe that this paper offers limited contributions to the current field of learning with label noise. Therefore, I will maintain my current score.

Program Chairsdecision2023-09-21

Decision

Accept (poster)

© 2026 NYSGPT2525 LLC