Pith. sign in

REVIEW 3 major objections 5 minor 63 references

$\epsilon$-Softmax: Approximating One-Hot Vectors for Mitigating Label Noise

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper claims that a simple softmax modification — adding a constant to the largest class probability before renormalizing — lets almost any loss function tolerate asymmetric label noise, with an excess-risk bound that shrinks as the…

desk verdict Neat activation trick with strong experiments, but the central noise-tolerance theorem doesn't apply to the CE and FL losses the paper actually uses. read the letter →

arxiv 2508.02387 v1 pith:5QSDV3MN submitted 2025-08-04 cs.LG cs.CV

Jialiang Wang , Xiong Zhou , Deming Zhai , Junjun Jiang , Xiangyang Ji , Xianming Liu This is my paper · ORCID
classification cs.LGcs.CV
keywords labelnoiserobustlossfunctionsepsilon-softmaxone-hotapproximationtoleranceexcessriskboundall-kconsistencyasymmetric
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes replacing the standard softmax layer with $\epsilon$-softmax, which nudges prediction vectors toward one-hot vectors by a controlled amount. It argues that, under a mild continuity condition, this makes almost any loss function noise-tolerant under symmetric and asymmetric label noise, with an explicit excess-risk bound that vanishes as the approximation tightens. A reader would care because noisy labels are common in practice, and this is essentially a two-line, plug-and-play modification that can be applied to an existing classifier without designing a new loss. The paper also proves All-k consistency for the cross-entropy loss combined with $\epsilon$-softmax, and shows experimentally that blending it with MAE yields top accuracy on synthetic, human-annotated, and web-scale noisy datasets.

What carries the argument

The key object is the $\epsilon$-softmax layer: it takes the usual softmax probabilities $p$, adds $m$ to the component with the largest value, and divides by $m+1$. This forces every output into an $\epsilon$-relaxation of the one-hot vectors, where $\epsilon = \sqrt{1-1/K}/(m+1)$, so the hypothesis class becomes approximately constant across class labels. That approximate symmetry is what lets the excess-risk bound in Theorem 1 hold, turning robustness into a property of the layer rather than of a specially designed loss. The layer also rescales the cross-entropy gradient by $p_y/(p_y+m)$ when the predicted class is correct, which slows learning on already-confident examples and acts like a soft early-stopping mechanism against memorizing noisy labels.

What would settle it

Take two predictions $u_1, u_2$ within Euclidean distance $\epsilon$ of the same one-hot vector for the cross-entropy or focal loss and compute $|\sum_{k=1}^K (L(u_1,k) - L(u_2,k))|$; if, as $u$ approaches the simplex boundary, this quantity does not shrink to zero — for cross-entropy it instead diverges — then the excess-risk bound of Theorem 1 does not apply to the paper's central examples.

Watch

Extended reading notes

Core claim

The central claim is that $\epsilon$-softmax provides a controllable approximation to one-hot vectors: after standard softmax, it adds $m$ to the largest probability and renormalizes, giving distance at most $\epsilon = \sqrt{1-1/K}/(m+1)$ from the set of one-hot vectors. Within this constrained hypothesis class, Theorem 1 bounds the clean-label excess risk of the noisy-risk minimizer by $2\delta + 2c\delta/a$ under asymmetric label noise whenever the loss satisfies the stated $\delta$-condition. Thus, the paper argues, any loss can be made noise-tolerant as $m \to \infty$, and the cross-entropy loss with $\epsilon$-softmax is All-k consistent, meaning its minimizer achieves Bayes optimal top-$k$ error for every $k$. The practical instantiation $CE_{\epsilon}+MAE$ combines this robustness with the fitting ability of MAE and achieves the best reported accuracies in the paper's experiments.

Load-bearing premise

The excess-risk theorem depends on a $\delta$-condition: the sum over classes of the loss must be nearly constant for predictions within $\epsilon$ of a one-hot vector, with the discrepancy $\delta$ shrinking to zero as $\epsilon$ does, and the paper does not show that this holds for the cross-entropy or focal losses it actually uses.

Editorial extensions

If this is right

  • Under the theorem, training with $CE_{\epsilon}$ or $FL_{\epsilon}$ at large $m$ gives a clean-label risk close to the Bayes risk even when labels are corrupted asymmetrically, so standard losses no longer need to be replaced by specially designed robust losses.
  • $CE_{\epsilon}$ is All-k consistent, so its global minimizer achieves Bayes optimal top-$k$ error for every $k$, extending the usual top-1 consistency guarantee.
  • Adding a symmetric loss like MAE to $CE_{\epsilon}$ leaves the excess-risk bound unchanged (Lemma 3), while restoring the fitting ability that the one-hot constraint removes.
  • Across CIFAR-10/100 with symmetric, asymmetric, and instance-dependent noise, $CE_{\epsilon}+MAE$ and $FL_{\epsilon}+MAE$ rank among the top methods, and on WebVision, ILSVRC12, and Clothing1M they reach the best accuracy reported in the paper.
  • Because the modification is a standalone layer, it can be inserted into any softmax-based classifier without changing the training pipeline beyond two lines of code.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • One extension the paper leaves implicit is annealing $m$ over training: small $m$ fits clean samples early, while large $m$ suppresses memorization later, which would likely improve the clean-versus-noisy trade-off beyond fixed $m$ settings.
  • Because $\epsilon$-softmax is a generic layer, it could be dropped into other pipelines that end in a softmax, such as knowledge distillation or language-model alignment, wherever noisy supervision is a concern.
  • The paper does not verify Theorem 1's $\delta$-condition for the cross-entropy and focal losses it actually uses; for cross-entropy, $\sum_k \log u_k$ diverges near the simplex boundary, so checking whether that condition holds, or replacing it with a condition the losses satisfy, is the natural next step.
  • The All-k consistency result suggests that $\epsilon$-softmax may be particularly useful in extreme classification settings where top-$k$ accuracy, rather than top-1 accuracy, is the evaluation metric.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes ε-softmax, a modification of the softmax layer that adds a constant m to the largest predicted probability and renormalizes, so that outputs lie within L2 distance ε = sqrt(1 - 1/K)/(m + 1) of a one-hot vector. The main theoretical claim is that this constrained output class makes almost any loss approximately symmetric, leading to an excess-risk bound under asymmetric label noise (Theorem 1), and that CE_ε is All-k consistent (Lemma 2 and Theorem 2). The authors combine CE_ε or FL_ε with MAE and report strong accuracy on CIFAR-10/100 synthetic noise, CIFAR-10N/100N, WebVision/ILSVRC12, and Clothing1M, with code and hyperparameters provided.

Significance. The proposed module is extremely simple and the experimental evaluation is broad: standard synthetic benchmarks, human-annotated noise, and large real-world noisy datasets, with multiple seeds and error bars. If the theoretical guarantees were valid, the 'almost any loss' statement would be a substantial generalization of prior symmetric-loss results. However, the central theorem does not apply to the losses actually used, and the consistency proofs are not rigorous; in its current form the theoretical contribution does not support the paper's main claims.

major comments (3)
  1. [§3.1, Theorem 1 (Eq. 3.2)] The δ-condition in Theorem 1 is not satisfied by the losses used in the paper. For the cross-entropy loss, define S(u) = Σ_{k=1}^K -log u_k. Even in the binary case, take u = (1-a, a) and v = (1-ε, ε) with 0 < a < ε; both lie in H_{e1,ε} for fixed ε, yet |S(u) - S(v)| = |log(ε/a)| → ∞ as a → 0. Hence no finite δ exists for fixed ε, so the requirement δ → 0 as ε → 0 is vacuous for CE_ε. The same divergence occurs for FL_ε, whose per-label terms -(1-u_k)^γ log u_k are unbounded as u_k → 0. The proof of Theorem 1 also relies on L(f*(x), k) = C/(K-1) for k ≠ y, a relation that is false for CE at a one-hot vector, where those terms are infinite. Therefore the central robustness guarantee does not apply to the two losses, CE_ε and FL_ε, for which the paper claims noise tolerance.
  2. [Appendix B, Lemma 2] The proof of Lemma 2 equates a first-order condition with global optimality. Setting ∂L_CEε(f(x), y)/∂h(y|x) = 0 and concluding p_y = 1 does not show that the resulting point minimizes the risk, and the proof checks only one coordinate of the gradient. No convexity argument or verification of the calibration inequality in Definition 2 (Eq. 3.3) is provided. Since Lemma 2 and Theorem 2 are the basis for the All-k consistency claims in Section 3.2 and Table 1, these claims are not established.
  3. [§3.1, abstract] The claim that ε-softmax achieves 'noise-tolerant learning with controllable excess risk bound for almost any loss function' is not supported by the stated theorem. Theorem 1 requires a uniform δ-condition over pairs in H_{v,ε}, and many standard losses (CE, FL) fail this condition; the paper never verifies it for a loss actually used in the experiments. The quantifier 'almost any loss' should be replaced by a precise statement of the loss class for which the condition holds, and the theorem should be instantiated with a concrete δ for each proposed loss.
minor comments (5)
  1. [Appendix A] There are typos: 'var the negative Box-Cox transformation' should be 'via', and 'cimparing' and 'comparetion' should be 'comparing' and 'comparison'.
  2. [Appendix B, Lemma 2 proof] The symbol e_k is used without definition; it should be defined as the k-th coordinate vector of the one-hot label.
  3. [Table 1] Table 1 appears to have an empty 'All-k Consistency' row; if check/cross symbols are intended, they should be included in the rendered version.
  4. [Appendix C] In the algorithm details, T_robust is set to both 65 and 300; the second value is presumably the total number of epochs and should be given a distinct name.
  5. [§3.4] The statement that CE and CE_ε are 'strictly convex' is made with respect to p_y only; as a statement about functions of the logits it needs qualification.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the theoretical derivation is self-contained, though Theorem 1's delta-condition is unverified for CE/FL, which is a correctness gap rather than a circular step.

full rationale

The derivation chain does not reduce to its own inputs. Lemma 1 computes the one-hot approximation error of epsilon-softmax directly from the operation f=(p+m e_t)/(m+1), giving epsilon = sqrt(1-1/K)/(m+1); this is a direct calculation, not a restatement of the target result. Theorem 1 is an excess-risk bound proved in Appendix B under an explicit delta-condition (|Sigma_k (L(u1,k)-L(u2,k))| <= delta when ||u1-u2||_2 <= epsilon), and the bound is expressed in terms of delta, c, and a without fitting or renaming. The proof is self-contained and does not depend on the authors' prior work [14]; that citation is used only as motivation and as a pointer to a symmetric-noise precursor. The consistency results in Lemmas 2-3 and Theorem 2 use external calibration-to-consistency results from Yang-Koyejo [17] and Zhu et al. [8], not self-citations. Hyperparameters m, alpha, beta are tuned per dataset and noise setting and reported as empirical results, not relabeled as theoretical predictions. The main rigor concern is that the paper never verifies Theorem 1's delta-condition for CE_epsilon or FL_epsilon, and for CE/FL the sum Sigma_k L(u,k) diverges on H_{e1,epsilon}, so the theorem's guarantee is vacuous for the paper's own losses. That is a correctness gap, not a circularity: the theorem does not assume what it proves, and the failure is a missing verification of an explicit hypothesis.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central result relies on a stability condition that is not true for cross-entropy, plus a separability assumption that is strong. The method introduces hyperparameters m, α, β that are extensively tuned per experiment. No new physical or mathematical entities are postulated.

free parameters (3)
  • m = 1e2 to 1e6 (e.g., 1e5 for CIFAR-10 symmetric, 1e3 for WebVision)
    Controls the one-hot approximation error. Chosen separately for each dataset and noise type, and its optimal value changes sharply with noise structure (Table 3).
  • alpha = e.g., 0.01, 0.05, 0.0075, 0.015 depending on dataset/noise rate
    Weight of the CEϵ term in CEϵ+MAE; tuned per noise rate and dataset in Appendix D.
  • beta = 1 or 5
    Weight of the MAE term; set per experiment.
assumptions (4)
  • ad hoc to paper The loss L satisfies |Σ_k (L(u1,k)-L(u2,k))| ≤ δ whenever ||u1-u2||₂ ≤ ε, with δ→0 as ε→0.
    Invoked in Theorem 1 but not verified for CE or CEϵ. For cross-entropy, Σ_k -log u_k diverges near the one-hot boundary, so the condition is false.
  • domain assumption The clean risk of the optimal classifier is zero: RL(f*)=0.
    Assumed in Theorem 1 (stated as 'if RL(f*) = 0'). Only holds for separable clean data, unrealistic for most real benchmarks.
  • ad hoc to paper First-order optimality conditions are sufficient to identify the global minimizer in the calibration proofs.
    In Lemma 2, the proof sets derivatives to zero and concludes p_y=1, but does not establish global optimality, and in the t≠y branch the conclusion contradicts the branch condition.
  • standard math Existing All-k calibration and consistency theorems from [17,8] are correct and applicable.
    Used as building blocks for Lemma 2 and Theorem 2.

how reviews work

0 comments
Cite this review

Pith. "Pith review of $\epsilon$-Softmax: Approximating One-Hot Vectors for Mitigating Label Noise." pith.science (2026). https://pith.science/paper/5QSDV3MN

@misc{pith2026250802387,
  author       = {Pith},
  title        = {Pith review of: $\epsilon$-Softmax: Approximating One-Hot Vectors for Mitigating Label Noise},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5QSDV3MN}},
  note         = {Machine review of arXiv:2508.02387}
}
abstract

Noisy labels pose a common challenge for training accurate deep neural networks. To mitigate label noise, prior studies have proposed various robust loss functions to achieve noise tolerance in the presence of label noise, particularly symmetric losses. However, they usually suffer from the underfitting issue due to the overly strict symmetric condition. In this work, we propose a simple yet effective approach for relaxing the symmetric condition, namely $\epsilon$-softmax, which simply modifies the outputs of the softmax layer to approximate one-hot vectors with a controllable error $\epsilon$. Essentially, $\epsilon$-softmax not only acts as an alternative for the softmax layer, but also implicitly plays the crucial role in modifying the loss function. We prove theoretically that $\epsilon$-softmax can achieve noise-tolerant learning with controllable excess risk bound for almost any loss function. Recognizing that $\epsilon$-softmax-enhanced losses may slightly reduce fitting ability on clean datasets, we further incorporate them with one symmetric loss, thereby achieving a better trade-off between robustness and effective learning. Extensive experiments demonstrate the superiority of our method in mitigating synthetic and real-world label noise. The code is available at https://github.com/cswjl/eps-softmax.

Figures

Figures reproduced from arXiv: 2508.02387 by the authors.

Figure 1
Figure 1. Test accuracies on CIFAR-10 under symmetric noise with different [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Visualizations of learned representations on CIFAR-10 with symmetric label noise. The [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Visualizations of learned representations on CIFAR-10 with different symmetric label noise [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

63 extracted references · 41 canonical work pages

  1. [1]

    Deep learning

    Yann LeCun, Yoshua Bengio, and Geoffrey Hinton. Deep learning. nature, 521(7553):436–444, 2015

    2015

  2. [2]

    A survey of label-noise representation learning: Past, present and future

    Bo Han, Quanming Yao, Tongliang Liu, Gang Niu, Ivor W Tsang, James T Kwok, and Masashi Sugiyama. A survey of label-noise representation learning: Past, present and future. arXiv preprint arXiv:2011.04406, 2020

    arXiv 2011

  3. [3]

    A closer look at memorization in deep networks

    Devansh Arpit, Stanisław Jastrz˛ ebski, Nicolas Ballas, David Krueger, Emmanuel Bengio, Maxinder S Kanwal, Tegan Maharaj, Asja Fischer, Aaron Courville, Yoshua Bengio, et al. A closer look at memorization in deep networks. In International conference on machine learning, pages 233–242. PMLR, 2017

    work page 2017

  4. [4]

    Weak-to-strong gener- alization: Eliciting strong capabilities with weak supervision

    Collin Burns, Pavel Izmailov, Jan Hendrik Kirchner, Bowen Baker, Leo Gao, Leopold Aschen- brenner, Yining Chen, Adrien Ecoffet, Manas Joglekar, Jan Leike, et al. Weak-to-strong gener- alization: Eliciting strong capabilities with weak supervision. arXiv preprint arXiv:2312.09390, 2023

    arXiv 2023

  5. [5]

    Robust loss functions under label noise for deep neural networks

    Aritra Ghosh, Himanshu Kumar, and P Shanti Sastry. Robust loss functions under label noise for deep neural networks. In Proceedings of the AAAI conference on artificial intelligence , volume 31, 2017

    work page 2017

  6. [6]

    Normalized loss functions for deep learning with noisy labels

    Xingjun Ma, Hanxun Huang, Yisen Wang, Simone Romano, Sarah Erfani, and James Bailey. Normalized loss functions for deep learning with noisy labels. In International conference on machine learning, pages 6543–6553. PMLR, 2020. 10

    work page 2020

  7. [7]

    Asymmetric loss functions for learning with noisy labels

    Xiong Zhou, Xianming Liu, Junjun Jiang, Xin Gao, and Xiangyang Ji. Asymmetric loss functions for learning with noisy labels. In International conference on machine learning, pages 12846–12856. PMLR, 2021

    work page 2021

  8. [8]

    Label distributionally robust losses for multi-class classification: Consistency, robustness and adaptivity

    Dixian Zhu, Yiming Ying, and Tianbao Yang. Label distributionally robust losses for multi-class classification: Consistency, robustness and adaptivity. In International Conference on Machine Learning, pages 43289–43325. PMLR, 2023

    work page 2023

Show all 63 references
  1. [9]

    Noise tolerance under risk minimization

    Naresh Manwani and PS Sastry. Noise tolerance under risk minimization. IEEE transactions on cybernetics, 43(3):1146–1151, 2013

    2013

  2. [10]

    Learning with symmetric label noise: The importance of being unhinged

    Brendan Van Rooyen, Aditya Menon, and Robert C Williamson. Learning with symmetric label noise: The importance of being unhinged. Advances in neural information processing systems, 28, 2015

    2015

  3. [11]

    Generalized cross entropy loss for training deep neural networks with noisy labels

    Zhilu Zhang and Mert Sabuncu. Generalized cross entropy loss for training deep neural networks with noisy labels. Advances in neural information processing systems, 31, 2018

    2018

  4. [12]

    Symmetric cross entropy for robust learning with noisy labels

    Yisen Wang, Xingjun Ma, Zaiyi Chen, Yuan Luo, Jinfeng Yi, and James Bailey. Symmetric cross entropy for robust learning with noisy labels. In Proceedings of the IEEE/CVF international conference on computer vision, pages 322–330, 2019

    2019

  5. [13]

    Generalized jensen-shannon divergence loss for learning with noisy labels

    Erik Englesson and Hossein Azizpour. Generalized jensen-shannon divergence loss for learning with noisy labels. Advances in Neural Information Processing Systems, 34:30284–30297, 2021

    2021

  6. [14]

    Learning with noisy labels via sparse regularization

    Xiong Zhou, Xianming Liu, Chenyang Wang, Deming Zhai, Junjun Jiang, and Xiangyang Ji. Learning with noisy labels via sparse regularization. In Proceedings of the IEEE/CVF international conference on computer vision, pages 72–81, 2021

    2021

  7. [15]

    Non-negative matrix factorization with sparseness constraints

    Patrik O Hoyer. Non-negative matrix factorization with sparseness constraints. Journal of machine learning research, 5(9), 2004

    2004

  8. [16]

    Variance-enlarged poisson learning for graph-based semi-supervised learning with extremely sparse labeled data

    Xiong Zhou, Xianming Liu, Hao Yu, Jialiang Wang, Zeke Xie, Junjun Jiang, and Xiangyang Ji. Variance-enlarged poisson learning for graph-based semi-supervised learning with extremely sparse labeled data. In The Twelfth International Conference on Learning Representations , page...

    2024

  9. [17]

    On the consistency of top-k surrogate losses

    Forest Yang and Sanmi Koyejo. On the consistency of top-k surrogate losses. In International Conference on Machine Learning, pages 10727–10735. PMLR, 2020

    2020

  10. [18]

    Convexity, classification, and risk bounds

    Peter L Bartlett, Michael I Jordan, and Jon D McAuliffe. Convexity, classification, and risk bounds. Journal of the American Statistical Association, 101(473):138–156, 2006

    2006

  11. [19]

    Focal loss for dense object detection

    Tsung-Yi Lin, Priya Goyal, Ross Girshick, Kaiming He, and Piotr Dollár. Focal loss for dense object detection. In Proceedings of the IEEE international conference on computer vision , pages 2980–2988, 2017

    2017

  12. [20]

    Understanding and improving early stopping for learning with noisy labels

    Yingbin Bai, Erkun Yang, Bo Han, Yanhua Yang, Jiatong Li, Yinian Mao, Gang Niu, and Tongliang Liu. Understanding and improving early stopping for learning with noisy labels. Advances in Neural Information Processing Systems, 34:24392–24403, 2021

    2021

  13. [21]

    Co-teaching: Robust training of deep neural networks with extremely noisy labels

    Bo Han, Quanming Yao, Xingrui Yu, Gang Niu, Miao Xu, Weihua Hu, Ivor Tsang, and Masashi Sugiyama. Co-teaching: Robust training of deep neural networks with extremely noisy labels. Advances in neural information processing systems, 31, 2018

    2018

  14. [22]

    Fixmatch: Simplifying semi- supervised learning with consistency and confidence.Advances in neural information processing systems, 33:596–608, 2020

    Kihyuk Sohn, David Berthelot, Nicholas Carlini, Zizhao Zhang, Han Zhang, Colin A Raf- fel, Ekin Dogus Cubuk, Alexey Kurakin, and Chun-Liang Li. Fixmatch: Simplifying semi- supervised learning with consistency and confidence.Advances in neural information processing systems, 33...

    2020

  15. [23]

    mixup: Beyond empirical risk minimization

    Hongyi Zhang, Moustapha Cisse, Yann N Dauphin, and David Lopez-Paz. mixup: Beyond empirical risk minimization. In International Conference on Learning Representations, 2018

    2018

  16. [24]

    Learning multiple layers of features from tiny images

    Alex Krizhevsky, Geoffrey Hinton, et al. Learning multiple layers of features from tiny images. 2009. 11

    2009

  17. [25]

    Nlnl: Negative learning for noisy labels

    Youngdong Kim, Junho Yim, Juseung Yun, and Junmo Kim. Nlnl: Negative learning for noisy labels. In Proceedings of the IEEE/CVF international conference on computer vision, pages 101–110, 2019

    2019

  18. [26]

    Mitigating memorization of noisy labels by clipping the model prediction

    Hongxin Wei, Huiping Zhuang, Renchunzi Xie, Lei Feng, Gang Niu, Bo An, and Yixuan Li. Mitigating memorization of noisy labels by clipping the model prediction. In International Conference on Machine Learning, pages 36868–36886. PMLR, 2023

    2023

  19. [27]

    Visualizing data using t-sne

    Laurens Van der Maaten and Geoffrey Hinton. Visualizing data using t-sne. Journal of machine learning research, 9(11), 2008

    2008

  20. [28]

    Learning with noisy labels revisited: A study using real-world human annotations

    Jiaheng Wei, Zhaowei Zhu, Hao Cheng, Tongliang Liu, Gang Niu, and Yang Liu. Learning with noisy labels revisited: A study using real-world human annotations. In International Conference on Learning Representations, 2021

    2021

  21. [29]

    Making deep neural networks robust to label noise: A loss correction approach

    Giorgio Patrini, Alessandro Rozza, Aditya Krishna Menon, Richard Nock, and Lizhen Qu. Making deep neural networks robust to label noise: A loss correction approach. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1944–1952, 2017

    1944

  22. [30]

    Are anchor points really indispensable in label-noise learning? Advances in neural information processing systems, 32, 2019

    Xiaobo Xia, Tongliang Liu, Nannan Wang, Bo Han, Chen Gong, Gang Niu, and Masashi Sugiyama. Are anchor points really indispensable in label-noise learning? Advances in neural information processing systems, 32, 2019

    2019

  23. [31]

    Peer loss functions: Learning from noisy labels without knowing noise rates

    Yang Liu and Hongyi Guo. Peer loss functions: Learning from noisy labels without knowing noise rates. In International conference on machine learning, pages 6226–6236. PMLR, 2020

    2020

  24. [32]

    When optimizing f-divergence is robust with label noise

    Jiaheng Wei and Yang Liu. When optimizing f-divergence is robust with label noise. In International Conference on Learning Representations, 2021

    2021

  25. [33]

    To smooth or not? when label smoothing meets noisy labels

    Jiaheng Wei, Hangyu Liu, Tongliang Liu, Gang Niu, Masashi Sugiyama, and Yang Liu. To smooth or not? when label smoothing meets noisy labels. In International Conference on Machine Learning, pages 23589–23614. PMLR, 2022

    2022

  26. [34]

    Provably end-to-end label-noise learning without anchor points

    Xuefeng Li, Tongliang Liu, Bo Han, Gang Niu, and Masashi Sugiyama. Provably end-to-end label-noise learning without anchor points. In International conference on machine learning, pages 6403–6413. PMLR, 2021

    2021

  27. [35]

    Asymmetric loss functions for noise-tolerant learning: Theory and applications

    Xiong Zhou, Xianming Liu, Deming Zhai, Junjun Jiang, and Xiangyang Ji. Asymmetric loss functions for noise-tolerant learning: Theory and applications. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2023

    2023

  28. [36]

    How does disagreement help generalization against label corruption? In International Conference on Machine Learning, pages 7164–7173

    Xingrui Yu, Bo Han, Jiangchao Yao, Gang Niu, Ivor Tsang, and Masashi Sugiyama. How does disagreement help generalization against label corruption? In International Conference on Machine Learning, pages 7164–7173. PMLR, 2019

    2019

  29. [37]

    Combating noisy labels by agreement: A joint training method with co-regularization

    Hongxin Wei, Lei Feng, Xiangyu Chen, and Bo An. Combating noisy labels by agreement: A joint training method with co-regularization. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 13726–13735, 2020

    2020

  30. [38]

    Early- learning regularization prevents memorization of noisy labels

    Sheng Liu, Jonathan Niles-Weed, Narges Razavian, and Carlos Fernandez-Granda. Early- learning regularization prevents memorization of noisy labels. Advances in neural information processing systems, 33:20331–20342, 2020

    2020

  31. [39]

    Dividemix: Learning with noisy labels as semi-supervised learning

    Junnan Li, Richard Socher, and Steven CH Hoi. Dividemix: Learning with noisy labels as semi-supervised learning. In International Conference on Learning Representations, 2020

    2020

  32. [40]

    Learning with instance-dependent label noise: A sample sieve approach

    Hao Cheng, Zhaowei Zhu, Xingyu Li, Yifei Gong, Xing Sun, and Yang Liu. Learning with instance-dependent label noise: A sample sieve approach. In International Conference on Learning Representations, 2021

    2021

  33. [41]

    A second-order approach to learning with instance- dependent label noise

    Zhaowei Zhu, Tongliang Liu, and Yang Liu. A second-order approach to learning with instance- dependent label noise. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 10113–10123, 2021. 12

    2021

  34. [42]

    Robust training under label noise by over- parameterization

    Sheng Liu, Zhihui Zhu, Qing Qu, and Chong You. Robust training under label noise by over- parameterization. In International Conference on Machine Learning , pages 14153–14172. PMLR, 2022

    2022

  35. [43]

    Rethinking noisy label learning in real-world annotation scenarios from the noise-type perspective

    Renyu Zhu, Haoyu Liu, Runze Wu, Minmin Lin, Tangjie Lv, Changjie Fan, and Haobo Wang. Rethinking noisy label learning in real-world annotation scenarios from the noise-type perspective. arXiv preprint arXiv:2307.16889, 2023

    2023 arXiv

  36. [44]

    Webvision database: Visual learning and understanding from web data

    Wen Li, Limin Wang, Wei Li, Eirikur Agustsson, and Luc Van Gool. Webvision database: Visual learning and understanding from web data. arXiv preprint arXiv:1708.02862, 2017

    2017 arXiv

  37. [45]

    Imagenet: A large- scale hierarchical image database

    Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large- scale hierarchical image database. In 2009 IEEE Conference on Computer Vision and Pattern Recognition, pages 248–255, 2009. doi: 10.1109/CVPR.2009.5206848

    2009

  38. [46]

    Learning from massive noisy labeled data for image classification

    Tong Xiao, Tian Xia, Yi Yang, Chang Huang, and Xiaogang Wang. Learning from massive noisy labeled data for image classification. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2691–2699, 2015

    2015

  39. [47]

    Randaugment: Practical automated data augmentation with a reduced search space

    Ekin D Cubuk, Barret Zoph, Jonathon Shlens, and Quoc V Le. Randaugment: Practical automated data augmentation with a reduced search space. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition workshops, pages 702–703, 2020

    2020

  40. [48]

    mean±std

    Xiaobo Xia, Tongliang Liu, Bo Han, Nannan Wang, Mingming Gong, Haifeng Liu, Gang Niu, Dacheng Tao, and Masashi Sugiyama. Part-dependent label noise: Towards instance-dependent label noise. Advances in Neural Information Processing Systems, 33:7597–7610, 2020. 13 A Limitation a...

    2020

  41. [49]

    Specifically, we provide a simple yet effective method for mitigating label noise with elaborated descriptions and theoretical results

    Claims Question: Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? Answer: [Yes] Justification: The main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope. Specific...

  42. [50]

    Limitations

    Limitations Question: Does the paper discuss the limitations of the work performed by the authors? Answer: [Yes] Justification: We have discussed the limitations of the work in the Appendix A. Guidelines: • The answer NA means that the paper has no limitation while the answer ...

  43. [51]

    Guidelines: • The answer NA means that the paper does not include theoretical results

    Theory Assumptions and Proofs Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof? 21 Answer: [Yes] Justification: We provide the full set of assumptions in the main paper and all proofs in Appendix B. Gu...

  44. [52]

    Guidelines: • The answer NA means that the paper does not include experiments

    Experimental Result Reproducibility Question: Does the paper fully disclose all the information needed to reproduce the main ex- perimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and da...

  45. [53]

    And the datasets are obtained from open source

    Open access to data and code 22 Question: Does the paper provide open access to the data and code, with sufficient instruc- tions to faithfully reproduce the main experimental results, as described in supplemental material? Answer: [Yes] Justification: We have submitted the co...

  46. [54]

    Guidelines: • The answer NA means that the paper does not include experiments

    Experimental Setting/Details Question: Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results? Answer: [Yes] Justification: We have specified all the tra...

  47. [55]

    Guidelines: • The answer NA means that the paper does not include experiments

    Experiment Statistical Significance Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments? Answer: [Yes] Justification: For all experiments, we include error bars for add...

  48. [56]

    All experiments are implemented by PyTorch and are conducted on NVIDIA GeForce RTX 4090

    Experiments Compute Resources Question: For each experiment, does the paper provide sufficient information on the com- puter resources (type of compute workers, memory, time of execution) needed to reproduce the experiments? Answer: [Yes] Justification: We provide the informat...

  49. [57]

    Guidelines: • The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics

    Code Of Ethics Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https://neurips.cc/public/EthicsGuidelines? Answer: [Yes] Justification: We promise that the research conducted in the paper conforms, in every respect,...

  50. [58]

    Guidelines: • The answer NA means that there is no societal impact of the work performed

    Broader Impacts Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed? Answer: [Yes] Justification: We have discussed broader impact of this work. Guidelines: • The answer NA means that there is no societa...

  51. [59]

    Guidelines: • The answer NA means that the paper poses no such risks

    Safeguards Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)? Answer: [NA] Justification: We do not use p...

  52. [60]

    Guidelines: • The answer NA means that the paper does not use existing assets

    Licenses for existing assets Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected? Answer: [Yes] Justification: The existing ass...

  53. [61]

    Guidelines: • The answer NA means that the paper does not release new assets

    New Assets Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets? Answer: [NA] Justification: We do not introduce any new assets. Guidelines: • The answer NA means that the paper does not release new assets. • R...

  54. [62]

    Guidelines: • The answer NA means that the paper does not involve crowdsourcing nor research with human subjects

    Crowdsourcing and Research with Human Subjects Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)? A...

  55. [63]

    Guidelines: • The answer NA means that the paper does not involve crowdsourcing nor research with human subjects

    Institutional Review Board (IRB) Approvals or Equivalent for Research with Human Subjects Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals...

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.