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REVIEW 4 major objections 6 minor 39 references

NLNL: Negative Learning for Noisy Labels

T0 review · 4 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Training a network to know what an image is not lets it learn from noisy labels.

desk verdict Simple and effective noisy-label method with strong empirical results, but the threshold assumption and lack of code/variance are real soft spots. read the letter →

arxiv 1908.07387 v1 pith:FYPGE3O2 submitted 2019-08-19 cs.LG

Youngdong Kim , Junho Yim , Juseung Yun , Junmo Kim This is my paper · ORCID
classification cs.LG
keywords negativelearningcomplementarylabelsnoisylabelclassificationselectivepositivesemi-supervisedpseudo-labelingnoisefilteringCIFAR-10
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

This paper is trying to establish that a classifier can be trained on badly labeled images by, at first, refusing to say what each image is rather than asserting what it is. The method, negative learning (NL), picks a random complementary label and trains the network to assign that label probability zero, which is almost always a true statement about the image and therefore safe even when the original label is wrong. The authors further claim that once NL has separated confident clean samples from low-confidence noisy ones, selectively applying ordinary positive learning to the confident half of the data (SelNLPL) filters out the noise and lets a simple semi-supervised pseudo-labeling step achieve leading test accuracy. Why it matters: if true, noisy-label training needs no knowledge of the noise rate, no clean validation data, and no specialized loss functions.

What carries the argument

The machinery is a complementary-label cross-entropy that drives the probability of a randomly chosen 'not this' label to zero. Because the softmax output sums to one, suppressing one class redistributes probability over the remaining classes, including, most of the time, the true class, so the network learns genuine visual content without being told a possibly false positive label. Two confidence gates then steer training: SelNL keeps samples with $p_y > 1/c$, and SelPL keeps samples with $p_y > \gamma = 0.5$ for ordinary positive cross-entropy. The paper also derives that NL's gradient on the true class scales as $1/(c(c-1))$, which is why CIFAR100 needed 110 complementary losses per image to converge in the same epoch budget.

What would settle it

Train SelNLPL on a noise process engineered so some wrong labels become highly confident, for example asymmetric flips between visually similar classes at high noise, then inspect the confidence histograms: if the clean and noisy peaks overlap around $\gamma = 0.5$, the fixed-threshold filter mislabels a nontrivial fraction and the method would have to fall back on noise-rate knowledge.

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Extended reading notes

Core claim

The paper's central claim is that a CNN trained with negative learning (NL), whose loss is $$L(f,\bar y) = -\sum_{k=1}^{c} \bar y_k \log(1-p_k),$$ where $\bar y$ is a uniformly random label different from the given label $y$, does not overfit to noisy labels: the confidence of clean samples climbs while the confidence of noisy samples stays low. The authors then add Selective Negative Learning (SelNL), which keeps only samples with confidence above $1/c$, and Selective Positive Learning (SelPL), which trains with the usual cross-entropy only on samples whose confidence exceeds $\gamma = 0.5$. They claim that this SelNLPL schedule separates clean from noisy training data with high precision and recall, and that a simple pseudo-label semi-supervised stage on the filtered data reaches state-of-the-art accuracy on noisy CIFAR10, CIFAR100, MNIST, and FashionMNIST without any prior knowledge of the noise type or ratio.

Load-bearing premise

The load-bearing premise is that one fixed confidence threshold cleanly separates clean from noisy samples after negative learning - a separation the paper demonstrates empirically rather than proves - so the method never needs to know the noise ratio or type.

Editorial extensions

If this is right

  • Training with NL before any PL gives a confidence gap that can be used to estimate the noise rate of a training set: the fraction of samples below the 0.5 threshold tracks the true noise fraction to within a few percent in the paper's CIFAR10 experiments.
  • Because the method never consults a validation set and does not tune hyper-parameters to known noise levels, it is portable to settings where label quality is unknown in advance.
  • The filtering step is strong enough that the subsequent semi-supervised stage can be a plain pseudo-labeling procedure rather than a specially designed noise-robust loss.
  • Large class counts slow NL convergence by a factor related to $c(c-1)$; the authors' multi-complementary-label extension restores convergence on CIFAR100 with the same epoch budget as CIFAR10.

Reading between the lines

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

  • Editorial inference: The fixed threshold $\gamma = 0.5$ is a tuning choice, and the CIFAR100 modification suggests the clean/noisy confidence gap itself shifts with class count, so per-class or annealed thresholds could make the filter more portable.
  • Editorial inference: Because the method only needs a 'not this label' signal, it could generalize to web-scraped or weakly supervised data where errors are not simple class flips, and even to settings where some labels are plain misinformation.
  • Editorial inference: If the confidence gap is the mechanism, then the natural stress test is asymmetric noise between visually similar classes at high noise; the paper's own failure to converge at 80% symmetric-exclusive noise hints that the gap closes under extreme corruption.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The paper proposes Negative Learning (NL), in which a CNN is trained with randomly drawn complementary labels using the loss -log(1-p_ybar), as a noise-robust alternative to Positive Learning (PL). The authors then combine NL with two selective stages called SelNL (keeping only samples whose given-label confidence exceeds 1/c) and SelPL (keeping only samples whose confidence exceeds gamma=0.5), producing SelNLPL. After training with SelNLPL, the network is used to divide the training set into clean and noisy parts, noisy labels are discarded, and the network is re-trained by pseudo-labeling. The paper reports state-of-the-art accuracy on CIFAR10, CIFAR100, FashionMNIST, and MNIST under symmetric and asymmetric label noise, and claims that the method requires no tuning based on prior knowledge of the noise type or noise rate.

Significance. If the claims are sustained, the paper makes a useful practical contribution: the core NL idea is simple, intuitively motivated, and is tested across four datasets, three noise types, and multiple noise levels. The ablation study in Table 7, the filtering precision/recall analysis in Table 1 and Figure 6, and the gradient analysis in Eq. 3 are valuable explanatory elements beyond a bare benchmark comparison. The claim of state-of-the-art accuracy without noise-rate-dependent hyper-parameters is attractive for real-world use. The main weaknesses are that the no-tuning claim is contradicted by the CIFAR100 extension and the 80% symmetric-exclusive failure, and that the fixed threshold gamma=0.5 is only visualized for one noise setting. The paper also reports no variance or error bars, so the magnitude of the claimed improvements (often 1-5%) cannot be assessed statistically.

major comments (4)
  1. [Section 5.2, Table 3] The paper states that the method 'only failed to converge when the symm-exc noise is 80%, which can be neglected because such a scenario is unrealistic.' Since the claimed contribution is a method that works without prior knowledge of the noise level, dismissing a tested operating point where the method diverges undermines the claim. A practitioner who does not know the noise rate will not know that 80% is 'unrealistic.' Please either explain why the method fails at 80% symmetric-exclusive noise, provide evidence that the failure is specific to this synthetic setting, or revise the no-tuning claim.
  2. [Section 6.1] The base SelNLPL method is stated to fail to converge on CIFAR100, and the authors introduce an ad hoc extension that computes 110 complementary-label losses per image. This introduces a new hyper-parameter (the number of complementary labels) that depends on the class count, which contradicts the contribution in Section 1 that the method 'does not require any tuning of hyper-parameters that depend on prior knowledge.' The number of complementary labels is a dataset-dependent choice, not a fixed parameter. Please state clearly that this is a separate variant with its own hyper-parameter, and adjust the no-tuning claim accordingly.
  3. [Section 3.3 and Algorithm 2] The clean/noisy separation after NL/SelNL and the fixed threshold gamma=0.5 are the load-bearing elements of the filtering step, yet the histograms in Figure 3 are only shown for CIFAR10 with 30% symmetric-inclusive noise. No histograms are provided for asymmetric noise, for 80% symmetric-exclusive noise (where the method fails), or for the CIFAR100 extension. If the confidence separation is not clean in these settings, the filtering step and the subsequent pseudo-labeling are unreliable. Please provide confidence-separation evidence for these settings or perform a sensitivity analysis of gamma across noise types and levels.
  4. [Section 1 and Section 3.1] The motivation that NL 'decreases the risk of providing incorrect information' is incomplete. For a noisy example whose given label is wrong, the true label is a member of the complementary-label set, and if it is selected as ybar, Eq. 2 actively drives the probability of the true class toward zero. Thus the safety of NL is an empirical property of the training dynamics, not a guaranteed consequence of random complementary labels. The text should present the 'safe' property as an empirical observation, not as a logical implication of the sampling scheme.
minor comments (6)
  1. [Section 5.2, Tables 3-6] The reported results are single runs without variance, error bars, or statistical significance tests. Given that many of the claimed improvements are 1-5%, please report multiple seeds or at least indicate the variability.
  2. [Section 5.1] The learning rates differ across stages (0.02 for NL and SelNL, 0.1 for SelPL) and across datasets (MNIST uses 0.1 for NL and SelNL). This is reasonable engineering, but it weakens the statement that the method requires no tuning; please clarify which parameters are fixed and which are dataset-dependent.
  3. [Section 6.2, Table 7] The ablation shows that omitting SelPL or SelNL from SelNLPL yields small accuracy drops at 30% symmetric-inclusive noise (1.38 and 0.41 points), but large drops at 50% noise. Please discuss whether the significance of each step depends on the noise level, and whether the 30% row genuinely supports the claim that each step contributes.
  4. [Section 4] In the fourth paragraph of Section 4, 'This resulted in state-of-the-accuracy' appears to be a typo for 'state-of-the-art accuracy.'
  5. [Algorithm 1] Algorithm 1 uses the symbol y for both the original label and the complementary label; please rename the complementary label (e.g., ybar) consistently with Eq. 2.
  6. [Section 3.5] The description of pseudo-labeling says 'noisy data's label is updated with the output of the CNN...' but does not specify whether the soft label is computed from the network trained in Figure 5(b) or from the final network in Figure 5(c). Please clarify the exact two-stage re-training protocol.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: SelNLPL is an empirical training scheme evaluated on held-out benchmarks; no fitted parameter is relabeled as a prediction.

full rationale

The paper's derivation chain is self-contained and empirically evaluated. The loss functions (Eq. 1 for positive learning and Eq. 2 for negative learning) are applied directly to training labels; no parameter is fitted to the test labels or to the reported benchmark accuracies. The confidence threshold gamma = 0.5 used in Selective PL (Section 3.3 and Algorithm 2) is fixed in advance and not tuned per noise rate or per dataset, so the filtering results in Section 4 are measurements of a fixed rule against known synthetic noise, not predictions derived from the noise labels themselves. The claim that clean and noisy confidences separate after NL/SelNL is supported by histograms and precision-recall curves, which are external evidence rather than a restatement of the method's definitions. The CIFAR100 extension in Section 6.1 computes 110 complementary labels from the ratio of gradient magnitudes (1/(c(c-1)) for c=10 vs c=100), a calculation based on class counts, not on the final accuracy; even if this heuristic is debatable, it is not circular. The paper does contain a self-citation to the authors' prior work ([7], Deep Pyramidal Residual Networks) in the introductory overview of CNN architectures, but that citation is not load-bearing for the noisy-label method. The admitted limitations (failure to converge at 80% symmetric-exclusive noise, and the need for a modified scheme on CIFAR100) are empirical caveats, not circular reasoning. Overall, no step reduces by construction to its own inputs, so the appropriate finding is no significant circularity.

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

The method's core depends on a few empirical assumptions: the complementary label selection rarely hits the true label, and confidence separates clean/noisy data. These are demonstrated empirically but not guaranteed. The main free parameters are the confidence threshold, the long training schedule, and the multi-label count for CIFAR100. No new entities are introduced.

free parameters (3)
  • SelPL confidence threshold gamma = 0.5
    Hand-set threshold for selecting clean samples; not tuned per dataset, but arbitrary and affects performance.
  • Training epochs per stage (NL, SelNL, SelPL) = 720 each
    Large fixed epoch count chosen so that NL converges; not justified beyond observation that training was slow.
  • Number of complementary labels for CIFAR100 extension = 110
    Chosen to compensate for slow convergence due to 100 classes; derived from gradient ratio analysis (factor of 110), so it is a calculated number rather than purely arbitrary.
assumptions (3)
  • domain assumption Complementary labels are chosen uniformly at random from all classes except the given label.
    Algorithm 1 defines this selection rule; it is a design choice that makes the true label less likely to be chosen as a complementary label.
  • domain assumption With high probability, a randomly selected complementary label is not the true label, implying that NL mostly provides correct information.
    Core motivation of the paper; fails when noise is high and classes are few, since the chance of picking the true label as complementary increases as 1/(c-1).
  • ad hoc to paper After NL and SelNL, the confidence of clean data is reliably higher than that of noisy data, so a fixed threshold can separate them.
    Empirically demonstrated in Figure 3 and Table 1, but not theoretically guaranteed; this separation is central to SelPL's filtering and the overall method's success.

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Cite this review

Pith. "Pith review of NLNL: Negative Learning for Noisy Labels." pith.science (2026). https://pith.science/paper/FYPGE3O2

@misc{pith2026190807387,
  author       = {Pith},
  title        = {Pith review of: NLNL: Negative Learning for Noisy Labels},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FYPGE3O2}},
  note         = {Machine review of arXiv:1908.07387}
}
read the original abstract

Convolutional Neural Networks (CNNs) provide excellent performance when used for image classification. The classical method of training CNNs is by labeling images in a supervised manner as in "input image belongs to this label" (Positive Learning; PL), which is a fast and accurate method if the labels are assigned correctly to all images. However, if inaccurate labels, or noisy labels, exist, training with PL will provide wrong information, thus severely degrading performance. To address this issue, we start with an indirect learning method called Negative Learning (NL), in which the CNNs are trained using a complementary label as in "input image does not belong to this complementary label." Because the chances of selecting a true label as a complementary label are low, NL decreases the risk of providing incorrect information. Furthermore, to improve convergence, we extend our method by adopting PL selectively, termed as Selective Negative Learning and Positive Learning (SelNLPL). PL is used selectively to train upon expected-to-be-clean data, whose choices become possible as NL progresses, thus resulting in superior performance of filtering out noisy data. With simple semi-supervised training technique, our method achieves state-of-the-art accuracy for noisy data classification, proving the superiority of SelNLPL's noisy data filtering ability.

Figures

Figures reproduced from arXiv: 1908.07387 by the authors.

Figure 1
Figure 1. Conceptual comparison between Positive Learn￾ing (PL) and Negative Learning (NL). Regarding noisy data, while PL provides CNN the wrong information (red balloon), with a higher chance, NL can provide CNN the correct information (blue balloon) because a dog is clearly not a bird. approaches address this problem by applying a number of techniques and regularization terms along with Posi￾tive Learning (PL), a typical s… view at source ↗
Figure 2
Figure 2. Comparison between PL and NL. (a): Loss graph [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Histogram showing the distribution of CIFAR10 training data with 30% [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Accuracy graph of SelNLPL. Training is per [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: Pseudo labeling for semi-supervised learning. (a): Division of training data into either clean or noisy data with CNN [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 6
Figure 6. Figure 6: Precision-Recall curve when filtering noisy data. [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]
Figure 7
Figure 7. Figure 7: Histogram showing the distribution of CIFAR10 training data with 50% [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

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