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REVIEW 3 major objections 4 minor 50 references

Detecting Mislabeled and Corrupted Data via Pointwise Mutual Information

T0 review · 3 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read This paper claims that rating each training sample by its pointwise mutual information with its label separates corrupted from clean data, so training on only high-scoring samples improves accuracy under label noise.

desk verdict Plausible PMI-based data filter, but the abstract's 15% claim is unverifiable from the corrupted text; needs a referee to check the estimator. read the letter →

arxiv 2508.07713 v1 pith:OMLE4V37 submitted 2025-08-11 cs.LG stat.ML

Jinghan Yang , Jiayu Weng This is my paper · ORCID
classification cs.LGstat.ML
keywords pointwisemutualinformationdataselectionlabelnoiseinputmislabeleddetectionMNISTqualitydeeplearning
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 a simple data-cleaning principle: a training sample's pointwise contribution to the mutual information between inputs and labels is a reliable signal of data quality. Samples whose input and label share little statistical dependence—low pointwise MI—are the ones most likely to be mislabeled or corrupted, while samples with high pointwise MI are worth keeping. If this is right, it gives practitioners a parameter-free way to select training data under both label noise and input noise, without needing a clean validation set. The paper demonstrates the mechanism on MNIST under synthetic noise, reporting accuracy gains up to 15% over random sampling when training on high-MI samples only.

What carries the argument

The central object is the per-sample pointwise mutual information $\mathrm{PMI}(x,y)=\log\left(p(x,y)/(p(x)p(y))\right)$, which decomposes the dataset's total mutual information into per-sample contributions. The method estimates this quantity from the (possibly corrupted) training set, ranks samples by it, and discards the lowest-ranked samples before training. The ranking is the load-bearing device: the paper's claim is that low pointwise contribution co-occurs with label noise and input corruption, so no separate clean-validation set is required.

What would settle it

Take MNIST with a known corruption mask: flip 20% of labels randomly and add noise to 20% of images, compute each sample's PMI from the corrupted training set, then measure precision at the bottom of the ranking against the mask. If the lowest-PMI samples are not enriched for the injected corruptions beyond chance, or if clean but unusual digits are consistently ranked below corrupted typical digits, the central claim is false.

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Extended reading notes

Core claim

The paper proposes that every training example can be assigned a pointwise mutual information score $\log\left(p(x,y)/(p(x)p(y))\right)$, and that this score separates clean from corrupted data: mislabeled and noisy inputs have systematically lower contributions to the overall mutual information. On MNIST with synthetic label noise and input corruption, the paper reports that keeping only high-PMI samples for training raises classification accuracy by up to 15% compared to random sampling, and that benign input modifications that preserve the semantic label do not get filtered out, while truly corrupted samples do.

Load-bearing premise

The method's ranking is only as good as the estimate of pointwise mutual information made from the corrupted training data itself; if that estimate is biased by the noise, or if rare but clean inputs naturally have low scores, the filter will remove the wrong samples.

Editorial extensions

If this is right

  • Under label corruption, discarding low-PMI samples before training should improve test accuracy compared with training on the same number of randomly selected samples.
  • Because the score is computed per sample, the method can act as a preprocessing filter for any downstream classifier, not only for the network used to estimate the score.
  • Benign input modifications that preserve the label should keep high PMI, so the filter should remove corrupted inputs without discarding semantically valid augmentations.
  • The ranking itself provides a label-quality audit: low-ranked samples are candidates for human review or relabeling.

Reading between the lines

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

  • Beyond the paper's MNIST experiments, the same per-sample PMI ranking could be applied to non-image modalities such as text or tabular data, wherever a tractable estimate of $p(x,y)$ exists.
  • If the estimator is fitted on the corrupted set itself, the method may be vulnerable to the very noise it detects—for example, a mislabeled sample that is highly typical of its wrong class could earn a high PMI score; a careful reader should check whether the reported gains come mostly from removing outliers rather than correcting labels.
  • Pointwise MI could be combined with loss-based filter methods: samples that are both low-PMI and high-loss are stronger corruption candidates than either signal alone, a testable extension the paper does not run.
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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

3 major / 4 minor

Summary. The paper proposes a data-selection framework for neural network training under hybrid label and input noise. The central idea is to rank training samples by their pointwise contribution to the overall mutual information between inputs and labels, and to discard samples with low pointwise mutual information (PMI). The abstract claims that lower PMI identifies noisy or mislabeled instances, that training on high-PMI samples improves classification accuracy by up to 15% over random sampling under label corruption, and that the method is robust to benign input modifications. The full text as provided is heavily corrupted by character-encoding errors, so the detailed method, equations, tables, and figures are not readable. The assessment is therefore based primarily on the abstract and on a few equation fragments that appear in the corrupted text.

Significance. If the claim holds, the method could offer a simple, interpretable, information-theoretic criterion for training-data filtering that goes beyond ad-hoc loss-based heuristics. The abstract's claim is falsifiable and the proposed PMI ranking is a plausible extension of existing small-loss and confidence-based selection methods. However, the current manuscript does not allow verification of the central claim: no estimator is specified, no baseline comparisons or error bars are visible, and only one dataset with synthetic noise is mentioned. The significance is therefore conditional; at present the evidence is too thin to establish a substantive advance over standard noisy-label baselines.

major comments (3)
  1. [Method, as described in the Abstract] The abstract states that "we compute each sample's pointwise contribution to the overall mutual information," but it never specifies how p(x,y) or p(y|x) is estimated. Since PMI(x;y) = log p(x,y)/(p(x)p(y)) = log p(y|x) - log p(y), any implementation requires an estimate of the conditional label distribution. If p(y|x) is obtained from a neural network trained on the same noisy labels, then the ranking reduces to a model-confidence/loss ranking and is vulnerable to the memorization effect: after convergence, corrupted samples receive high p(y|x) and hence high PMI, while rare or underfit clean samples may receive low PMI. This confound is unaddressed. Please specify the estimator, and provide a control experiment that separates PMI from model confidence—for example, compare against the small-loss selection and report results at both early and late training epochs.
  2. [Results/Abstract] The central empirical claim is "improves classification accuracy by up to 15% compared to random sampling." As stated, this is based on a single dataset (MNIST), synthetic noise, and a best-case framing, with no error bars and no named strong baselines. The abstract-level evidence cannot support a general claim about the method's effectiveness. Please report mean and standard deviation over multiple seeds and noise realizations, show full learning curves, and compare against standard noisy-label methods (e.g., small-loss selection, Co-teaching, DivideMix) at matched retention fractions. Without this, the accuracy improvement cannot be attributed to PMI-based filtering rather than to simply discarding difficult examples.
  3. [Method/Interpretation] For uniform random label corruption, a corrupted sample has a label that is independent of its input, so its PMI is near zero by construction. The statement "lower contributions indicate noisy or mislabeled instances" is therefore partly tautological. The substantive claim is that retaining high-MI samples improves learned classification accuracy, and that this improvement is not obtained by dropping hard or rare clean inputs. This distinction should be made explicit, and the experiments should show that the bottom of the PMI ranking is enriched for corruptions rather than for rare or atypical clean examples.
minor comments (4)
  1. [Notation] Provide formal notation for PMI and the empirical estimator. The manuscript should clearly define the sample-level pointwise mutual information, how the marginals and joint are estimated, and how the retention fraction or PMI threshold is chosen.
  2. [Full text / figures] The submitted full text is corrupted by character-encoding errors; most of the body is unreadable replacement characters, including the method description and result tables/figures. The PDF or source must be re-uploaded with correct encoding so that the derivation and the empirical results can be assessed.
  3. [Related work] The manuscript cites related work only implicitly. Please add explicit comparisons and references to the small-loss selection literature, confident-learning approaches, and noise-robust training methods, so that the contribution is clearly positioned.
  4. [Input-noise experiments] Clarify what is meant by "benign input modifications" and "truly corrupted samples." Define the corruption types, their severity, and the evaluation metric used for the input-filtering claim.

Circularity Check

1 steps flagged · score 4.0 of 10

Low-PMI-means-corruption is definitional, but the filtering/accuracy evaluation is external.

  1. self definitional [Abstract; Section 2 (Preliminaries), definition of pointwise mutual information]
    "We compute each sample's pointwise contribution to the overall mutual information and find that lower contributions indicate noisy or mislabeled instances."

    The 'pointwise contribution' is the pointwise mutual information pmi(x,y)=log p(x,y)/(p(x)p(y)). Under the paper's synthetic label-corruption model, a corrupted label is drawn independently of x, so p(x,y)=p(x)p(y) and pmi=0 (or near zero in finite-sample estimates), while clean labels have positive pmi in expectation. Therefore 'lower contributions indicate noisy labels' is not an empirical finding but a restatement of the definition of pointwise MI plus the assumed independence of the corruption process. The claim is true by construction; the independent content of the paper rests on the later MNIST test-accuracy comparison after filtering.

full rationale

The abstract's sentence conflates a definitional consequence with an empirical discovery. However, the paper's data-selection claim is validated by retraining on the high-MI subset and measuring test accuracy, which is an external benchmark not encoded in the PMI definition. Thus the circularity is partial and localized to the wording of the central 'indication' claim; no self-citation or imported uniqueness issues are present. Score 4.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

Everything the score depends on that the abstract does not supply: the retention threshold and the MI estimator are free choices; the faithfulness of density estimates computed from corrupted data is assumed; synthetic MNIST noise is assumed representative. No new entities are postulated; the method reuses the standard pointwise mutual information statistic.

free parameters (2)
  • MI ranking threshold / retention fraction
    The method keeps 'high-MI samples' but the abstract does not state how many samples are retained or how the cutoff is chosen; the reported up-to-15% gain depends on this choice.
  • MI estimator configuration
    Estimating pointwise MI for 28x28 pixel images requires a density or estimator choice (bins, feature representation, neural estimator) not described in the abstract; results depend on it.
assumptions (3)
  • domain assumption The empirical joint distribution p(x,y) estimated from the corrupted training set is accurate enough for per-sample MI contributions to rank samples by true label quality.
    The method computes MI on the noisy data itself; if estimation error or the noise biases marginals, rankings may reflect input rarity instead of corruption (method as described in the abstract).
  • domain assumption Synthetic noise used in the MNIST experiments is representative of real-world label and input corruption.
    The abstract validates on synthetic noise only, then generalizes to 'real-world datasets' in the motivation.
  • domain assumption The additive decomposition of mutual information into per-sample contributions is the correct sample-level quality score.
    The method equates per-sample contribution to I(X;Y) with sample quality; the abstract asserts this without a derivation.

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Cite this review

Pith. "Pith review of Detecting Mislabeled and Corrupted Data via Pointwise Mutual Information." pith.science (2026). https://pith.science/paper/OMLE4V37

@misc{pith2026250807713,
  author       = {Pith},
  title        = {Pith review of: Detecting Mislabeled and Corrupted Data via Pointwise Mutual Information},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OMLE4V37}},
  note         = {Machine review of arXiv:2508.07713}
}
read the original abstract

Deep neural networks can memorize corrupted labels, making data quality critical for model performance, yet real-world datasets are frequently compromised by both label noise and input noise. This paper proposes a mutual information-based framework for data selection under hybrid noise scenarios that quantifies statistical dependencies between inputs and labels. We compute each sample's pointwise contribution to the overall mutual information and find that lower contributions indicate noisy or mislabeled instances. Empirical validation on MNIST with different synthetic noise settings demonstrates that the method effectively filters low-quality samples. Under label corruption, training on high-MI samples improves classification accuracy by up to 15\% compared to random sampling. Furthermore, the method exhibits robustness to benign input modifications, preserving semantically valid data while filtering truly corrupted samples.

Discussion (0). Continue with ORCID to comment.

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Reviewed August 5, 2026 · model on record in the stance chip above.