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REVIEW 2 major objections 6 minor 64 references

Quantifying Correlations of Machine Learning Models

T0 review · 2 major / 6 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read Errors of machine learning models are not independent: shared data, algorithms, and foundation models create strong correlations that raise the risk of simultaneous failure.

desk verdict Useful measurement for same-data and overlapping-feature scenarios, but the foundation-model experiment does not estimate the correlation defined in the paper. read the letter →

arxiv 2502.03937 v1 pith:KFTCGLCC submitted 2025-02-06 cs.LG cs.NAmath.NA

Yuanyuan Li , Neeraj Sarna , Yang Lin This is my paper · ORCID
classification cs.LGcs.NAmath.NA
keywords modelerrorcorrelationaggregatedriskfoundationhomogenizationensemblediversitycorrelatedfailuresmachinelearningphi_Kcoefficientportfolio
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 argues that errors of different machine learning models are not independent: models that share a training dataset, similar algorithms, overlapping predictive features, or a common foundation model make errors that are strongly correlated. If true, portfolios of AI models deployed together can fail simultaneously more often than individual failure rates suggest, which matters for safety-critical uses such as medical dosing prediction or connected vehicles. The authors define correlation coefficients for model errors, then measure them empirically across tabular, image, and text tasks, finding pervasive positive correlations in all three scenarios they construct. The intended contribution is a framework for quantifying the systemic risk that arises when many models share common building blocks, rather than treating each model's error in isolation.

What carries the argument

The central objects are the two correlation coefficients: the per-input error correlation rho between two models (Definition 1) and the aggregate performance correlation Pi between two fine-tuned models built from the same foundation model (Definition 2). The mechanism is that error randomness comes from training and test data, so models that share data, architecture, features, or pretrained weights produce dependent error terms. For regression, Pearson's coefficient is used; for classification, the phi_K coefficient, which captures nonlinear dependence among categorical variables, is used. These coefficients are estimated empirically on real datasets across the three scenarios.

What would settle it

Fine-tune two models from the same foundation model on the same training set and compute the per-input error correlation (Definition 1) on a held-out test set; if that per-input correlation is close to zero while only the aggregated error-frequency correlation (Definition 2) stays high, the homogenization conclusion would not follow. The claim predicts both should be substantial.

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Extended reading notes

Core claim

The central claim is that error correlations between machine learning models are substantial and systematic. Definition 1 formalizes the correlation of per-input error terms between two models, with randomness coming from training and test data, and Definition 2 formalizes the correlation of aggregate performance between two fine-tuned models that share a foundation model. Empirically, on the California Housing dataset, random forest, XGBoost, and generalized additive models show strong positive error correlations, and two neural networks correlate strongly with each other and with linear regression. On CIFAR-10, similar architectures (the two convolutional networks, the two small neural networks) have high correlated errors, while on a financial text task the eight tested large language models, all transformer-based, show widespread correlated errors. When models share highly predictive overlapping features, their errors correlate strongly, and when different models are fine-tuned from the same foundation model on different datasets, their error frequencies across datasets are positively correlated, particularly for text tasks that are semantically related. The authors interpret this as empirical evidence for homogenization: downstream models inherit the foundation model's error patterns, making simultaneous failures more likely.

Load-bearing premise

The Scenario-3 experiments treat the correlation of error frequencies across different datasets and across different foundation models as a valid estimate of Definition 2's correlation between two fine-tuned models that share one foundation model, but the experiments never directly compute the per-input error correlation between two models sharing the same foundation model on the same test set.

Editorial extensions

If this is right

  • A portfolio of models trained on the same public dataset will have a higher-than-independent probability of simultaneous failure, so risk assessment must account for error correlation, not just individual accuracy.
  • Widespread use of transformer-based foundation models concentrates error correlations: different applications fine-tuned from similar base models can fail in unison.
  • Organizations that build models from the same highly predictive public features will have correlated errors even if they use different model algorithms.
  • Fine-tuning many downstream models from one foundation model propagates that model's defect patterns; the resulting homogenization is measurable through correlation of error frequencies across tasks.
  • Mitigation strategies should actively diversify data sources, model architectures, and foundation models to reduce systemic risk from correlated errors.

Reading between the lines

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

  • If error correlations persist at scale, model risk management should treat a set of foundation-model-derived systems as a single correlated exposure, analogous to a loan portfolio with a common factor; diversifying across several independent foundation models could become a concrete mitigation lever.
  • The framework could be extended to tail dependence, measuring the correlation of rare catastrophic errors, which would capture joint failures better than Pearson correlation when error distributions are heavy-tailed.
  • A testable extension is to predict cross-dataset performance correlation from a quantitative measure of task similarity between the fine-tuning datasets; the paper's ag_news outlier suggests such a relationship exists but is not formalized.
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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

2 major / 6 minor

Summary. The paper defines three scenarios in which errors of multiple ML models may be correlated—models trained on the same dataset with different architectures (Scenario 1), models trained on overlapping feature sets (Scenario 2), and fine-tuned models sharing a foundation model (Scenario 3)—and provides formal definitions of error correlation (Definition 1) and performance correlation for fine-tuned models (Definition 2). It then reports empirical correlation matrices for tabular regression (California Housing), image classification (CIFAR-10, EUROSAT, MNIST, Fashion-MNIST), and text classification (financial_phrasebank, twitter-financial-news-sentiment, emotion-balanced, ag_news), using Pearson and ϕK coefficients. The central claim is that aggregate risks are substantial when models share algorithms, training data, or foundation models.

Significance. The paper addresses an important and understudied problem: correlated failures across concurrently deployed ML models. The decomposition into three practical scenarios and the attempt to measure correlations directly are useful contributions, and the availability of code supports reproducibility. If the empirical claims were fully supported, the work would be valuable for AI risk management and portfolio-level analysis of model failures. However, the Scenario 3 experiment does not estimate the quantity in Definition 2, and the single-split point estimates provide thin support for the quantitative conclusions. The framework is a good starting point, but the current evidence does not yet establish the advertised homogenization claim.

major comments (2)
  1. [Section III-A / Section IV] The experiment reported in Section IV-C3 does not estimate the correlation defined in Definition 2. Eq. (4) is the correlation, for a fixed foundation model F, between the performance metrics E(f1(F), Z1) and E(f2(F), Z2) of two fine-tuned models derived from that same F. Figures 6b and 7b instead compute, for each pair of datasets, the Pearson correlation across the set of foundation models F of the error frequencies E(f_F, Zi) and E(f_F, Zj). Because each foundation model is fine-tuned only once per dataset, there is no replication from which a within-F correlation between two fine-tuned models could be estimated. The cross-foundation correlation Corr_F(E(f_F,Zi), E(f_F,Zj)) can be large even when downstream errors are independent given F, simply because some datasets are easier than others; it therefore cannot support the abstract's claim that risks are substantial 'when models share ... foundational models' or the homogenization conclusion in Section V. To support this claim, the authors need to fine-tune each foundation model multiple times per dataset (varying seeds or data order) and estimate the within-F correlation of Eq. (4); the text should also specify the probability distribution over f1(F) and f2(F), since Eq. (4) is degenerate if fine-tuning is deterministic.
  2. [Section IV-C2] Definition 1 states that the randomness in Eq. (3) comes from the training and test datasets, but the experiments in Sections IV-C1 and IV-C2 use one fixed random split and one training run per model, then correlate the error vectors over the test set. This estimates a conditional correlation between two realized fitted models, not the marginal correlation over training randomness specified in Definition 1. This distinction matters for the paper's message: two algorithms that are similar on average may still show a different empirical correlation for a particular pair of trained models. The authors should either perform multiple training runs and test splits (with bootstrap or standard-error reporting) and average the resulting correlations, or explicitly redefine the estimand as the correlation of errors of fixed models. The absence of any uncertainty quantification for Figures 1-4, 6b, and 7b is a further concern, since the conclusions are quantitative statements about the magnitude of risk.
minor comments (6)
  1. [Section IV] The code is described as 'available online at this repository' but no URL is given; please provide a working link.
  2. [Section IV-C3] The subsection heading contains a typo: 'fintuning' should be 'fine-tuning'.
  3. [Section IV-C2] The symbol 'M∫' in the paragraph after Figure 4 should be 'M_f' (or 'Mf') for consistency with the earlier definition.
  4. [Section I] The first contribution bullet contains a grammar error: 'We introduces' should be 'We introduce'.
  5. [References] The reference for the twitter-financial-news-sentiment dataset [36] points to a Hugging Face model URL rather than a dataset citation; please cite the dataset properly.
  6. [Section III-A] The notation f1(F) in Definition 2 is awkward because F is a model, not a family; consider writing f_{1,F} or 'fine-tuned from F' to avoid confusion.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the paper measures error correlations directly from data, and the Scenario 3 gap is a construct-validity concern, not a derivation that reduces to its inputs.

full rationale

The paper's central quantities (Definition 1 and Definition 2) are defined independently of the empirical results. Scenario 1 and Scenario 2 correlations are computed directly from model errors on held-out test data, with no fitted parameters and no prediction that is later shown to be equivalent to its own input. Scenario 3 defines the target as Corr(E(f1(F), Z1), E(f2(F), Z2)) for two fine-tuned models derived from the same foundation model, but the reported experiment instead computes, for a set of different foundation models, the Pearson correlation across F of error frequencies on dataset pairs. This is a mismatch between definition and operationalization, meaning the homogenization claim may be unsupported by the experiment as described. However, a mismatch is not circularity: the experiment does not define the correlation in terms of the conclusion, and no parameter is fitted and then renamed as a prediction. The load-bearing issue, if any, is construct validity, not circular reduction. There are also no load-bearing self-citations: references [6] and [7] merely introduce the term 'homogenization' and are not used to justify the empirical estimates. Accordingly, the appropriate circularity score is 0.

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

The paper introduces no new free parameters or entities; it measures a standard quantity, correlation of errors, on existing datasets and models. Its load-bearing assumptions are the representativeness of the sampled datasets and splits and the validity of the Scenario 3 operationalization.

assumptions (3)
  • domain assumption Error terms are random variables whose randomness comes from the training and test datasets (Section III-A, Definition 1).
    The correlation definition relies on this source of randomness; in experiments, only one training/test split is used, so this randomness is not actually sampled.
  • domain assumption Pearson and phi-K correlation coefficients are appropriate measures for continuous and categorical errors (Section III, Remark 2).
    The choice is reasonable, but no check that the assumptions of these coefficients, such as linearity for Pearson, hold for the error distributions.
  • domain assumption Fine-tuned foundation models inherit a meaningful component of their error behavior from the base model (Section III Scenario 3).
    This is the premise underlying the homogenization hypothesis; the paper measures correlations rather than testing causality.

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Cite this review

Pith. "Pith review of Quantifying Correlations of Machine Learning Models." pith.science (2026). https://pith.science/paper/KFTCGLCC

@misc{pith2026250203937,
  author       = {Pith},
  title        = {Pith review of: Quantifying Correlations of Machine Learning Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KFTCGLCC}},
  note         = {Machine review of arXiv:2502.03937}
}
read the original abstract

Machine Learning models are being extensively used in safety critical applications where errors from these models could cause harm to the user. Such risks are amplified when multiple machine learning models, which are deployed concurrently, interact and make errors simultaneously. This paper explores three scenarios where error correlations between multiple models arise, resulting in such aggregated risks. Using real-world data, we simulate these scenarios and quantify the correlations in errors of different models. Our findings indicate that aggregated risks are substantial, particularly when models share similar algorithms, training datasets, or foundational models. Overall, we observe that correlations across models are pervasive and likely to intensify with increased reliance on foundational models and widely used public datasets, highlighting the need for effective mitigation strategies to address these challenges.

Figures

Figures reproduced from arXiv: 2502.03937 by the authors.

Figure 1
Figure 1. Pearson correlations between errors of different models [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 4
Figure 4. Pearson correlations between errors of different models [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Feature importance of XGBoost model on California [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figures from the paper (1 more)
Figure 7
Figure 7. Figure 7: Model performance and their correlations on text [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]

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Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.