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REVIEW 4 major objections 4 minor 32 references

Unveiling the Role of Data Uncertainty in Tabular Deep Learning

T0 review · 4 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read A large share of tabular deep learning's recent wins comes from implicitly handling high data uncertainty, and making that explicit yields a better embedding.

desk verdict A useful uncertainty lens for tabular DL with solid mechanism sections, but the headline 'disproportionate benefit' claim needs quantitative backup beyond absolute ΔMSE curves. read the letter →

arxiv 2509.04430 v1 pith:G3VVRKPS submitted 2025-09-04 cs.LG

Nikolay Kartashev , Ivan Rubachev , Artem Babenko This is my paper · ORCID
classification cs.LG
keywords datauncertaintyaleatorictabulardeeplearningnumericalfeatureembeddingsretrieval-augmentedmodelsparameter-efficientensemblinglocaltargetconsistencytripletloss
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 argues that data uncertainty, meaning the irreducible aleatoric noise in target labels, is the key to understanding why several recent tabular deep learning techniques succeed. Concretely, it claims that numerical feature embeddings, retrieval-augmented models such as ModernNCA, and parameter-efficient ensembling such as TabM all produce their largest gains precisely on test points with the highest data uncertainty. Each technique manages this uncertainty through its own mechanism: embeddings make local neighborhoods more target-consistent, retrieval averages over many neighbors, and TabM averages gradients across branches to damp the noise component. The authors then turn this insight into a practical result: a new embedding scheme, LRLRtriplet, trained with a triplet loss to explicitly maximize local target consistency, which beats standard embeddings on regression benchmarks.

What carries the argument

The central object is the per-sample data uncertainty estimate, obtained by fitting the model $y_i = f(x_i) + e^{g(x_i)} \cdot \mathcal{N}(0,1)$ to predict both the noiseless target and the noise scale, using CatBoost with a Gaussian likelihood loss. Around this, the paper builds uncertainty plots that sort test points by estimated uncertainty and plot per-sample MSE differences between models. For the new embedding method, the load-bearing device is the triplet loss: for each anchor, the closer-in-target object is the positive and the farther one the negative, so the embedder is trained to make embeddings reflect target similarity; this pretrained embedder's last linear layer is discarded and the rest initializes the LRLR embedding of an MLP. For TabM, the key identity is the gradient decomposition $\frac{\partial(\phi(x_i)-y_i)^2}{\partial\theta} = 2(\phi(x_i)-f(x_i))\frac{\partial\phi(x_i)}{\partial\theta} - 2 e^{g(x_i)}\mathcal{N}(0,1)\frac{\partial\phi(x_i)}{\partial\theta}$, which lets the paper show in synthetic experiments that sharing parameters and averaging gradients across branches suppresses the noisy term more than the clean term.

What would settle it

On a real regression dataset with clean targets, inject known heteroscedastic noise; if the performance gains of MLP-PLR, ModernNCA, and TabM do not concentrate on samples with the largest injected noise, the paper's main claim fails.

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Extended reading notes

Core claim

The central claim is that a significant portion of the success of numerical feature embeddings, retrieval-augmented models, and advanced ensembling in tabular deep learning can be attributed to their implicit yet effective mechanisms for handling datapoints with high data uncertainty. The paper demonstrates, on real and synthetic regression datasets, that the per-sample performance gap between a plain MLP and each of these techniques grows as estimated uncertainty grows, often faster than the MLP's own error. For embeddings, the mechanism is improved local target consistency: the learned feature space makes neighbors more likely to share similar targets, which matters most where labels are noisy. For retrieval (ModernNCA), averaging over many neighbors resists memorizing label noise, though it can underfit in low-uncertainty regions. For ensembling (TabM), averaging gradients across shared branches reduces the noisy component of the gradient relative to the clean component, making training robust at high uncertainty. As a direct payoff, the paper introduces LRLRtriplet embeddings, which are pretrained with a triplet loss to maximize local target consistency and then fine-tuned; this scheme achieves an average rank of 1.17 across regression datasets compared to 1.67 for standard LRLR embeddings and 2.75 for a plain MLP.

Load-bearing premise

The CatBoost-based estimates of per-sample data uncertainty reflect the true aleatoric uncertainty on the real datasets; if that mapping is wrong, the apparent concentration of performance gains on 'high-uncertainty' points could be an artifact of the estimator rather than a property of the data.

Editorial extensions

If this is right

  • Numerical feature embeddings, retrieval heads, and parameter-efficient ensembles share a common explanatory mechanism; future tabular designs can be evaluated by whether they improve handling of high-uncertainty samples.
  • The LRLRtriplet scheme offers a concrete accuracy gain on regression benchmarks, with an average rank of 1.17 versus 1.67 for standard LRLR embeddings.
  • Uncertainty plots become a diagnostic tool: comparing per-sample errors sorted by estimated uncertainty reveals why one method beats another on a given dataset.
  • TabM's gradient-averaging analysis predicts that ensembling variants that reduce the noisy gradient component will be especially robust to label noise.

Reading between the lines

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

  • Beyond the paper: if the shared mechanism is real, then the unresolved DL-versus-GBDT gap on tabular data is largely a high-uncertainty phenomenon; combining uncertainty-aware losses with GBDT-style smoothing could close it further.
  • Beyond the paper: the triplet-pretraining recipe could be adapted to classification by treating targets as soft labels, or to tabular foundation models to make their few-shot gains interpretable through uncertainty handling.
  • Beyond the paper: the analysis only covers regression; a direct test would inject heteroscedastic noise into clean classification datasets and check whether the same techniques' gains concentrate on noisy points.
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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 / 4 minor

Summary. The paper proposes data (aleatoric) uncertainty as a unifying lens for explaining why several recent tabular deep learning techniques outperform a plain MLP: numerical feature embeddings (PLR/LRLR), retrieval-augmented models (ModernNCA), and parameter-efficient ensembling (TabM). The authors estimate the conditional target variance using a CatBoost model with an uncertainty-aware loss, sort test examples by estimated uncertainty, and present smoothed curves of absolute MSE differences (MSE_MLP minus MSE_model) to argue that the gains are concentrated on high-uncertainty points. They support this with synthetic datasets with known ground-truth noise, including an MLP-generated heteroscedastic regression, a saw-like 2D regression, and an 'Uncertain CIFAR-10' classification experiment. They also propose a new embedding scheme, LRLR_triplet, trained with a triplet loss to maximize local target consistency, and report improved average rank over standard LRLR embeddings on regression benchmarks.

Significance. If the uncertainty-attribution claim is established, the paper would provide a genuinely unifying explanation for several seemingly unrelated design choices in tabular deep learning and a principled basis for future method development. The paper is strengthened by multi-dataset evidence, synthetic ground-truth validation, robustness checks across alternative uncertainty estimators (Appendix H), and the release of code. The proposed LRLR_triplet embedding is a useful practical artifact. However, the central quantitative support currently rests on visual inspection of absolute-error curves, and the real-data conclusions depend on an uncertainty estimator whose accuracy on real data is not directly validated; both issues are addressable in revision.

major comments (4)
  1. [Sections 5–7 (Figures 3, 6, 8, 10)] The claim that the methods are 'disproportionately more beneficial' on high-uncertainty points is supported only by absolute ΔMSE = MSE_MLP − MSE_model versus estimated uncertainty. Under the paper's own generative model (Eq. 1), the expected MSE of any model is e^{2g(x)} plus an excess-error term, and the irreducible variance cancels in ΔMSE. Thus an increasing absolute ΔMSE is expected for any better model on harder (high-uncertainty) points, even if the model provides a constant relative improvement everywhere; in that case ΔMSE ∝ MSE_MLP, which grows with uncertainty because MSE_MLP itself grows. The paper explicitly claims the growth is faster than MSE_MLP (Section 5), but no slopes, normalized curves, or confidence intervals are reported. The same absolute metric is used in Figure 3 even though true uncertainty is known, so the synthetic validation does not resolve this artifact. Please provide a relative-improvement analysis, e.g., ΔMSE/MSE_MLP as a function of uncertainty or quantitative slope comparisons with confidence intervals, for Figures 3, 6, 8, and 10; without this, the attribution to an uncertainty-specific mechanism is not established.
  2. [Section 3.1, Figure 2b, Appendix H] The real-data conclusions require that the CatBoost-based uncertainty estimates order test examples by true aleatoric variance. The only validation against ground truth is on synthetic data with MLP-generated f and g, and Figure 2b shows only a scatterplot without a quantitative accuracy measure. Appendix H demonstrates robustness to the choice of estimator (CatBoost vs MLP/MLP-PLR), but it does not validate any estimator against true uncertainty on the real datasets where the main conclusions are drawn. A concrete test would be to inject controlled label noise into real features (or use datasets with repeated labels) and verify that the estimated-uncertainty ranking correlates with the known noise levels; at minimum, report a rank correlation or calibration statistic for the estimators on real data. Without this, the observed concentration of gains could reflect the estimator's error model rather than true data uncertainty.
  3. [Section 4.2 and Appendix D] The saw-like synthetic dataset is described inconsistently between the main text and the appendix. Section 4.2 samples uniformly from a rectangle with vertices (0,0) and (1,10) and sets the noise standard deviation to e^{g(x)} = x_2^6/62500, depending on the vertical coordinate. Appendix D instead describes triangles with vertices (2i,0), (2i+1,1), (2i+2,0) for i=0..4 (which extend to x_1=10) and a noise standard deviation of x_1^6/4 for x_1 from 0 to 10. The coordinate ranges and the noise formula disagree, so the synthetic experiments in Figures 5, 11, and 12 cannot be reproduced from the paper as written. Please correct the text to match the released code and align the two descriptions.
  4. [Section 7, Figure 10, Appendix E] The comparison between TabM and Deep Ensemble is not controlled for the number of ensemble members. Section 4.2 specifies that the Deep Ensemble averages five independently trained MLPs, while Appendix E fixes 16 branches for TabM; if the same settings are used for Figure 10, the larger effective ensemble size for TabM could be partly responsible for its larger gains on high-uncertainty points. Please compare TabM against a Deep Ensemble with a matched number of members (or otherwise match capacity and computation) before attributing the difference to TabM's parameter-sharing gradient-averaging mechanism.
minor comments (4)
  1. [Appendix B] Please state the Gaussian smoothing bandwidth used for the uncertainty plots and provide a sensitivity check; the smoothing parameter is a free choice that can affect the visual conclusions.
  2. [Figure 2b] Please report a rank correlation coefficient (e.g., Spearman) and, if possible, a calibration measure between the CatBoost uncertainty estimates and the ground-truth values; the scatterplot alone does not quantify the claimed strong agreement.
  3. [Section 5.2, Table 2, Appendix G] The statement that LRLR_triplet 'substantially outperforms' standard LRLR should be supported by the fraction of datasets with statistically significant improvements and by effect sizes, because many dataset-wise differences in Appendix G are within one standard deviation of each other.
  4. [Figure 1 caption] The caption uses 'significantly worse performance' in an informal sense; please either use a statistical test and report the result, or rephrase to avoid implying formal significance testing.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the uncertainty analysis, mechanism tests, and proposed embedding are each evaluated on quantities distinct from their construction inputs.

full rationale

The paper's derivation chain is not circular. The data-uncertainty estimates in Section 3.1 are fitted from Eq. (1) to the target variable, but the claims about method effectiveness are tested on the difference MSE_MLP - MSE_model, which removes the irreducible variance term e^{2g(x)}; therefore the observed growth of Delta-MSE with estimated uncertainty is an empirical excess-error comparison rather than a definitional identity. The estimator is not the sole input: Figure 2b validates CatBoost estimates against true g(x) on a synthetic dataset with MLP-generated f and g, and Appendix H repeats the main plots with MLP- and MLP-PLR-based estimators, so the x-axis ordering is not an artifact of the very model family whose behavior is being explained. For TabM, the gradient clean/noisy decomposition is computed on synthetic data where f and g are known, so the proposed mechanism is measured rather than assumed. For the novel LRLRtriplet embedding, the training objective (triplet loss maximizing local target consistency) is different from the evaluation metric (downstream regression MSE), so the reported improvement in Table 2 is not guaranteed by construction; it is an independent benchmark result. The paper's self-citations to TabReD datasets and to LRLR/TabM methods supply baselines and objects of study, but the load-bearing support for the uncertainty explanation comes from the synthetic ground-truth experiments and the estimator-robustness checks, not from those citations. Concerns about absolute Delta-MSE curves or about the reliability of CatBoost-based uncertainty on real datasets are empirical validity risks, not circularity.

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

The paper introduces no new physical or mathematical entities. Its main dependencies are the parametric noise model, the reliability of the uncertainty estimator on real data, and the causal interpretation of correlational sample-wise performance differences.

free parameters (2)
  • CatBoost uncertainty estimator configuration = not reported
    The data uncertainty values that sort all samples come from a CatBoost model with RMSEWithUncertainty loss; the hyperparameters are not specified in the text, so the central analysis variable is not fully pinned down.
  • Uncertainty plot smoothing bandwidth = not reported
    Smoothed curves use scipy gaussian_filter1d but the sigma value is not reported, which affects the visual shape of all uncertainty plots and the apparent size of the high-uncertainty effect.
assumptions (3)
  • domain assumption Tabular regression targets follow y = f(x) + exp(g(x)) * N(0,1), with label noise independent of features.
    Equation (1) in Section 3.1; the entire uncertainty estimation and the synthetic data generation depend on this parametric noise model.
  • domain assumption CatBoost uncertainty estimates approximate true aleatoric uncertainty on real datasets.
    Section 3.1 and Figure 2b validate on one synthetic family, but real datasets have no ground truth; all real-data conclusions rely on this premise.
  • ad hoc to paper Observed performance differences on high-uncertainty points are caused by the methods' mechanisms rather than by correlated dataset structure or estimator artifacts.
    The central causal framing in Sections 5, 6, and 7 relies on this interpretive leap; no ablation isolates the mechanism.

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Cite this review

Pith. "Pith review of Unveiling the Role of Data Uncertainty in Tabular Deep Learning." pith.science (2026). https://pith.science/paper/G3VVRKPS

@misc{pith2026250904430,
  author       = {Pith},
  title        = {Pith review of: Unveiling the Role of Data Uncertainty in Tabular Deep Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/G3VVRKPS}},
  note         = {Machine review of arXiv:2509.04430}
}
read the original abstract

Recent advancements in tabular deep learning have demonstrated exceptional practical performance, yet the field often lacks a clear understanding of why these techniques actually succeed. To address this gap, our paper highlights the importance of the concept of data uncertainty for explaining the effectiveness of the recent tabular DL methods. In particular, we reveal that the success of many beneficial design choices in tabular DL, such as numerical feature embeddings, retrieval-augmented models and advanced ensembling strategies, can be largely attributed to their implicit mechanisms for managing high data uncertainty. By dissecting these mechanisms, we provide a unifying understanding of the recent performance improvements. Furthermore, the insights derived from this data-uncertainty perspective directly allowed us to develop more effective numerical feature embeddings as an immediate practical outcome of our analysis. Overall, our work paves the way to foundational understanding of the benefits introduced by modern tabular methods that results in the concrete advancements of existing techniques and outlines future research directions for tabular DL.

Figures

Figures reproduced from arXiv: 2509.04430 by the authors.

Figure 1
Figure 1. The performance differences measured by MSE between MLP and XGBoost are shown [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. a) The scatterplots show a high correlation between the log-transformed data uncertainty estimates from CatBoost and an MLP. b) The scatterplot shows the relationship between CatBoost’s log-estimated data uncertainty and the logarithms of the true data uncertainty values used for target sampling in the controlled synthetic experiment. To analyze how various tabular DL methods perform on datapoints with different lev… view at source ↗
Figure 3
Figure 3. This figure reports performance differences on the synthetic dataset described in this [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (16 more)
Figure 4
Figure 4. Figure 4: The plots show visualization of the synthetic data generation process used in subsection 4.2. The left plot shows the func￾tion f(x) in color, while the right plot shows e g(x) on the x-axis. Targets y are generated as y = f(x) + e g(x) · N (0, 1). In the previous subs…
Figure 5
Figure 5. Figure 5: The plots show predictions of different models on the synthetic dataset described in sub [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: Uncertainty plots report the differences in MSE between MLP and MLP-PLR. The increase [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: Squared difference between a test sample’s target and the target of its [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: Uncertainty plots, built in the same way as in Figure 1, but showing difference in MSE [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 9
Figure 9. Figure 9: Difference in MSE performance of MLP and ModernNCA on train samples, with samples [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]
Figure 10
Figure 10. Figure 10: The plots show sample-wise differences in MSE between MLP and TabM in blue and [PITH_FULL_IMAGE:figures/full_fig_p010_10.png]
Figure 12
Figure 12. Figure 12: The plot shows the ratio of the aver￾age norm of a per-branch gradient to a norm of the gradient averaged between branches, taken separately for clean and noisy components. In this experiment, TabM model was tuned and trained. Higher value shows alignment between the …
Figure 13
Figure 13. Figure 13: Uncertainty plots depicting differences between MLP and XGBoost, Deep Ensemble, [PITH_FULL_IMAGE:figures/full_fig_p013_13.png]
Figure 14
Figure 14. Figure 14: Uncertainty plots depicting differences between MLP and XGBoost, Deep Ensemble, [PITH_FULL_IMAGE:figures/full_fig_p013_14.png]
Figure 15
Figure 15. Figure 15: Version of Figure 6, but using MLP as a basic model for estimating data uncertainty. As [PITH_FULL_IMAGE:figures/full_fig_p016_15.png]
Figure 16
Figure 16. Figure 16: Version of Figure 6, but using MLP-PLR as a basic model for estimating data uncertainty. [PITH_FULL_IMAGE:figures/full_fig_p016_16.png]
Figure 17
Figure 17. Figure 17: Version of Figure 8, but using MLP as a basic model for estimating data uncertainty. As [PITH_FULL_IMAGE:figures/full_fig_p017_17.png]
Figure 18
Figure 18. Figure 18: Version of Figure 8, but using MLP-PLR as a basic model for estimating data uncertainty. [PITH_FULL_IMAGE:figures/full_fig_p017_18.png]
Figure 19
Figure 19. Figure 19: Version of Figure 10, but using MLP as a basic model for estimating data uncertainty. As [PITH_FULL_IMAGE:figures/full_fig_p017_19.png]
Figure 20
Figure 20. Figure 20: Version of Figure 10, but using MLP-PLR as a basic model for estimating data uncertainty. [PITH_FULL_IMAGE:figures/full_fig_p017_20.png]

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    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.