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REVIEW 4 major objections 7 minor 43 references

Geodesic Flow Kernels for Semi-Supervised Learning on Mixed-Variable Tabular Dataset

T0 review · 4 major / 7 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper proposes GFTab, a semi-supervised method that corrupts continuous and categorical variables differently and measures the corruption with a geodesic flow kernel, and claims it outperforms existing ML/DL methods on mixed-variable…

desk verdict A useful but sloppy empirical paper: the geodesic similarity loss is not well-defined as printed and no code hash is provided, so the central claims cannot yet be attributed to the proposed kernel. read the letter →

arxiv 2412.12864 v2 pith:P7OKCDDQ submitted 2024-12-17 cs.LG

Yoontae Hwang , Yongjae Lee This is my paper · ORCID
classification cs.LG
keywords semi-supervisedlearningtabulardatamixed-variablegeodesicflowkernelGrassmannmanifoldcontrastivecorruptiontree-basedembeddinglabelnoise
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

GFTab is a semi-supervised method for tabular data that contains both continuous and categorical columns, and the paper tries to establish that it beats established machine-learning and deep-learning baselines when labels are scarce or noisy. Each row is corrupted twice, once gently and once heavily, with corruption rules tuned to variable type; a Transformer encodes both views, and a geodesic-flow kernel—an integral over the shortest curved path between the two views' linear subspaces—measures how far the corruption moved the representation. The training objective pulls the soft and hard views together in that geometry and adds a supervised cross-entropy term from tree-based embeddings of labeled rows. On a curated set of 21 mixed-variable datasets, the paper reports the highest F1 score in 10 of 21 cases at 20% labeled data, top-three placement in 7 more, and a similar pattern at 10% labels and under label noise. The advantage is largest on datasets dominated by categorical variables.

What carries the argument

The load-bearing object is the geodesic flow kernel, a positive semi-definite matrix $A$ defined by integrating the projections of the corrupted representations $z_{hard}$ and $z_{soft}$ onto every intermediate subspace along the geodesic between their PCA subspaces $P_{hard}$ and $P_{soft}$ on the Grassmann manifold $G(D, d_{lin})$ (the manifold of $D$-dimensional linear subspaces). The generalized SVD of $P_{hard}^\top P_{soft}$ and $R_{hard}^\top P_{soft}$ supplies the principal angles, and $A$ has a closed form, so the similarity loss $L_{sim} = 1 - z_{soft}^\top A z_{hard} / (\sqrt{z_{soft}^\top A z_{soft}} \sqrt{z_{hard}^\top A z_{hard}})$ can be computed without sampling the path. This loss is what turns 'how much did the corruption change this representation' into a manifold-aware quantity, and the paper's ablation attributes its advantage over InfoNCE, Barlow Twins, and uniformity-alignment losses to that geometric sensitivity. Two supporting pieces are the variable-specific corruption (permutation mixing for continuous columns, neighborhood shifts for categorical columns) and the tree-based embedding of labeled rows from a gradient-boosted decision tree, which enters the supervised cross-entropy term.

What would settle it

Train GFTab with the geodesic-flow similarity loss replaced by ordinary cosine similarity between $z_{hard}$ and $z_{soft}$, keeping the corruption methods and tree embedding unchanged; if the F1 scores on the 21 datasets do not drop materially, the geodesic kernel is not the component carrying the claimed improvement.

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Extended reading notes

Core claim

The central claim is that the geometric relationship between a soft and a hard corrupted view of the same tabular instance, integrated along a geodesic on the Grassmann manifold, is a better similarity signal for mixed-variable tabular data than Euclidean losses such as InfoNCE, Barlow Twins, or alignment-uniformity. GFTab corrupts continuous variables by a variable-selection network followed by weighted row and column shuffles, and categorical variables by neighborhood shifts sized by a corruption rate; a Transformer encodes both views; PCA of mini-batch representations produces a subspace for each view; and the geodesic flow kernel between those subspaces defines the similarity loss. The paper reports that, with 20% labeled training data, GFTab achieves the highest F1 score on 10 of 21 curated mixed-variable datasets and ranks in the top three on 7 more, that the wins concentrate on categorical-dominant datasets, and that the ordering is largely preserved when 20% label noise is added.

Load-bearing premise

The load-bearing premise is that the relationship between the soft and hard corrupted versions of a data point is faithfully captured by low-dimensional linear subspaces of the learned representations, so the curved path between those subspaces is a meaningful similarity signal.

Editorial extensions

If this is right

  • Learning from mixed-variable tabular data in low-label regimes can be improved by corrupting continuous and categorical columns differently rather than applying the same noise to every feature.
  • A similarity loss defined by a geodesic path between subspaces can replace Euclidean contrastive losses as the self-supervised signal for tabular representation learning.
  • The reported gains are concentrated on categorical-dominant datasets, so variable-type-aware geometry matters most where tabular data are most heterogeneous.
  • The method maintains its ranking when labels are noisy, implying the geometric similarity signal is not simply memorizing label information from the small labeled set.

Reading between the lines

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

  • The paper compares its full loss against other similarity losses but does not isolate the geodesic geometry from the two-view corruption scheme; replacing the kernel with ordinary cosine similarity on the same views would show how much of the gain is geometric.
  • Since the kernel is built from PCA bases of mini-batch representations, its usefulness plausibly depends on batch size and subspace dimension $D$; sensitivity to those two hyperparameters is a natural next experiment.
  • Dataset curation intentionally excluded purely continuous or purely categorical tables, so the contribution of the variable-specific corruption on those edge cases remains an open question.
  • The tree-based embedding consumes labeled examples only; an unlabeled-data extension via pseudo-labels would be a natural way to scale the supervised component as more data are encountered.
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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 / 7 minor

Summary. The paper proposes GFTab, a semi-supervised learning framework for mixed-variable tabular data. The method combines variable-specific corruption of continuous and categorical features, a geodesic-flow-kernel similarity loss that aligns clean and corrupted representations on a Grassmann manifold, and tree-based embeddings to exploit labeled structures. The authors evaluate GFTab on 21 curated datasets at 10% and 20% labeled fractions, with and without label noise, comparing against seven ML/DL baselines and reporting F1 scores. The paper claims that GFTab outperforms existing models on many datasets, especially under limited labels, and includes ablations of each component (corruption, loss function, VSN, tree embedding, trade-off parameter β).

Significance. If the method were precisely specified, the paper would constitute a useful empirical study of semi-supervised tabular learning: the benchmark suite is broader than in many prior works, baselines are tuned, and component-level ablations are provided. The paper's central formal contribution, the geodesic flow kernel loss, is, however, not well-defined as printed, so the current version does not permit independent verification of the method or attribution of the reported gains to the proposed kernel. The empirical results themselves would also benefit from statistical tests that account for paired dataset comparisons. The paper's strengths (broad evaluation, ablations, effort toward mixed-variable realism) are substantial, and the formal issues appear fixable, so the appropriate course is a major revision.

major comments (4)
  1. [The GFTab Framework II: Geodesic Flow Kernel, Eqs. (5)-(9)] The geodesic flow kernel loss is not well-defined as printed. Eq. (7) writes z_hard^T A z_soft but Def. 2 declares A ∈ R^{D×D}, whereas z_hard and z_soft are both in R^{dlin}; for the quadratic form to make sense A must be dlin×dlin. In Eq. (5), the block matrix [[U1Γ(π), 0],[0, -U2Σ(π)]] cannot multiply [P_hard R_hard] (dlin×dlin) to produce a dlin×D matrix; the correct geodesic flow formula from Gong et al. uses a vertical stack [[U1Γ(π)],[-U2Σ(π)]] and no zero blocks. Eq. (8) further mixes R_hard and R_soft (Eq. (5) uses R_hard but Eq. (8) uses R_soft) and does not specify the dimensions of U2, D, E, and G. Finally, Eq. (9) divides by sqrt(A z_soft) and sqrt(A z_hard), which are vectors, not scalar norms; the loss should be normalized by sqrt(z_soft^T A z_soft) sqrt(z_hard^T A z_hard). These are not mere typos: because L_sim is contribution (2) of the paper and the basis for Figure 3, the equations must be corrected and the computation of P_hard, P_soft, U1, U2, Γ, Σ, and D precisely specified.
  2. [The GFTab Framework II / Implementation details] The procedure for obtaining the Grassmannian subspaces is omitted. The paper states 'we leverage the assumption that data lie in a low-dimensional linear subspace' and models z_soft and z_hard with bases P ∈ R^{dlin×D}, but does not say how P_hard and P_soft are computed (e.g., PCA of the minibatch embeddings, PCA of the full training set, recomputed each iteration), how D is chosen, or how differentiation through the PCA/SVD steps is handled. Appendix B lists d_emb, dim_head, layers, and depths for GFTab but not D, γ, λ, or β (β is later fixed to 1.0 after the analysis in Figure 4). Without this information, the method cannot be reimplemented, and the loss ablation in Figure 3 cannot be attributed to the geodesic kernel rather than to the other components.
  3. [Categorical Variable Corruption, Remark] The Remark states that to achieve a corruption rate of at least γ, the minimum neighborhood size s must satisfy s ≥ ⌈2n(1−γ)−1⌉. This inequality is not derived and appears inconsistent with the paper's own definition of corruption rate. Since s controls the size of the neighborhood from which a replacement category is sampled, larger s should increase the chance of corruption; however, the inequality is easiest to satisfy for γ near 1 and impossible for small γ (e.g., γ=0.2, n=10 requires s≥15, exceeding the number of categories). The authors should define the corruption rate explicitly (probability that a category is changed, or expected fraction of altered categories) and give a correct derivation.
  4. [Experiments / Tables 1, 2, 7, 8] The central empirical claim of superiority over baseline models is based on point estimates of mean F1 with standard deviations over (presumably) a small number of runs. Many differences in Tables 1 and 2 are within one standard deviation of the baseline, and the win matrices in Figures 2-4 do not account for the paired structure of the comparison. I recommend adding a paired test across datasets (e.g., Wilcoxon signed-rank test comparing per-dataset scores) or at least reporting the number of seeds and a corrected resampled t-test, so that the reader can assess whether the reported wins reflect a reliable difference.
minor comments (7)
  1. [The GFTab Framework II, Eq. (9)] Eq. (9) uses z_soft^T A z_hard while Eq. (7) uses z_hard^T A z_soft; since A is symmetric (if it is the GFK matrix), the order is fine, but the asymmetric notation should be unified for readability.
  2. [Appendix B, Table 4] The hyperparameter table header 'GKSMT' appears to be a typo for 'GFTab'; please correct it.
  3. [The GFTab Framework II, Eq. (8)] The symbols 'd1i', 'e2i', and 'g3i' below Eq. (8) should be 'd_i', 'e_i', and 'g_i', and the definitions should be checked for typographical errors (e.g., the sign in e2i).
  4. [Categorical Variable Corruption] The sentence 'Unlike continuous variables, Because ordered categories allow for the concept of relative closeness, ...' is grammatically broken and should be rephrased.
  5. [The GFTab Framework III: Tree-Based Embedding] The tree-based embedding section is under-specified: it is unclear whether the GBDT is trained on the labeled subset, which target is used, and how the leaf embedding is combined with the soft/hard representations in the total loss. A short pseudocode or an architecture figure with tensor dimensions would help.
  6. [The GFTab Framework I, Eq. (2)] The text says 'randomly shuffling the row and columns within the Ξcont' but the permutation matrix P appears to permute columns; please clarify the exact permutation operation.
  7. [Implementation details / Code availability] The code is stated to be publicly available, but the manuscript itself contains no code or commit hash; please provide an anonymized repository or detailed pseudocode in the revision so that reviewers can verify the implementation.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the geodesic-flow kernel is imported from external sources and the central claims are benchmark measurements, not constructed outputs.

full rationale

The paper's derivation chain is self-contained in the relevant sense. The geodesic-flow kernel is not derived from GFTab's own outputs; Eq. (7) defines the kernel as an integral over projections onto Grassmannian points, and Eq. (8) is explicitly cited to Gong et al. (2012) and Simon, Koniusz, and Harandi (2021), both external works, so the closed-form matrix A is imported independent support rather than a self-citation. The 'low-dimensional linear subspace' premise is stated as an assumption ('we leverage the assumption that data lie in a low-dimensional linear subspace to derive features from both z_soft and z_hard'), not as a conclusion obtained from the method. The empirical claims in Tables 1 and 2 and the ablations in Figures 2 and 3 are benchmark measurements; hyperparameters are tuned and reported in Appendix B, not hidden as predictions. The dimensional inconsistency in Eqs. (7)-(9) (A declared as D x D while z_hard and z_soft are d_lin-dimensional, and Eq. (9) normalizing by vector-valued quantities) is a formal specification gap, but it is not circular: the loss is not equivalent by construction to the data used to fit it. No self-citation chain is load-bearing, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 5 free parameters · 3 assumptions · 0 invented entities

The kernel relies on a stated low-dimensional subspace assumption and on standard Grassmann geometry cited from prior work. The method also depends on several hand-set hyperparameters (beta, lambda, gamma, D, architecture sizes), none of which are derived from theory. No new physical or unobserved entities are introduced.

free parameters (5)
  • beta (balance between L_sim and L_ce) = 1.0
    Chosen via Figure 4 experiments; controls the relative contribution of supervised loss and affects all reported results.
  • corruption rate gamma for categorical corruption = not stated in paper
    Controls neighborhood size s(gamma) in Eq. (3); no default value is given in the main text.
  • lambda in continuous soft/hard views = not stated in paper
    Mixes original and permuted representations in Eq. (2); no default value is specified.
  • Grassmann subspace dimension D = not stated in paper
    Defines the basis P in Section II and the kernel in Eqs. (7)-(8); no selection procedure is described.
  • architecture hyperparameters (d_emb, dim_head, layers, depths) = grid-searched values
    Appendix B lists search ranges for these dimensions; they are tuned per dataset.
assumptions (3)
  • domain assumption Learned representations of soft and hard views lie in a low-dimensional linear subspace.
    Stated explicitly in Section 'The GFTab Framework II'; used to justify PCA bases and the Grassmann geodesic flow.
  • domain assumption Benchmark data samples are i.i.d.
    Stated in Section 'Tabular Benchmarks Dataset'; used to exclude sequential or temporal datasets.
  • standard math Standard gSVD and Grassmann geodesic flow formulas from prior work.
    Eqs. (5)-(8) rely on Van Loan 1976 and Gong et al. 2012; these are accepted mathematical results.

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Cite this review

Pith. "Pith review of Geodesic Flow Kernels for Semi-Supervised Learning on Mixed-Variable Tabular Dataset." pith.science (2026). https://pith.science/paper/P7OKCDDQ

@misc{pith2026241212864,
  author       = {Pith},
  title        = {Pith review of: Geodesic Flow Kernels for Semi-Supervised Learning on Mixed-Variable Tabular Dataset},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/P7OKCDDQ}},
  note         = {Machine review of arXiv:2412.12864}
}
read the original abstract

Tabular data poses unique challenges due to its heterogeneous nature, combining both continuous and categorical variables. Existing approaches often struggle to effectively capture the underlying structure and relationships within such data. We propose GFTab (Geodesic Flow Kernels for Semi- Supervised Learning on Mixed-Variable Tabular Dataset), a semi-supervised framework specifically designed for tabular datasets. GFTab incorporates three key innovations: 1) Variable-specific corruption methods tailored to the distinct properties of continuous and categorical variables, 2) A Geodesic flow kernel based similarity measure to capture geometric changes between corrupted inputs, and 3) Tree-based embedding to leverage hierarchical relationships from available labeled data. To rigorously evaluate GFTab, we curate a comprehensive set of 21 tabular datasets spanning various domains, sizes, and variable compositions. Our experimental results show that GFTab outperforms existing ML/DL models across many of these datasets, particularly in settings with limited labeled data.

Figures

Figures reproduced from arXiv: 2412.12864 by the authors.

Figure 1
Figure 1. The proposed model (GFTab) is a semi-supervised framework specifically designed for handling tabular data. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Win matrices for different categorical variable cor [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Win matrix between GFTab with three different [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Performance of GFTab with different levels of bal [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

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