{"id":"d965b067-3c34-4d4b-8100-7d424efe8b2e","arxiv_id":"2412.12864","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"GFTab, a semi-supervised tabular method with variable-specific corruptions and geodesic flow kernel similarity, reports the best F1 on about half of 21 mixed-variable benchmarks with sparse labels.","lead":"The authors propose GFTab, a semi-supervised method for tabular data with mixed numeric and categorical columns; it learns from shuffled copies of each row and from a geometric similarity between the copies. On 21 tabular benchmarks with only 10-20% of labels, GFTab reports the best F1 score in about half of the cases and top-three performance in most others.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The geodesic-flow kernel loss is not well-defined as printed (Eqs. 7–9 mix dimensions and normalize by a vector); without released code/hash, the reported gains cannot be traced to the proposed kernel, so the conditional verdict stands.","rationale":"I agree with the reader that the paper is not ready for full acceptance, but I would place the load-bearing gap slightly earlier than the low-dimensional linear subspace assumption. The subspace assumption is a genuine conceptual risk: if mini-batch PCA bases are not faithful, the geodesic kernel is a heuristic. However, the larger immediate problem is that the exact objective is impossible to reconstruct from the text: Eqs. (7)–(9) have inconsistent matrix dimensions and a vector-valued normalization, and the code is not available. This blocks verification of both the main tables and the loss ablation that is supposed to show the kernel matters. The Figure 3 win matrices are useful independent support for the kernel's role, and the empirical results are plausible descriptive evidence, so this is an addressable condition rather than grounds for rejection. The reader's other conditions (significance tests, Appendix E/Table 8 noise-level mismatch, missing code hash) remain. I therefore keep the conditional verdict unchanged.","tokens_in":22468,"tokens_out":11311,"duration_ms":103806,"concrete_test":"Obtain the exact released code with a commit hash and rerun the 20%-labeled experiments together with the Figure 3 loss ablation under two implementations: (i) the printed Eqs. (7)–(9) verbatim, and (ii) the corrected kernel with A ∈ R^{dlin×dlin} and denominator sqrt(z_soft^T A z_soft) · sqrt(z_hard^T A z_hard). If the verbatim loss cannot be evaluated or produces different rankings, the paper must state the actual objective, the PCA basis-fitting procedure, and the selected D before the empirical claim can be verified.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is empirical, but it can be assessed only if the proposed objective is actually specified. In the geodesic-flow kernel section, z_hard and z_soft are dlin-dimensional embeddings while A is declared to be D×D (Def. 2). Expanding Eq. 7 gives A = ∫ GF(π)GF(π)^T dπ, which must live in R^{dlin×dlin}; the printed Eq. 8 can yield such a matrix only if the gSVD factors in Eq. 6 are sized consistently, but the text says Γ and Σ have diagonal entries for i=1,...,D, which is dimensionally impossible except in special cases such as dlin=2D. Eq. 9 then normalizes by sqrt(A z_soft) and sqrt(A z_hard), which are vector-valued, not scalar norms of the projected embeddings. These are not merely typographical issues: the paper never states whether the implemented loss is z_soft^T A z_hard divided by sqrt(z_soft^T A z_soft) sqrt(z_hard^T A z_hard), how D is chosen, or how the PCA bases are fit. Because no code or commit hash is provided, the Table 1/Table 2 gains and the Figure 3 loss ablation cannot be attributed to the geodesic-flow component. This is an internal formal gap in the method definition, not a disagreement with any external consensus.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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).","tokens_in":22831,"tokens_out":11586,"duration_ms":98107,"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":[{"comment":"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.","section":"The GFTab Framework II: Geodesic Flow Kernel, Eqs. (5)-(9)"},{"comment":"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.","section":"The GFTab Framework II / Implementation details"},{"comment":"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.","section":"Categorical Variable Corruption, Remark"},{"comment":"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.","section":"Experiments / Tables 1, 2, 7, 8"}],"minor_comments":[{"comment":"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.","section":"The GFTab Framework II, Eq. (9)"},{"comment":"The hyperparameter table header 'GKSMT' appears to be a typo for 'GFTab'; please correct it.","section":"Appendix B, Table 4"},{"comment":"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).","section":"The GFTab Framework II, Eq. (8)"},{"comment":"The sentence 'Unlike continuous variables, Because ordered categories allow for the concept of relative closeness, ...' is grammatically broken and should be rephrased.","section":"Categorical Variable Corruption"},{"comment":"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.","section":"The GFTab Framework III: Tree-Based Embedding"},{"comment":"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.","section":"The GFTab Framework I, Eq. (2)"},{"comment":"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.","section":"Implementation details / Code availability"}],"recommendation":"major_revision","confidential_remarks":"The paper appears to be a camera-ready AAAI paper (copyright footer and DOI), yet this arXiv version contains serious formal errors in the core equations. The journal should insist on a corrected version of Eqs. (5)-(9) and on code release before publication. I do not see signs of intentional circularity or overclaiming beyond normal hyperparameter tuning; the main problem is internal consistency and completeness of the method definition."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague — GFTab is a semi-supervised method for mixed-variable tabular data that combines three known ingredients: variable-specific soft/hard corruption, a geodesic flow kernel similarity loss, and tree-based embedding. The new part is the assembly and the 21-dataset benchmark. On its own terms, the empirical claim is credible as descriptive evidence: GFTab is top-1 on 10 of 21 datasets at 20% labels and top-3 on 7 more, with a sensible split between categorical-heavy and continuous-heavy panels. The ablation studies (categorical corruption, loss functions, VSN, tree embedding) are a useful check, and the benchmark curation is more careful than most tabular papers. The citation pattern is appropriate; they credit Gong et al. for GFK and Kim et al. for DATE.\n\nBut the paper has a real formal problem in the definition of the geodesic similarity loss. Eq. (7) declares A ∈ R^{D×D} even though z_hard and z_soft are dlin-dimensional, so z_hard^T A z_soft cannot be a scalar; Eq. (9) divides by sqrt(A z_soft) and sqrt(A z_hard), which are vector-valued, not norms; and the gSVD decomposition in Eq. (6) is dimensionally impossible in general unless dlin = 2D. These are not just typos: the paper never states the implemented loss, how D is chosen, or how the PCA bases are fit. Without released code or a commit hash, the reported gains and the Figure 3 loss ablation cannot be traced to the geodesic-flow component. That is a load-bearing gap: the gains could come from the corruption and tree embedding alone.\n\nThere are also smaller issues: Table 8's caption says 20% label noise while the text says 10%; no significance tests are reported; the GitHub link is present but no snapshot is indicated. The prose has several garbled passages, which adds to the impression of haste.\n\nIf the equations are fixed — the intended formula is almost certainly the standard GFK cosine similarity z_soft^T A z_hard divided by sqrt(z_soft^T A z_soft) times sqrt(z_hard^T A z_hard) — this is a reasonable applied contribution for people working on semi-supervised tabular learning, especially categorical-heavy low-label settings. As printed, the central mechanism is not well-defined. A serious referee should be asked to verify the corrected loss and to require code release with a hash. I would engage with it because the benchmark is useful, but I would not cite it until the formal gap is closed.","headline":"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.","tokens_in":23332,"tokens_out":5424,"would_cite":false,"duration_ms":46988,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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…","keywords":["semi-supervised learning","tabular data","mixed-variable data","geodesic flow kernel","Grassmann manifold","contrastive corruption","tree-based embedding","label noise"],"falsifier":"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.","tokens_in":22275,"feed_emoji":"📊","tokens_out":10628,"duration_ms":85928,"temperature":0.7,"pith_summary":"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.","feed_headline":"GFTab wins 10 of 21 tabular benchmarks at 20% labels","feed_subtitle":"Manifold-aware similarity plus variable-specific corruption lifts F1 when labels are scarce and noisy.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Introduced the geodesic flow kernel for unsupervised domain adaptation and supplies the closed-form matrix $A$ used in the similarity loss.","marker":"Gong et al. 2012"},{"why":"Provides the geodesic flow parameterization on Grassmann manifolds that defines the path between the two corrupted-view subspaces.","marker":"Gallivan et al. 2003"},{"why":"Generalized SVD result that lets the kernel matrix be decomposed via shared right singular vectors and principal angles.","marker":"Van Loan 1976"},{"why":"Cited alongside Gong et al. for the closed-form computation of the geodesic flow kernel matrix.","marker":"Simon, Koniusz, and Harandi 2021"},{"why":"SCARF baseline and the random feature corruption approach whose uniform treatment of variables GFTab extends and compares against.","marker":"Bahri et al. 2022"},{"why":"VIME baseline, the prior semi-supervised tabular framework based on consistency regularization and mask estimation.","marker":"Yoon et al. 2020"},{"why":"SubTab baseline that corrupts by feature subsetting and reconstruction, another uniform-corruption method GFTab compares with.","marker":"Ucar, Hajiramezanali, and Edwards 2021"},{"why":"DATE, the source of the tree-based embedding idea used to feed labeled rows through a gradient-boosted decision tree.","marker":"Kim et al. 2020"},{"why":"GRANDE baseline, and its hyperparameter search space is reused for the gradient-boosting baselines to keep comparisons fair.","marker":"Marton et al. 2024"},{"why":"TabPFN baseline, a transformer-based tabular classifier that must be beaten for the performance claim.","marker":"Hollmann et al. 2023"}],"fun_headline_variants":["GFTab: 10/21 tabular wins at 20% labels","Geodesic flow kernel beats Euclidean losses on tabular SSL","Variable-specific corruption + geodesic similarity lift F1","Grassmann geometry improves semi-supervised tabular learning"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["GFTab: 10/21 tabular wins at 20% labels","Geodesic flow kernel beats Euclidean losses on tabular SSL","Variable-specific corruption + geodesic similarity lift F1","Grassmann geometry improves semi-supervised tabular learning"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000732,"raw_usage":{"total_tokens":3260,"prompt_tokens":913,"completion_tokens":2347,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":529,"completion_tokens_details":{"reasoning_tokens":2275}},"tokens_in":529,"tokens_out":2347,"duration_ms":15534,"temperature":1.0,"reasoning_tokens":2275,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T13:40:08.946057+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduced the geodesic flow kernel for unsupervised domain adaptation and supplies the closed-form matrix $A$ used in the similarity loss."},{"cited_title":"A.; Srivastava, A.; Liu, X.; and Van Dooren, P","cited_arxiv_id":null,"evidence_quote":"Provides the geodesic flow parameterization on Grassmann manifolds that defines the path between the two corrupted-view subspaces."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Generalized SVD result that lets the kernel matrix be decomposed via shared right singular vectors and principal angles."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Cited alongside Gong et al. for the closed-form computation of the geodesic flow kernel matrix."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"SCARF baseline and the random feature corruption approach whose uniform treatment of variables GFTab extends and compares against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"VIME baseline, the prior semi-supervised tabular framework based on consistency regularization and mask estimation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"SubTab baseline that corrupts by feature subsetting and reconstruction, another uniform-corruption method GFTab compares with."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"DATE, the source of the tree-based embedding idea used to feed labeled rows through a gradient-boosted decision tree."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"GRANDE baseline, and its hyperparameter search space is reused for the gradient-boosting baselines to keep comparisons fair."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"TabPFN baseline, a transformer-based tabular classifier that must be beaten for the performance claim."}],"review_version":1}