GOTabPFN: From Feature Ordering to Compact Tokenization for Tabular Foundation Models on High-Dimensional Data

Al Zadid Sultan Bin Habib; Donald A. Adjeroh; Gianfranco Doretto; Md Younus Ahamed; Prashnna Kumar Gyawali

arxiv: 2606.05441 · v2 · pith:2GMNAVW5new · submitted 2026-06-03 · 💻 cs.LG · cs.AI· stat.ML

GOTabPFN: From Feature Ordering to Compact Tokenization for Tabular Foundation Models on High-Dimensional Data

Al Zadid Sultan Bin Habib , Md Younus Ahamed , Prashnna Kumar Gyawali , Gianfranco Doretto , Donald A. Adjeroh This is my paper

Pith reviewed 2026-06-28 06:43 UTC · model grok-4.3

classification 💻 cs.LG cs.AIstat.ML

keywords tabular foundation modelshigh-dimensional datafeature orderingtoken compressionHDLSS regimesminimum linear arrangementsubunit compressionTabPFN

0 comments

The pith

GOTabPFN uses graph-guided ordering and local feature compression to make TabPFN-style models accurate on high-dimensional low-sample tabular data under tight token budgets without retraining.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper seeks to establish that small tabular foundation models can succeed on high-dimensional low-sample-size data by first arranging features according to their graph relationships and then pooling nearby ones into fewer meta-features. It introduces GO-LR ordering, proves its equivalence to weighted minimum linear arrangement, and interprets the solver as a TSP-path surrogate before applying neuro-inspired subunit compression. A reader would care because this produces compact tokens that let pre-trained models handle cases with many features but few examples, yielding gains in stability and accuracy when token limits are strict. The work focuses on avoiding backbone retraining while preserving predictive information through the ordering-plus-pooling pipeline.

Core claim

GOTabPFN builds on GO-LR, shown equivalent to weighted Minimum Linear Arrangement and solved practically as a TSP-path-style surrogate, together with Neuro-Inspired Subunit Compression (NSC) to pool locally adjacent ordered features into meta-features, yielding a compact representation that makes TabPFN-style prediction practical in HDLSS regimes and improves stability and accuracy across tabular benchmarks under tight token budgets.

What carries the argument

Graph-guided Ordering with Local Refinement (GO-LR) for feature arrangement equivalent to weighted minimum linear arrangement, paired with Neuro-Inspired Subunit Compression (NSC) to create meta-features from adjacent tokens.

If this is right

TabPFN-style prediction becomes practical in high-dimensional low-sample-size regimes.
Stability and accuracy improve on tabular benchmarks when token budgets are tight.
Compact representations can be generated without retraining the underlying foundation model backbone.
Feature relationships captured in a graph allow effective local pooling that reduces input size while retaining signal.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same ordering-plus-pooling steps could be tested on other tabular foundation models to check if token efficiency gains generalize beyond TabPFN.
Treating feature arrangement as a graph linear arrangement problem opens the door to importing solvers from combinatorial optimization for tabular preprocessing.
If the TSP surrogate ordering proves robust, it might reduce the need for exhaustive feature selection in HDLSS settings by focusing computation on locally coherent groups.

Load-bearing premise

The ordering found by the TSP-path-style solver for GO-LR produces adjacent features whose pooling via NSC keeps enough information for the TabPFN backbone to predict accurately without retraining.

What would settle it

On a new collection of HDLSS tabular datasets, if GOTabPFN shows no gains in accuracy or stability versus direct TabPFN or other baselines when both are restricted to the same small token budget, the central claim would be falsified.

Figures

Figures reproduced from arXiv: 2606.05441 by Al Zadid Sultan Bin Habib, Donald A. Adjeroh, Gianfranco Doretto, Md Younus Ahamed, Prashnna Kumar Gyawali.

**Figure 1.** Figure 1: Graph-based feature ordering. GO-LR linearizes a weighted feature graph to keep related features nearby for local segmentation and compression. It uses NNPath for local initialization, then refines the order with a global MinLA-style objective over pairwise placements. See Appendix T for more clarifications. Existing approaches often struggle in HDLSS settings with m≫n, since they either assume moderate f… view at source ↗

**Figure 2.** Figure 2: Meta-feature construction. GO-LR first orders features globally; NSC then segments the ordered axis into contiguous neighborhoods and compresses each segment by PCA into a scalar meta-feature. The final vector Z(x)=(z_1,\ldots ,z_M) is passed to the frozen TabPFN-2.5 head. See Appendix T for additional clarifications. 3.1. Feature Ordering as a Combinatorial Optimization Problem. Problem Setup: Feature Ord… view at source ↗

**Figure 3.** Figure 3: End-to-end architecture of GOTabPFN. The feature clustering block denotes the discovery of local feature-dependence groups, implemented by estimating cluster-wise feature graphs G_c from local sample contexts; GO-LR then obtains a global order \Pi ^\ast , and NSC compresses contiguous ordered segments into metafeatures Z(x) , which are passed to a frozen TabPFN-2.5 head. Global Aggregation (Mean-Rank Inte… view at source ↗

**Figure 4.** Figure 4: HDLSS ablation accuracy. GOTabPFN vs. tabular foundation models on 8 HDLSS datasets [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 5.** Figure 5: Ablation gains. Absolute and relative gains of GOTabPFN over the best original foundation-model head. compresses each sample into a fixed-dimensional representation Z(x) ∈ RM (or Z(x) ∈ RM×d , flattened to RMd). We then use TabPFN-2.5 as the predictor head: for each train/validation split, we fit TabPFN-2.5 on {(Z(xi), yi)}i∈Itrain and evaluate on Z(xj ) for j ∈ Ival without backpropagation through the he… view at source ↗

**Figure 6.** Figure 6: Accuracy-resource profile on Colon. Wall-clock time, peak GPU memory, and CPU RSS for GOTabPFN [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

**Figure 7.** Figure 7: Dolan-More profiles. ´ Performance profiles over 8 HDLSS datasets against the top-10 baselines. cross-domain(App. T) high-dimensional datasets ( [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗

read the original abstract

We investigate how to make small tabular foundation models effective for High-Dimensional, Low-Sample Size (HDLSS) tabular prediction without retraining large backbones. We introduce Graph-guided Ordering with Local Refinement (GO-LR), show its equivalence to weighted Minimum Linear Arrangement, and interpret the practical solver as a TSP-path-style surrogate. We propose GOTabPFN,which builds on GO-LR, and a Neuro-Inspired Subunit Compression (NSC) unit to pool locally adjacent ordered features into meta-features, yielding a compact representation that makes TabPFN-style prediction practical in HDLSS regimes. Across tabular benchmarks, GOTabPFN improves stability and accuracy under tight token budgets.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper sketches GO-LR as equivalent to weighted minimum linear arrangement plus NSC local pooling to let TabPFN handle HDLSS tabular data without retraining, but the abstract supplies no equations, solver details, or results.

read the letter

The main point is that the authors frame feature ordering as a graph-guided problem (GO-LR) they equate to weighted minimum linear arrangement, then apply a neuro-inspired subunit compression step (NSC) to create meta-features that fit inside TabPFN's token budget for high-feature, low-sample regimes.

The practical motivation is solid. Many scientific datasets really do have far more columns than rows, and current tabular foundation models hit hard limits on sequence length. Treating the ordering task as an arrangement problem and using local adjacency for pooling is a coherent way to try to keep the backbone frozen.

The weakness is that none of the central claims can be checked. The abstract states the equivalence and the TSP-path surrogate interpretation but gives no equations, no proof sketch, and no description of how the heuristic is implemented or how large its gap to the true objective might be. There are also no datasets, no protocols, and no numbers showing that the induced neighborhoods actually preserve the correlations the pretrained model relies on. The stress-test concern about uncontrolled misalignment between the surrogate ordering and the original feature dependencies therefore stands, because nothing in the given text controls or measures that gap.

This is aimed at people working on tabular foundation models and HDLSS applications. A reader in that niche might pick up the high-level idea, but the absence of technical substance means the work does not yet support a serious referee process.

Referee Report

2 major / 0 minor

Summary. The manuscript introduces GOTabPFN for making TabPFN-style tabular foundation models practical on high-dimensional low-sample-size (HDLSS) data without retraining. It defines Graph-guided Ordering with Local Refinement (GO-LR), claims equivalence to weighted Minimum Linear Arrangement, interprets a practical solver as a TSP-path surrogate, and combines it with Neuro-Inspired Subunit Compression (NSC) to pool locally adjacent features into meta-features, yielding compact tokenizations that improve stability and accuracy under tight token budgets on tabular benchmarks.

Significance. If the TSP-path surrogate for the claimed MLA equivalence produces orderings whose NSC meta-features retain the feature dependencies needed by the frozen TabPFN backbone, the method could extend tabular foundation models to HDLSS regimes. The equivalence claim and surrogate interpretation would be useful contributions if independently derived and if the no-retraining assumption holds empirically.

major comments (2)

[Abstract] Abstract: the central claims of equivalence between GO-LR and weighted Minimum Linear Arrangement, the TSP-path surrogate interpretation, and the resulting accuracy/stability gains are stated without any equations, proof sketches, experimental protocols, error bars, dataset details, or baseline comparisons, so the soundness of the claims cannot be assessed from the provided information.
[Abstract] The manuscript does not address whether the approximation gap of the TSP-path heuristic for the MLA objective can produce orderings that systematically misalign local neighborhoods with the original feature correlations, which would invalidate the assumption that NSC pooling preserves the statistical structure required by the pretrained TabPFN backbone in HDLSS settings.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. Below we respond point by point to the major comments.

read point-by-point responses

Referee: [Abstract] Abstract: the central claims of equivalence between GO-LR and weighted Minimum Linear Arrangement, the TSP-path surrogate interpretation, and the resulting accuracy/stability gains are stated without any equations, proof sketches, experimental protocols, error bars, dataset details, or baseline comparisons, so the soundness of the claims cannot be assessed from the provided information.

Authors: The abstract is written to be concise and highlight the core contributions within length limits. The full manuscript contains the equivalence to weighted Minimum Linear Arrangement with a proof sketch in Section 3, the TSP-path surrogate interpretation in the same section, and all experimental protocols, error bars, dataset descriptions, and baseline comparisons in Section 5. We will revise the abstract to include a short reference to the theoretical result and experimental validation if space allows. revision: partial
Referee: [Abstract] The manuscript does not address whether the approximation gap of the TSP-path heuristic for the MLA objective can produce orderings that systematically misalign local neighborhoods with the original feature correlations, which would invalidate the assumption that NSC pooling preserves the statistical structure required by the pretrained TabPFN backbone in HDLSS settings.

Authors: This is a valid concern about the heuristic's approximation quality. Our empirical results across benchmarks demonstrate that the produced orderings enable effective NSC compression and yield accuracy and stability gains under tight token budgets. However, the manuscript does not include a formal analysis or bound on how the approximation gap may affect local feature correlations. We will add an explicit discussion of this limitation and its implications for the no-retraining assumption in a revised version. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation introduces independent components

full rationale

The provided abstract and description introduce GO-LR as a new ordering method, claim an equivalence to weighted Minimum Linear Arrangement (with TSP-path surrogate interpretation), and combine it with a new NSC pooling unit to enable compact tokenization for TabPFN in HDLSS settings. No equations or definitions are given that reduce the claimed equivalence or the downstream prediction performance to a tautological fit or self-referential input by construction. The central claims rest on the practical utility of the proposed ordering and compression steps rather than any self-definitional loop, fitted-input renaming, or load-bearing self-citation chain. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no equations, parameter lists, or background assumptions are supplied, so the ledger cannot be populated with concrete entries.

pith-pipeline@v0.9.1-grok · 5675 in / 1180 out tokens · 42519 ms · 2026-06-28T06:43:59.005390+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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extended this direction by studying feature ordering for LLM-based tabular inference. DynaTab (Habib et al., 2026b) systematically studied when feature ordering matters in high-dimensional tabular learning, introducing an Intrinsic Dimensionality Factor (IDF) and feature-to-sample ratio ρ=m/n based categorization of dataset regimes. It proposed a neurosci...

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50) has class-conditional mean difference E[zNSC |Y= 1]−E[z NSC |Y= 0] = ∆ and varianceVar(z NSC |Y) =σ 2/s, hence we get Eq

The NSC block mean (Eq. 50) has class-conditional mean difference E[zNSC |Y= 1]−E[z NSC |Y= 0] = ∆ and varianceVar(z NSC |Y) =σ 2/s, hence we get Eq. 50 and 51 zNSC = 1 s X j∈S Xj (50) SNRNSC := E[zNSC |Y= 1]−E[z NSC |Y= 0] 2 Var(zNSC |Y) = ∆2s σ2 (51)
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2.Intrinsic dimension.Estimate ˆdvia effective rank (Eqs

GO-LR ordering.Compute the GO-LR global feature permutation Π∗ on the training set using a chosen metric (e.g., correlation, cosine, euclidean, manhattan, or KL divergence), with local refinement passes as in Algorithm 1. 2.Intrinsic dimension.Estimate ˆdvia effective rank (Eqs. 27-29), and compute IDF= ˆd/m(Eq. 30). 3.NSC configuration.Configure NSC with...
[21]

This measures how well each DR method preserves label-relevant structure inMdimensions

Linear-probe accuracy.Train a logistic regression classifier on each latent space XNSC, XPCA, XRP, XAE, XUMAP, XPaCMAP using the same stratified cross-validation protocol. This measures how well each DR method preserves label-relevant structure inMdimensions. 2.k NN classification in latent space.Evaluate kNN accuracy using the compressed embeddings under...
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Label-based separability metrics.Compute silhouette and Davies-Bouldin scores on each latent representation using ground-truth class labels as the partition
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Sequential

Statistical comparison across datasets.Aggregate per-dataset metrics and apply nonparametric tests, using a Friedman test (Friedman, 1937) across methods followed by one-sided Wilcoxon signed-rank comparisons with NSC-pSP as the reference (see Tables D.1, D.2, D.3). Evaluation protocol.We report only quantitative DR-style evaluations under a fixed aggress...

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break contiguity

and controlled perturbations that partially preserve locality (block-shuffle) or explicitly destroy contiguity while keeping the same global order statistics (round-robin “break contiguity”). Figure E.2 (top) and Table E.1 show that ordering yields non-trivial AUC changes for the local-window Transformer, and GO-LR produces the strongest gains among the t...

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confident

(Fig. I.1), and (ii) pairwise Wilcoxon signed-rank tests (Demˇsar, 2006) comparing GOTabPFN to each baseline across the same 8 datasets, with Holm correction to control family-wise error (Table I.1). The Friedman test indicates a significant overall effect across methods, and the CD diagram visualizes the separation in average ranks, where GOTabPFN attain...

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high-risk

evaluates on 7 biomedical HDLSS datasets against 16 baselines and reports average rank as a primary aggregate measure, while LSPIN/LLSPIN (Yang et al., 2022a) evaluates on 6 real-world high-dimensional datasets, including 3 text and 3 biomedical datasets, and summarizes performance using median rank. Following this established practice, we report average ...

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Akiba, T., Sano, S., Yanase, T., Ohta, T., and Koyama, M

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start at arg mini P j dij and repeatedly append the nearest unvisited node

extended this direction by studying feature ordering for LLM-based tabular inference. DynaTab (Habib et al., 2026b) systematically studied when feature ordering matters in high-dimensional tabular learning, introducing an Intrinsic Dimensionality Factor (IDF) and feature-to-sample ratio ρ=m/n based categorization of dataset regimes. It proposed a neurosci...

2008

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50) has class-conditional mean difference E[zNSC |Y= 1]−E[z NSC |Y= 0] = ∆ and varianceVar(z NSC |Y) =σ 2/s, hence we get Eq

The NSC block mean (Eq. 50) has class-conditional mean difference E[zNSC |Y= 1]−E[z NSC |Y= 0] = ∆ and varianceVar(z NSC |Y) =σ 2/s, hence we get Eq. 50 and 51 zNSC = 1 s X j∈S Xj (50) SNRNSC := E[zNSC |Y= 1]−E[z NSC |Y= 0] 2 Var(zNSC |Y) = ∆2s σ2 (51)

[19] [19]

Let u= (u j)j∈S be a random projection direction withP j∈S u2 j = 1 and entries of order 1/√s, and define Eq. 52. Then we get Eq. 52 and Eq. 53. For typical random u, E (P j uj)2 = 1, so the typical SNR of zRP is defined by Eq. 54. zRP = X j∈S ujXj (52) E[zRP |Y= 1]−E[z RP |Y= 0] = ∆ X j∈S uj,Var(z RP |Y) =σ 2 (53) SNRRP := E[zRP |Y= 1]−E[z RP |Y= 0] 2 Va...

2009

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2.Intrinsic dimension.Estimate ˆdvia effective rank (Eqs

GO-LR ordering.Compute the GO-LR global feature permutation Π∗ on the training set using a chosen metric (e.g., correlation, cosine, euclidean, manhattan, or KL divergence), with local refinement passes as in Algorithm 1. 2.Intrinsic dimension.Estimate ˆdvia effective rank (Eqs. 27-29), and compute IDF= ˆd/m(Eq. 30). 3.NSC configuration.Configure NSC with...

[21] [21]

This measures how well each DR method preserves label-relevant structure inMdimensions

Linear-probe accuracy.Train a logistic regression classifier on each latent space XNSC, XPCA, XRP, XAE, XUMAP, XPaCMAP using the same stratified cross-validation protocol. This measures how well each DR method preserves label-relevant structure inMdimensions. 2.k NN classification in latent space.Evaluate kNN accuracy using the compressed embeddings under...

[22] [22]

Label-based separability metrics.Compute silhouette and Davies-Bouldin scores on each latent representation using ground-truth class labels as the partition

[23] [23]

Sequential

Statistical comparison across datasets.Aggregate per-dataset metrics and apply nonparametric tests, using a Friedman test (Friedman, 1937) across methods followed by one-sided Wilcoxon signed-rank comparisons with NSC-pSP as the reference (see Tables D.1, D.2, D.3). Evaluation protocol.We report only quantitative DR-style evaluations under a fixed aggress...

1937

[24] [24]

break contiguity

and controlled perturbations that partially preserve locality (block-shuffle) or explicitly destroy contiguity while keeping the same global order statistics (round-robin “break contiguity”). Figure E.2 (top) and Table E.1 show that ordering yields non-trivial AUC changes for the local-window Transformer, and GO-LR produces the strongest gains among the t...

2017

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confident

(Fig. I.1), and (ii) pairwise Wilcoxon signed-rank tests (Demˇsar, 2006) comparing GOTabPFN to each baseline across the same 8 datasets, with Holm correction to control family-wise error (Table I.1). The Friedman test indicates a significant overall effect across methods, and the CD diagram visualizes the separation in average ranks, where GOTabPFN attain...

2006

[26] [26]

high-risk

evaluates on 7 biomedical HDLSS datasets against 16 baselines and reports average rank as a primary aggregate measure, while LSPIN/LLSPIN (Yang et al., 2022a) evaluates on 6 real-world high-dimensional datasets, including 3 text and 3 biomedical datasets, and summarizes performance using median rank. Following this established practice, we report average ...

2000