Geometry-Aware Tabular Diffusion

David Turtora Zagardo

arxiv: 2606.02607 · v1 · pith:2SWWA3ADnew · submitted 2026-05-23 · 💻 cs.LG · cs.AI· cs.CR

Geometry-Aware Tabular Diffusion

David Turtora Zagardo This is my paper

Pith reviewed 2026-06-30 14:37 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.CR

keywords tabular diffusiongeometry-aware modelingrelational supervisiondata synthesisgenerative modelsinductive biasdenoiser augmentation

0 comments

The pith

Adding pairwise angles and lengths from column differences as explicit signals improves tabular diffusion across architectures.

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

The paper introduces Geometry-Aware Tabular Diffusion to address the reliance on implicit mechanisms in diffusion models for capturing inter-column relationships in tabular data. It augments denoisers with pairwise angles and lengths computed from column value differences, using these as both inputs and auxiliary targets. This explicit relational supervision yields state-of-the-art results in an MLP instantiation while requiring far fewer parameters. The same default loss weights also lift performance for GNN and Transformer denoisers on most tested cases, with an ablation confirming that the added supervision, rather than extra inputs or model size, produces the gains.

Core claim

Tabular diffusion can be improved by augmenting denoisers with pairwise angles and lengths computed from column value differences and used as inputs and auxiliary targets. The MLP instantiation wins 8/10 Shape, 7/10 Trend, and 9/10 downstream utility benchmarks while using 3.5x fewer parameters on average, cutting Shape and Trend error by 27% and 20%. Default loss weights transfer to GNN and Transformer denoisers, improving Shape on 27/30 and Trend on 25/30 architecture-dataset combinations. A matched ablation isolates supervision as the source of the improvement, establishing explicit relational supervision as a portable inductive bias.

What carries the argument

Geometry-Aware Tabular Diffusion (GATD), which augments tabular diffusion denoisers with pairwise angles and lengths computed from column value differences and used as inputs and auxiliary targets.

If this is right

The MLP version achieves wins on 8/10 Shape, 7/10 Trend, and 9/10 downstream utility metrics while using 3.5x fewer parameters on average.
Shape and Trend error drop by 27% and 20% respectively under the geometry-aware approach.
Default loss weights improve Shape on 27/30 and Trend on 25/30 cells when applied to GNN and Transformer denoisers.
A matched ablation isolates the auxiliary supervision, not extra inputs or added capacity, as the driver of gains.

Where Pith is reading between the lines

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

If explicit geometric relations improve diffusion for tabular data, the same signals may help other structured generative tasks that currently rely on implicit learning.
The architecture-agnostic transfer of default weights suggests the bias could be added as a lightweight module to existing tabular pipelines without per-model retuning.
More efficient parameter use could expand privacy-preserving data sharing to settings with strict compute limits.

Load-bearing premise

That pairwise angles and lengths computed from column value differences constitute the right explicit relational signals and that default loss weights chosen for the MLP transfer without retuning to GNN and Transformer denoisers.

What would settle it

Training the same MLP denoiser on the ten benchmark datasets without the auxiliary geometric targets and observing no reduction in Shape or Trend error relative to the unaugmented baseline.

Figures

Figures reproduced from arXiv: 2606.02607 by David Turtora Zagardo.

**Figure 1.** Figure 1: Geometric Intuition. Inter-column relationships are encoded as pairwise angles θij = arctan(vj − vi) and lengths ℓij = 1 2 log(1 + (vj − vi) 2 ), providing explicit relational targets. Diagrams (b) and (c) show sample rows from Adult and Default. and cout = σ · σdata/ p σ 2 + σ 2 data (Karras et al., 2022). We use learnable per-column ρ for noise scheduling (Shi et al., 2025). This deliberate choice isolat… view at source ↗

**Figure 2.** Figure 2: GeometryAwareMLP Architecture. The model receives noised data and geometric features (angles θ, lengths ℓ) as input. After processing through residual blocks, geometric heads predict angles and lengths, which are concatenated with the hidden state before the denoising heads. This augmentation path (red) encourages the model to leverage geometric structure. It is critical to note that the length head is sup… view at source ↗

**Figure 3.** Figure 3: Loss-ablation distributions by method. Each panel plots 10 dataset values across 6 methods using KDE violins, median bars, and colored dataset dots tracked across positions. The shaded band marks geometric supervision: medians drop sharply from Inputs Only to supervised methods for Shape (1.07 → 0.85) and Trend (1.93 → 1.40), while similar supervised violins show Angle Only / Angle + Length / Full have sma… view at source ↗

**Figure 4.** Figure 4: GNN backbone, no-geometry baseline. Standard graph denoiser: node embeddings (per-column projection + column-position embedding + time embedding) feed nrounds rounds of message passing with data-independent learned pair embeddings (npairs × 4) as edge attributes; mean-pooled node embeddings feed the denoising heads. 11 [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗

**Figure 5.** Figure 5: GNN+Geom architecture. Four-dimensional geometric edge features (angles θij , log-lengths ℓij , row-normalized endpoint values x˜i, x˜j ) replace the data-independent learned pair embeddings of the baseline ( [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗

**Figure 6.** Figure 6: Transformer backbone, no-geometry baseline. Time embedding, noised continuous values, and one-hot categoricals concatenate into a flat vector that the input-projection MLP maps to h0; a linear expansion produces ntokens latent tokens with learned positional embeddings, processed by a pre-norm Transformer encoder of depth nblocks. A linear contraction flattens the encoded tokens back to a single dmodel vect… view at source ↗

**Figure 7.** Figure 7: Transformer+Geom architecture. Pairwise input angles θij and lengths ℓij are concatenated alongside the standard inputs before the input-projection MLP; the latent-token Transformer backbone is unchanged from the baseline ( [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗

**Figure 8.** Figure 8: Training Dynamics (Default). Full Geometry (solid) vs. Inputs Only (dashed). Total Loss includes weighted geometric terms (λθ, λℓ, λc = 15, 15, 8) for Full Geometry but only diffusion losses (Lcont + Lcat) for Inputs Only. Inputs Only converges to lower total loss (0.60 vs. 2.08) yet fails to learn geometry: Angle 2.63 vs. 0.07 (37×), Length 0.11 vs. 0.01 (8×), Consistency 0.88 vs. 0.003 (339×). Weighted g… view at source ↗

**Figure 9.** Figure 9: Sampling-step ablation summary. Aggregate metrics across all 10 datasets as a function of GATD-MLP sampling steps, against TabDiff at its published 50-step protocol (red dashed lines). From left: Shape error (↓), Trend error (↓), MLE-1 gap to real (↓), MLE-2 gap to real (↓). GATD wins 3 of 4 aggregate metrics at 50 steps and all 4 by 100 steps; performance continues to improve up to 2000 steps with no clea… view at source ↗

**Figure 10.** Figure 10: Loss-weight sensitivity sweeps for the three geometric loss terms on four representative datasets. Each panel varies one weight while holding the other two at the default setting: angle sweep (λθ, λℓ, λc) = (X, 15, 8), length sweep (15, X, 8), and consistency sweep (15, 15, X), with X ∈ {0, 5, 10, 15, 20, 30} under the 1 × 1 protocol. Aggregate Shape and Trend errors remain within ±5% of the default (15, … view at source ↗

read the original abstract

Tabular synthesis is critical for privacy-preserving sharing and augmentation, yet diffusion models rely on implicit mechanisms to capture inter-column relationships. We introduce Geometry-Aware Tabular Diffusion (GATD), which augments tabular diffusion denoisers with pairwise angles and lengths computed from column value differences and used as inputs and auxiliary targets. Our MLP instantiation achieves state-of-the-art benchmark performance while using 3.5x fewer parameters on average (up to 25x for classification tasks): on ten datasets, it wins 8/10 Shape, 7/10 Trend, and 9/10 downstream utility (F1/RMSE), reducing Shape and Trend error by 27% and 20%. Default loss weights transfer to GNN and Transformer denoisers, improving Shape on 27/30 and Trend on 25/30 architecture-dataset cells. A matched ablation shows supervision (not extra inputs or capacity) drives the gain. This shows explicit relational supervision is a portable inductive bias for tabular diffusion.

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

Explicit pairwise geometry as auxiliary targets lifts tabular diffusion results on MLP backbones with fewer parameters, but the portability to GNNs and transformers rests on win counts without matching ablations.

read the letter

Hey,

The core move here is feeding pairwise angles and lengths computed from column differences into the denoiser both as extra inputs and as auxiliary regression targets. On the MLP version this produces wins on 8/10 shape metrics, 7/10 trend metrics, and 9/10 downstream tasks across ten datasets while averaging 3.5x fewer parameters. A matched ablation attributes the lift to the supervision signal rather than the extra inputs or capacity alone.

That ablation is the strongest part of the write-up because it tries to isolate the inductive bias instead of just showing another architecture tweak. The claim that the same default loss weights also improve most GNN and transformer cells is at least a start toward showing the bias is somewhat architecture-agnostic.

The soft spots are straightforward. No error bars or significance numbers appear, and the abstract gives no formulas for how shape and trend are computed, so the size of the reported 27 % and 20 % error reductions is hard to judge. More critically, the ablation that isolates supervision is reported only for the MLP; the GNN and transformer results are just win counts. If the optimal weighting between the auxiliary geometric losses and the main denoising loss shifts with the denoiser’s inductive bias, then the “default weights transfer” result does not actually demonstrate portability.

This is for groups working on practical tabular synthesis where model size or explicit relational modeling matters. A reader who already runs diffusion baselines on structured data would find the auxiliary-target idea easy to test.

I would send it to referees. The empirical setup is concrete enough that a reviewer could ask for the missing ablations and metric details without the paper falling apart.

Referee Report

3 major / 0 minor

Summary. The paper introduces Geometry-Aware Tabular Diffusion (GATD), which augments tabular diffusion denoisers with pairwise angles and lengths computed from column value differences, used both as additional inputs and as auxiliary supervision targets. The central empirical claims are that an MLP instantiation achieves SOTA results on ten datasets (winning 8/10 on Shape, 7/10 on Trend, 9/10 on downstream utility) while using 3.5× fewer parameters on average, that default loss weights transfer without retuning to GNN and Transformer denoisers (improving 27/30 and 25/30 architecture-dataset cells), and that a matched ablation isolates the benefit to the explicit supervision rather than extra inputs or capacity.

Significance. If the reported gains and cross-architecture transfer are robust, the work supplies a concrete, architecture-agnostic mechanism for injecting explicit relational inductive bias into tabular diffusion. The matched ablation and the parameter-efficiency numbers are genuine strengths that would, if verified, make the portability argument load-bearing for future tabular synthesis research.

major comments (3)

[Abstract] Abstract: the headline performance numbers (8/10 Shape wins, 27 % and 20 % error reductions, 3.5× parameter reduction) are stated without error bars, confidence intervals, or any mention of statistical significance testing. Because these quantities are the sole support for both the SOTA claim and the portability conclusion, their reliability cannot be assessed from the given information.
[Abstract] Abstract (final paragraph) and ablation description: the claim that “default loss weights transfer” to GNN and Transformer denoisers rests on a single set of weights chosen for the MLP; no sensitivity analysis or re-tuning experiment is reported for the other architectures. The matched ablation that isolates supervision from capacity is described only for the MLP, so it does not directly substantiate the portability statement when the denoiser inductive bias changes.
[Abstract] Abstract: the definitions and computation procedures for the Shape and Trend metrics are not supplied. These metrics are the primary evaluation axes for both the MLP results and the 27/30–25/30 transfer counts; without their precise formulation it is impossible to judge whether the reported improvements are comparable across architectures or datasets.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below and indicate planned revisions where appropriate.

read point-by-point responses

Referee: [Abstract] Abstract: the headline performance numbers (8/10 Shape wins, 27 % and 20 % error reductions, 3.5× parameter reduction) are stated without error bars, confidence intervals, or any mention of statistical significance testing. Because these quantities are the sole support for both the SOTA claim and the portability conclusion, their reliability cannot be assessed from the given information.

Authors: We agree that reliability indicators would strengthen the abstract. The main experimental section reports results averaged over multiple seeds; we will add standard deviations and note statistical significance (via paired tests) for the aggregate headline figures in the revised abstract and results summary. revision: yes
Referee: [Abstract] Abstract (final paragraph) and ablation description: the claim that “default loss weights transfer” to GNN and Transformer denoisers rests on a single set of weights chosen for the MLP; no sensitivity analysis or re-tuning experiment is reported for the other architectures. The matched ablation that isolates supervision from capacity is described only for the MLP, so it does not directly substantiate the portability statement when the denoiser inductive bias changes.

Authors: The reported transfer uses the MLP-derived weights without modification, which directly tests the portability hypothesis. No architecture-specific re-tuning or sensitivity sweep was performed, as that would contradict the zero-shot transfer claim. We will revise the text to explicitly state that weights were not re-tuned and to clarify that the matched ablation is MLP-specific while the cross-architecture gains provide complementary evidence of portability. revision: partial
Referee: [Abstract] Abstract: the definitions and computation procedures for the Shape and Trend metrics are not supplied. These metrics are the primary evaluation axes for both the MLP results and the 27/30–25/30 transfer counts; without their precise formulation it is impossible to judge whether the reported improvements are comparable across architectures or datasets.

Authors: Shape and Trend are formally defined in Section 4.2 (following the geometric and sequential formulations introduced in the method section). To make the abstract self-contained we will insert a concise parenthetical reference to these definitions in the revised version. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical benchmarks and ablations are independent of fitted inputs

full rationale

The paper reports benchmark wins, error reductions, and architecture-transfer results on external datasets, supported by a matched ablation isolating supervision. No equations, derivations, or self-citations are shown that reduce any reported quantity to a fitted parameter or input by construction. Claims rest on observable performance metrics rather than self-referential definitions or predictions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach rests on the domain assumption that geometric pairwise relations are a useful explicit signal for tabular column dependencies; no free parameters or invented entities are described in the abstract.

axioms (1)

domain assumption Pairwise angles and lengths computed from column value differences capture relevant inter-column relationships for synthesis
This premise underpins the decision to use these quantities as inputs and auxiliary targets.

pith-pipeline@v0.9.1-grok · 5695 in / 1385 out tokens · 33277 ms · 2026-06-30T14:37:08.640798+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

13 extracted references · 9 canonical work pages · 2 internal anchors

[1]

B., Mironov, I., Talwar, K., and Zhang, L

Abadi, M., Chu, A., Goodfellow, I., McMahan, H. B., Mironov, I., Talwar, K., and Zhang, L. Deep learning with differential privacy. InProceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security, pp. 308–318,

2016
[2]

Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges

Bronstein, M. M., Bruna, J., Cohen, T., and Veli ˇckovi´c, P. Geometric deep learning: Grids, groups, graphs, geodesics, and gauges.arXiv preprint arXiv:2104.13478,

work page internal anchor Pith review Pith/arXiv arXiv
[3]

Xgboost: A scalable tree boosting system,

doi: 10.1145/2939672.2939785. Gorishniy, Y ., Rubachev, I., Khrulkov, V ., and Babenko, A. Revisiting deep learning models for tabular data. In Advances in Neural Information Processing Systems, vol- ume 34, pp. 18932–18943,

work page doi:10.1145/2939672.2939785
[4]

Entity Embeddings of Categorical Variables

Guo, C. and Berkhahn, F. Entity embeddings of categorical variables.arXiv preprint arXiv:1604.06737,

work page internal anchor Pith review Pith/arXiv arXiv
[5]

Proceedings of the AAAI Conference on Artifi- cial Intelligence38(3), 2148–2156 (Mar 2024).https://doi.org/10.1609/aaai

doi: 10.1609/aaai. v34i04.5976. Patki, N., Wedge, R., and Veeramachaneni, K. The synthetic data vault. InIEEE International Conference on Data Science and Advanced Analytics, pp. 399–410,

work page doi:10.1609/aaai
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arXiv preprint arXiv:2410.20626 , year=

arXiv:2410.20626. Su, J., Lu, Y ., Pan, S., Murtadha, A., Wen, B., and Liu, Y . RoFormer: Enhanced transformer with rotary position embedding.Neurocomputing, 568:127063,

work page arXiv
[7]

2024 , issue_date =

doi: 10.1016/j.neucom.2023.127063. Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, Ł., and Polosukhin, I. Atten- tion is all you need. InAdvances in Neural Information Processing Systems, volume 30,

work page doi:10.1016/j.neucom.2023.127063 2023
[8]

categorical anchor

restores all four and routes the predicted angle into the augmentation path in the standard pattern. A.3. Architecture Ablation: Effect of Residual Blocks Table 6 compares 0 vs. 8 residual blocks across all datasets. The pattern is consistent: classification tasks favor 0 blocks for fidelity metrics (Shape, Trend), while regression tasks favor 8 blocks fo...

work page arXiv
[9]

Loss config

shows the pattern is supervision-dependent:Inputs Only produces no positive correlation, while every supervised configuration reproduces it. Loss config. SpearmanρSpearmanp Inputs Only -0.63 0.051 Angle Only+0.70 0.025 Angle + Length+0.70 0.025 Full+0.70 0.025 Table 8.Rank correlation between categorical-column count and per-dataset Shape improvement (vs ...

work page arXiv 1940
[10]

Metric Config Adult Default Diabetes Magic Shoppers Beijing Bikeshare California News Power Avg.Shape NoGeom 0.819±0.04541.17±0.07801.27±0.02100.943±0.1071.58±0.08210.797±0.04240.778±0.07341.00±0.05972.79±0.05181.15±0.1731.23 Inputs Only 0.936±0.05351.16±0.06641.29±0.02630.904±0.07681.79±0.08580.763±0.04110.805±0.07940.959±0.05363.06±0.1561.13±0.1681.28 A...

work page arXiv 1960
[11]

Single training seed, 20 sampling seeds

Extended training does not benefit TabDiff, validating our use of their published 8,000-epoch protocol. Single training seed, 20 sampling seeds. Geometry (Ours) TabDiff Ratio (Ours/TabDiff) Dataset Params Train (h) Sample (s) Params Train (h) Sample (s) Params Sample Adult 542K 1.25 47.8 10.6M 3.62 34.6 0.05×1.38× Beijing 4.67M 3.18 135.7 10.6M 4.21 33.0 ...

2000
[12]

Performance improves monotonically up to 2000 steps with no clear saturation point in our evaluated range

compare GATD at each step budget against TabDiff at 50 steps. Performance improves monotonically up to 2000 steps with no clear saturation point in our evaluated range. Configuration Shape↓Trend↓MLE-1 gap↓MLE-2 gap↓Wins (S/T/M1/M2) TabDiff (50 steps) 1.187 2.048 11.4% 9.7% — GATD (50 steps) 1.546 1.957 4.6% 7.2% 3/4/5/8 GATD (100 steps) 1.125 1.714 4.9% 5...

2000
[13]

Wall-clock cost

reports per-step-budget performance. At 50 sampling steps, GATD already wins 3 of 4 metrics in aggregate against TabDiff (Trend 1.96 vs 2.05; MLE-1 4.6% vs 11.4% gap; MLE-2 7.2% vs 9.7% gap), losing only on Shape (1.55 vs 1.19). By 100 sampling steps, GATD wins all 4 aggregate metrics. The story tightens further as step count increases: aggregate Shape er...

2000

[1] [1]

B., Mironov, I., Talwar, K., and Zhang, L

Abadi, M., Chu, A., Goodfellow, I., McMahan, H. B., Mironov, I., Talwar, K., and Zhang, L. Deep learning with differential privacy. InProceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security, pp. 308–318,

2016

[2] [2]

Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges

Bronstein, M. M., Bruna, J., Cohen, T., and Veli ˇckovi´c, P. Geometric deep learning: Grids, groups, graphs, geodesics, and gauges.arXiv preprint arXiv:2104.13478,

work page internal anchor Pith review Pith/arXiv arXiv

[3] [3]

Xgboost: A scalable tree boosting system,

doi: 10.1145/2939672.2939785. Gorishniy, Y ., Rubachev, I., Khrulkov, V ., and Babenko, A. Revisiting deep learning models for tabular data. In Advances in Neural Information Processing Systems, vol- ume 34, pp. 18932–18943,

work page doi:10.1145/2939672.2939785

[4] [4]

Entity Embeddings of Categorical Variables

Guo, C. and Berkhahn, F. Entity embeddings of categorical variables.arXiv preprint arXiv:1604.06737,

work page internal anchor Pith review Pith/arXiv arXiv

[5] [5]

Proceedings of the AAAI Conference on Artifi- cial Intelligence38(3), 2148–2156 (Mar 2024).https://doi.org/10.1609/aaai

doi: 10.1609/aaai. v34i04.5976. Patki, N., Wedge, R., and Veeramachaneni, K. The synthetic data vault. InIEEE International Conference on Data Science and Advanced Analytics, pp. 399–410,

work page doi:10.1609/aaai

[6] [6]

arXiv preprint arXiv:2410.20626 , year=

arXiv:2410.20626. Su, J., Lu, Y ., Pan, S., Murtadha, A., Wen, B., and Liu, Y . RoFormer: Enhanced transformer with rotary position embedding.Neurocomputing, 568:127063,

work page arXiv

[7] [7]

2024 , issue_date =

doi: 10.1016/j.neucom.2023.127063. Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, Ł., and Polosukhin, I. Atten- tion is all you need. InAdvances in Neural Information Processing Systems, volume 30,

work page doi:10.1016/j.neucom.2023.127063 2023

[8] [8]

categorical anchor

restores all four and routes the predicted angle into the augmentation path in the standard pattern. A.3. Architecture Ablation: Effect of Residual Blocks Table 6 compares 0 vs. 8 residual blocks across all datasets. The pattern is consistent: classification tasks favor 0 blocks for fidelity metrics (Shape, Trend), while regression tasks favor 8 blocks fo...

work page arXiv

[9] [9]

Loss config

shows the pattern is supervision-dependent:Inputs Only produces no positive correlation, while every supervised configuration reproduces it. Loss config. SpearmanρSpearmanp Inputs Only -0.63 0.051 Angle Only+0.70 0.025 Angle + Length+0.70 0.025 Full+0.70 0.025 Table 8.Rank correlation between categorical-column count and per-dataset Shape improvement (vs ...

work page arXiv 1940

[10] [10]

Metric Config Adult Default Diabetes Magic Shoppers Beijing Bikeshare California News Power Avg.Shape NoGeom 0.819±0.04541.17±0.07801.27±0.02100.943±0.1071.58±0.08210.797±0.04240.778±0.07341.00±0.05972.79±0.05181.15±0.1731.23 Inputs Only 0.936±0.05351.16±0.06641.29±0.02630.904±0.07681.79±0.08580.763±0.04110.805±0.07940.959±0.05363.06±0.1561.13±0.1681.28 A...

work page arXiv 1960

[11] [11]

Single training seed, 20 sampling seeds

Extended training does not benefit TabDiff, validating our use of their published 8,000-epoch protocol. Single training seed, 20 sampling seeds. Geometry (Ours) TabDiff Ratio (Ours/TabDiff) Dataset Params Train (h) Sample (s) Params Train (h) Sample (s) Params Sample Adult 542K 1.25 47.8 10.6M 3.62 34.6 0.05×1.38× Beijing 4.67M 3.18 135.7 10.6M 4.21 33.0 ...

2000

[12] [12]

Performance improves monotonically up to 2000 steps with no clear saturation point in our evaluated range

compare GATD at each step budget against TabDiff at 50 steps. Performance improves monotonically up to 2000 steps with no clear saturation point in our evaluated range. Configuration Shape↓Trend↓MLE-1 gap↓MLE-2 gap↓Wins (S/T/M1/M2) TabDiff (50 steps) 1.187 2.048 11.4% 9.7% — GATD (50 steps) 1.546 1.957 4.6% 7.2% 3/4/5/8 GATD (100 steps) 1.125 1.714 4.9% 5...

2000

[13] [13]

Wall-clock cost

reports per-step-budget performance. At 50 sampling steps, GATD already wins 3 of 4 metrics in aggregate against TabDiff (Trend 1.96 vs 2.05; MLE-1 4.6% vs 11.4% gap; MLE-2 7.2% vs 9.7% gap), losing only on Shape (1.55 vs 1.19). By 100 sampling steps, GATD wins all 4 aggregate metrics. The story tightens further as step count increases: aggregate Shape er...

2000