Test-Time Compute for Tabular Foundation Models: Mechanisms, Gains, and Limits

Kanghui Ning; Marin Biloš; James T. Wilson; Yilang Zhang; Kashif Rasul; Dongjin Song; Anderson Schneider; Yuriy Nevmyvaka

cs.LGOct 8, 2026

Test-Time Compute for Tabular Foundation Models: Mechanisms, Gains, and Limits

Authors: Kanghui Ning, Marin Biloš, James T. Wilson, Yilang Zhang, Kashif Rasul, Dongjin Song, Anderson Schneider, Yuriy Nevmyvaka

Organizations: School of Computing, University of Connecticut, Storrs, USA. · Department of Machine Learning Research, Morgan Stanley, New York, USA.

Abstract

Which forms of test-time compute improve the predictions of strong pretrained tabular foundation models (TFMs)? We systematically study this along three axes: adaptation, aggregation, and context construction. Our evaluation spans modern TFMs across the TabArena benchmark, supplemented by experiments on wide and large-scale tables from OpenML. For adaptation, we introduce DiagScale, a diagonal query-key similarity update. It trains only 0.003-0.03% of model parameters and achieves gains comparable to full fine-tuning across three independently pretrained backbones. For aggregation, both pool composition and selection strategy matter. TabPFN-3 already averages predictions from different preprocessing variants of the same data, and adding more such predictions yields diminishing returns. With a broader pool of 96 configurations, greedy selection reduces error by 2.4% relative to the default predictor, but uniform averaging increases error. For context construction, attention-guided retrieval improves TabPFN-3's predictions on some large tables and supports source pools beyond the full context memory limit. The context expansion methods we test yield no consistent improvement. Taken together, our results suggest that adaptation and selective aggregation yield consistent benchmark-level gains. The benefits of context construction depend more on the task and data regime. Adaptation and aggregation over the same backbone yield further gains when combined, but require substantially more computation than default inference. These trade-offs motivate choosing strategies according to the available computation budget. Code is available at https://github.com/kanghui-learning/test-time-compute-for-tabular-foundation-models.

Figures & tables

Figure 1: Three families of test-time compute modify different components of the inference pipeline. Top: an inference pipeline comprising preprocessing, a frozen tabular foundation model, and combination of predictions across data views. Bottom: context construction changes the conditioning data; adaptation changes model parameters; aggregation changes the prediction pool and the rule used to select or combine its members.

Setting	Updated	Params	$\Delta$ Elo	Norm. score
Full fine-tuning	all trainable weights	58.3M	$+25$	$\mathbf{0.704}$
LoRA ( $r=16$ )	low-rank updates	3.51M	$+15$	$0.684$
Value–output	$W_{V}$ , $W_{O}$	12.9M	$+19$	$0.693$
Query–key	$W_{Q}$ , $W_{K}$	12.9M	$+22$	$0.696$
SoftScale	query-side scaling	1.03M	$\mathbf{+26}$	$0.703$

Table 1: Selected adaptation recipes on TabPFN-3. LoRA uses the rank with the highest Elo. Each fit contains one recipe and the same 68 references;

\Delta

Elo is relative to the published TabPFN-3 default in that fit. Parameter counts use the regression checkpoint.

Figure 2: Per-dataset error reduction for DiagScale and full fine-tuning, relative to the same frozen backbone. Each panel orders 51 datasets by full fine-tuning’s reduction; shading marks its top five.

\rho

is the Spearman correlation between the two methods’ error reductions.

Backbone	Backbone params	Trainable params (% of backbone)	$\Delta$ Elo DiagScale	$\Delta$ Elo Full FT
TabPFN-3	58.3M	12.7K ( $0.022\%$ )	$+26$	$+25$
TabICL v2	28.5M	7.3K ( $0.026\%$ )	$+82$	$+77$
TabFM	1.65B	53.8K ( $0.0033\%$ )	$+20$	$+28$

Table 2: DiagScale and full fine-tuning across three backbones on 51 datasets. Each Elo fit contains one adapted model and 68 fixed references (67 TabArena entries plus frozen TabFM);

\Delta

Elo is relative to the corresponding reference baseline within that fit. Parameter counts and percentages use regression checkpoints.

Figure 3: Aggregation on TabPFN-3. A : varying native views within one configuration. B : varying configuration count under three reducers, with eight native views per configuration. Errors are relative to the released eight-view default; negative values indicate improvement. Error bars and shaded bands show 95% confidence intervals. Complete curves appear in Figure 8 .

Figure 4: Row curation on frozen, single-view TabPFN-3. A : error reduction of attention-selected versus matched random rows; 95% paired

t

intervals over three seeds. B/C : five-seed mean log loss across source-pool sizes. Open and filled points use separate splits from 3M-row subsets and full tables, respectively. Curve labels in B also apply to C. Dashed lines show the no-retrieval loss at 4M rows; shading marks the 4.0–4.5M memory boundary on a single 80 GB GPU.

Figure 5: Performance and runtime on TabArena. (A) TabPFN-3 recipes. (B) Each backbone’s frozen model and highest-Elo evaluated recipe, connected by an arrow. Annotations show

\Delta

Elo relative to the corresponding reference baseline within each fit. (C) Fitting and prediction time shares for TabPFN-3 recipes. Runtime includes fitting and prediction across 51 datasets (Appendix E.4 ).

Appendix figures & tables33 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	Reference (TPU/JAX)	Ours (bf16, H100)	$\Delta$ %
Binary — reported as $1\!-\!$ AUC (30 datasets)
Amazon_employee_access	0.1416	0.1419	$+0.24$
APSFailure	0.007387	0.005329	$-27.85$
bank-marketing	0.2309	0.2306	$-0.13$
Bank_Customer_Churn	0.1229	0.1233	$+0.30$
Bioresponse	0.1178	0.1136	$-3.55$

Appendix

Table 3: Single-H100 reproduction of TabFM. Per-dataset error for the TPU/JAX reference against our bfloat16 H100 run on all 51 TabArena datasets, with

\Delta=(\text{ours}-\text{reference})/\text{reference}

, so a negative value means our run has the lower error. All quantities are errors, lower is better.

Dataset	OpenML ID	Total rows	Predictors	Task	Largest pool
Higgs	45570	11,000,000	28	binary	10,000,000
US_Accidents	46650	7,728,394	43	4-class	7,678,394
COMET_MC	5889	7,619,400	4	binary	7,569,400
Poker-Hand	1567	1,025,009	10	10-class	900,000
Covertype	1596	581,012	54	7-class	500,000

Appendix

Table 4: External OpenML tables used for row curation. Predictors and task type are the effective inputs seen by the model. Largest pool is the biggest context pool evaluated. The US_Accidents and COMET pools use all remaining rows after the 50,000-row holdout; Higgs is capped at 10M.

Reference entry	Imputed (%)
TabFM (frozen reproduction)	0
AutoGluon 1.5 (extreme, 4h)	0
TabPFN-3 (default)	0
TabPFN-2.6 (default)	0
TabICLv2 (default)	0
RealTabPFN-2.5 (tuned + ensembled)	0

Appendix

Table 5: The 68 reference entries used in every Elo comparison. Imputed (%) records benchmark fallback results. The published TabPFN-3 and TabICLv2 defaults are distinct from our reproduced frozen models.

Backbone	Task	Full checkpoint	DiagScale	Fraction (%)
TabPFN-3	Classification	53,153,144	13,056	0.02456
	Regression	58,274,944	12,672	0.02175
TabICL v2	Classification	27,552,258	7,296	0.02648
	Regression	28,544,991	7,296	0.02556
TabFM	Classification	1,639,444,298	53,760	0.00328
	Regression	1,647,782,989	53,760	0.00326

Appendix

Table 6: Exact checkpoint and DiagScale parameter counts. Classification and regression use separate checkpoints. Full-model counts include fixed parameters. Percentages are rounded.

Figure 6: Learning-rate sensitivity for the cross-backbone adaptation comparison. Each point adds one candidate to the same 68 references;

\Delta

Elo is relative to the corresponding published default. Stars mark the rates with the highest unrounded

\Delta

Elo. All panels use five learning rates evaluated on the same 51 datasets.

Backbone	Method	Global	Five-fold (mean $\pm$ SD)
TabPFN-3	Full FT	$+25.27$	$+21.17\pm 2.17$
TabPFN-3	DiagScale	$+25.66$	$+19.90\pm 2.06$
TabICL v2	Full FT	$+77.20$	$+77.20\pm 0.00$
TabICL v2	DiagScale	$+82.12$	$+78.64\pm 3.64$

Appendix

Table 7: Learning-rate selection across datasets. Entries are

\Delta

Elo against the published default, with 68 references and one candidate per fit. Global selects one rate using all 51 datasets; five-fold results report the mean and standard deviation across 20 dataset partitions.

Setting	Updated	Params	$\Delta$ Elo	Score	Error [95% CI]	Wins	Fallback
softscale	query scaling	1.0M	$+26$	$0.703$	$-0.62\%$ $[-1.04\%,-0.24\%]$	34/51	$32\%$
full	all trainable weights	58.3M	$+25$	$0.704$	$-0.64\%$ $[-1.07\%,-0.26\%]$	37/51	$36\%$
qk	query + key projections	12.9M	$+22$	$0.696$	$-0.54\%$ $[-0.95\%,-0.16\%]$	33/51	$35\%$
middle3	middle ICL blocks 10-12	6.4M	$+20$	$0.696$	$-0.60\%$ $[-1.08\%,-0.19\%]$	36/51	$34\%$
attn	all attention sublayers	26.2M	$+20$	$0.693$	$-0.33\%$ $[-0.61\%,-0.09\%]$	35/51	$42\%$
mlp	all MLP sublayers	25.2M	$+19$	$0.693$	$-0.37\%$ $[-0.66\%,-0.11\%]$	38/51	$42\%$

Appendix

Table 8: All 25 adaptation settings on TabPFN-3, each at the global learning rate with the highest

\Delta

Elo from

\{10^{-6},10^{-5},10^{-4}\}

. Each candidate is added separately to the same 68 references;

\Delta

Elo is relative to the published TabPFN-3 default, and Score is TabArena’s normalized score. Error is the mean per-dataset relative change against the frozen backbone, with a 95% dataset-bootstrap interval; negative is better. Wins counts datasets with lower error. Fallback is the fraction of evaluations where validation selects pretrained weights. Parameter counts use the regression checkpoint. Rows are ordered by unrounded

\Delta

Elo.

Backbone	Error change	95% interval	Wins
TabPFN-3	$-0.091\%$	$[-0.283\%,+0.084\%]$	21/51
TabICL v2	$-0.458\%$	$[-1.064\%,-0.016\%]$	26/51
TabFM	$+0.102\%$	$[-0.054\%,+0.286\%]$	28/51

Appendix

Table 9: Paired error change of DiagScale relative to full fine-tuning; negative is better. Wins count datasets with

\bar{\ell}_{d}<0

. The intervals describe the comparison at the selected recipes and do not establish statistical equivalence.

Backbone	Method	Median	Mean	Best	Wins	$\rho$ (size)
TabPFN-3	full fine-tuning	$-0.10\%$	$-0.64\%$	$-5.9\%$	37/51	$+0.13$
TabPFN-3	DiagScale	$-0.08\%$	$-0.73\%$	$-7.8\%$	31/51	$+0.05$
TabICL v2	full fine-tuning	$-0.34\%$	$-1.30\%$	$-10.9\%$	35/51	$+0.26$
TabICL v2	DiagScale	$-0.27\%$	$-1.60\%$	$-11.4\%$	34/51	$+0.26$
TabFM	full fine-tuning	$-0.08\%$	$-0.32\%$	$-5.8\%$	31/51	$+0.16$
TabFM	DiagScale	$+0.01\%$	$-0.29\%$	$-5.8\%$	25/51	$-0.15$

Appendix

Table 10: Per-dataset relative error change against the frozen backbone, 51 datasets per row, full protocol; negative is better. Best is the largest single reduction. Wins counts datasets with any reduction. These are the deployed arms at fixed learning rates, including checkpoint selection and fallback.

\rho

is the Spearman correlation between training-set size and the reduction.

Figure 7: SoftScale component diagnostics. Blue circles, orange squares, and green triangles denote houses, protein, and bankruptcy. A: fraction of the joint-training gain recovered by separately training only the context-size branch

{\bm{s}}

or the query-dependent gate

{\bm{g}}

; gray bars show the mean across datasets. B: each point summarizes one module group: the feature embedder or ICL stack, plus the classification decoder for bankruptcy. C: feature-embedder controls relative to its pretrained weights: trained change plus random perturbation (

\Delta+R

), random perturbation alone (

R

), or reversion (

0

); other scale modules remain trained. Error bars in C show standard deviations over five draws for

\Delta+R

and

R

. Gains in A and C are normalized by the corresponding loss reduction from jointly training both scale branches relative to pretrained weights along the same inference path.

Dataset	Train ${\bm{s}}$ only	Train ${\bm{g}}$ only
Houses	$96.7\%$	$9.2\%$
Protein	$92.8\%$	$16.0\%$
Bankruptcy	$106.2\%$	$8.1\%$

Appendix

Table 11: Separate branch training on the three diagnostic datasets. Entries report the percentage of the joint SoftScale training gain recovered; training both branches defines

100\%

. All other parameters remain frozen in each run.

Figure 8: Complete aggregation curves, including native views below the released default and random single configurations. The three reducers coincide at

K=1

. Both panels use the same paired estimator and transformed 95% dataset-cluster bootstrap intervals as Figure 3 , with independent vertical ranges and all intervals visible. The additional

V=48

point is included between the labeled 32- and 64-view ticks.

$K$	$V$	Reducer	$\Delta$ error [95% CI]	Wins
1	1	inner uniform	$+3.74\%$ $[+0.81\%,+6.70\%]$	4/51
1	2	inner uniform	$+1.68\%$ $[+0.90\%,+2.75\%]$	9/51
1	4	inner uniform	$+0.42\%$ $[+0.05\%,+0.84\%]$	18/51
1	8	inner uniform	— (baseline)
1	16	inner uniform	$-0.48\%$ $[-0.93\%,-0.14\%]$	33/51
1	32	inner uniform	$-0.60\%$ $[-1.12\%,-0.20\%]$	42/51

Appendix

Table 12: Every arm of Figure 8 , full protocol (816 cells), against the default baseline

p_{\rm base}

V{=}8

. Error is the percentage change

100(\exp(\bar{\ell})-1)

over 51 equally weighted datasets with a transformed 95% dataset-cluster bootstrap interval; negative is better. Configuration rows average over independent random subsets. Wins counts datasets with reduced error and is reported for native-view settings and the complete configuration pool; dashes indicate counts not reported. Inner uniform averages native views within one configuration.

Type	Metric	Reducer	Median	Worst	Wins
binary (30)	ROC AUC	uniform	$+0.30\%$	$+5.29\%$	9/30
		best-single	$+0.05\%$	$+4.20\%$	13/30
		greedy	$-0.31\%$	$+1.02\%$	22/30
multiclass (8)	log loss	uniform	$+5.80\%$	$+164.30\%$	1/8
		best-single	$-0.85\%$	$+0.35\%$	7/8
		greedy	$-1.21\%$	$-0.32\%$	8/8

Appendix

Table 13: Relative error change against the default at

K=96

, by task type; negative is better. Wins count datasets with reduced error.

Figure 9: Greedy aggregation with different fractions of training-side selector labels. All panels share the same axes and fixed member predictions. Points use the dataset-weighted mean log-error ratio against the released default; bars show transformed 95% dataset-bootstrap intervals. Pool breadth improves each curve’s point estimates, while fewer selector labels reduce the gains. Intervals exclude zero for

f\in\{1/2,1\}

and

K\geq 16

; all others include zero.

$K$	$f=0.125$	$f=0.25$	$f=0.5$	$f=1.0$
1	$+11.35\%$	$+11.35\%$	$+11.35\%$	$+11.35\%$
8	$+1.37\%$	$+0.36\%$	$-0.35\%$	$-0.77\%$
16	$+0.83\%$	$-0.19\%$	$-0.99\%$	$-1.45\%$
32	$+0.61\%$	$-0.48\%$	$-1.34\%$	$-1.85\%$
64	$+0.44\%$	$-0.72\%$	$-1.66\%$	$-2.27\%$
96	$+0.39\%$	$-0.81\%$	$-1.77\%$	$-2.44\%$

Appendix

Table 14: Greedy selection: relative error change against the default baseline

p_{\rm base}

V{=}8

, by pool size and out-of-fold label fraction; negative is better. The last row is the change from

K=8

K=96

at that budget, in percentage points. The

K=1

row is the mean over randomly sampled single-member pools, not

p_{0}

; the reducer has nothing to choose between there, so it does not vary with

f

Figure 10: Complete source-pool sweeps with single-view TabPFN-3 on five large tables, including the geometric construction omitted from the main figure. Points are the five-seed mean log losses; each panel has an independent linear vertical axis. For the three largest tables, open and filled markers distinguish the 3M-subset and full-table splits; lines connect only points from the same split. Feed-all curves contain only measured values, ending at 4M where the pool exceeds capacity. Beyond 4M, dashed lines hold that reference fixed and gray bands mark the 4.0–4.5M capacity boundary. Green lines on US_Accidents and Higgs are tuned LightGBM endpoint references (Table 17 ).

Dataset	$N$	Eval. $N$	Geo.	Model-aware	Model-aware
	Total	Within memory			Beyond wall
Poker-Hand	1.03M	900k	$+12.0$	$\mathbf{+87.2}$	—
Covertype	0.58M	500k	$-67.9$	$\mathbf{+22.9}$	—
US_Accidents	7.73M	2.9M	$-19.8$	$+1.5$	$\mathbf{+5.2}$ at 7.68M
Higgs	11M	2.9M	$-4.2$	$+0.9$	$+2.2$ at 6M, $\mathbf{+3.5}$ at 10M
COMET_MC	7.62M	2.9M	$-11.3$	$-2375$	$-2808$ at 7.57M

Appendix

Table 15: Row construction on large tables, frozen TabPFN-3, single view. Relative log-loss reduction against the full-context reference for the regime, in per cent; positive is better. Within memory the reference is feed-all at the same

N

; beyond the memory wall no such run exists, so it is feed-all at 4M. A dash marks a source pool that never reaches the wall. Entries summarize five seeds. The 2.9M results use the 3M-subset splits; beyond-capacity results and their 4M references use the full-table splits.

Pool	Capped union	Recursive splitting	Time ( $\times$ )
			Capped	Split
6M	$0.46279\pm 0.00316$	$0.46266\pm 0.00343$	$1.95$	$2.32$
8M	$0.46868\pm 0.00283$	$0.45848\pm 0.00328$	$2.20$	$3.16$
10M	$0.48530\pm 0.00362$	$0.45637\pm 0.00279$	$2.47$	$3.95$

Appendix

Table 16: Higgs union-capacity comparison. Log loss is mean

\pm

standard deviation over five seeds. Time includes attention scoring and is relative to feed-all at 4M rows. Both variants keep the retrieval budget and scoring shards fixed.

Dataset	Seed	LR	Rounds	Val. loss	Test loss
US_Accidents	0	0.02	7,972	0.14011	0.13994
	1	0.02	8,093	0.14328	0.14279
	2	0.02	8,056	0.13990	0.14081
	3	0.02	8,411	0.13998	0.14279
	4	0.02	7,479	0.14216	0.14276
Higgs	0	0.02	72,769	0.45890	0.45808

Appendix

Table 17: Validation-tuned LightGBM endpoints, five seeds. All selected models use 255 leaves. US_Accidents fits 7,524,827 rows with 153,567 validation rows; Higgs fits 10M rows with 200k additional validation rows. “Rounds” is the selected best iteration under a 100k cap.

Dataset	$n$	$k$	attn. %	union	$\Delta$ 1 view	$\Delta$ 8 views
blood-transfusion-service-center	499	4	100	499	$+0.00$ $\pm 0.00$	$+0.00$ $\pm 0.00$
diabetes	512	4	99	512	$+0.00$ $\pm 0.85$	$+0.04$ $\pm 0.45$
maternal_health_risk	676	4	91	634	$+2.98$ $\pm 5.72$	$+0.77$ $\pm 2.43$
concrete_compressive_strength	687	4	93	684	$-0.57$ $\pm 1.96$	$-0.12$ $\pm 0.80$
airfoil_self_noise	1,002	4	83	972	$+0.63$ $\pm 3.58$	$-0.29$ $\pm 1.23$
students_dropout_and_academic_success	2,950	4	50	1,814	$-0.25$ $\pm 1.24$	$-0.19$ $\pm 0.62$

Appendix

Table 18: Model-aware row construction at TabArena scale, all 15 datasets, 30 splits per dataset.

n

is the maximum number of training rows across splits,

k

the number of query clusters, attn. the mean attention mass retained by the rows selected for each query, and union the median per-cluster context size. The last two columns give mean paired relative error reductions at one view and at the released eight-view default, in per cent, with approximate

95\,\%

intervals from Equation ( 8 ); positive is better. Bold marks intervals excluding zero.

Dataset	$N$	Feed-all	Random ids	Attention	Attention vs. random
Covertype	500k	$0.0728$	$0.1613$	$0.0558$	$+65.3\%$ $[+60.0,+70.6]$
Poker-Hand	900k	$0.3928$	$0.5272$	$0.0469$	$+91.1\%$ $[+89.1,+93.1]$
Higgs	900k	$0.4885$	$0.5018$	$0.4859$	$+3.2\%$ $[+2.8,+3.6]$
Higgs	2.9M	$0.4759$	$0.4911$	$0.4717$	$+3.9\%$ $[+3.5,+4.3]$

Appendix

Table 19: Matched-row identity control. Log loss, mean over three seeds. The final column is the relative change from the random-identity arm to the attention arm; positive means the attention-selected rows are better. This is the contrast plotted in Figure 4 A. All four 95% intervals exclude zero.

Arm	Log loss	vs. feed-all	AUC	Rare-class share
Feed-all ( $N=900$ k)	$0.0151$	—	$0.998$	$0.017$
Attention union	$0.2302$	$-1425\%$	$0.950$	$\mathbf{0.403}$
Random identities, same size	$0.0158$	$-4.9\%$	$0.998$	$0.017$
Class-marginal repair	$0.1270$	$-741\%$	$0.569$	$0.017$

Appendix

Table 20: COMET_MC at

N=900

k, five seeds, source pool

98.3\%/1.7\%

. Every constructed arm refits on the same

25

clusters with a median context of

977

rows; only the contents differ. The rare-class share is the median over

125

cluster observations.

Dataset	$N$	$\|Q\|$	Draws	Union	Overlap
COMET_MC	900k	$2{,}270$	$1{,}135{,}000$	$977$	$\mathbf{1162\times}$
Covertype	500k	$1{,}487$	$743{,}500$	$40{,}794$	$18\times$
Poker-Hand	900k	$1{,}570$	$785{,}000$	$73{,}731$	$11\times$
Higgs	900k	$1{,}383$	$691{,}500$	$85{,}188$	$8\times$
Higgs	2.9M	$1{,}202$	$601{,}000$	$154{,}159$	$4\times$

Appendix

Table 21: Retrieval concentration within a query cluster. Query count, draws, and union size are medians over clusters and seeds (five seeds for COMET, three for the other settings). “Overlap” is the ratio of the reported median draws to median union size. Poker and Higgs statistics use the matched random-control runs, whose context sizes equal those of attention selection.

			Default	Selected	$F=500$ controls
Dataset	Domain	$D$	vs. 1 view	vs. default	Per view vs. fixed	Imp. vs. random
Bioresponse	molecular	$1{,}776$	$+8.9$	$-1.4$	$+4.5$	$+4.5$
hiva_agnostic	molecular	$1{,}617$	$+12.8$	$-4.5$	$+4.7$	$-2.7$
QSAR-TID-11	molecular	$1{,}024$	$+2.0$	$+0.5$	$+0.0$	$+2.5$
CIFAR_10	image	$3{,}072$	$+6.6$	$-2.1$	$+1.2$	$+0.0$
micro-mass	mass-spec	$1{,}300$	$-10.5$	$+35.1$	$-7.1$	$+19.2$

Appendix

Table 22: Column curation on seven wide tables, frozen TabPFN-3. Entries are relative error reductions from the reference in each header; positive is better. The main selected result fixes 200 columns across all eight views for classification and 500 for QSAR-TID-11 regression, matching the default’s per-view counts. “1 view” uses all

D

columns. The two rightmost columns report the separate

F=500

controls: fixed views each use all 500 selected columns, while per-view subsampling uses the native cap; importance and random selection are compared with 500 columns fixed across eight views. All percentages use unrounded four-seed mean errors. Task metrics and absolute errors appear in Table 23 .

		No selection			Importance, $F=500$			Random, $F=500$			$F=200$
Dataset	Metric	1 v.	8 v.	gini	1 v.	pin	p.v.	1 v.	pin	p.v.	Imp. pin
Bioresponse	1 $-$ AUC	$0.1427$	$0.1300$	$0.1320$	$0.1394$	$0.1331$	$0.1270$	$0.1459$	$0.1393$	$0.1358$	$0.1319$
hiva_agnostic	log loss	$0.2085$	$0.1818$	$0.1840$	$0.2121$	$0.1912$	$0.1822$	$0.1951$	$0.1862$	$0.1831$	$0.1899$
QSAR-TID-11	RMSE	$0.7432$	$0.7282$	$0.7269$	$0.7312$	$0.7246$	$0.7244$	$0.7624$	$0.7429$	$0.7414$	—
CIFAR_10	log loss	$1.6399$	$1.5310$	$1.5531$	$1.6099$	$1.5523$	$1.5330$	$1.6267$	$1.5529$	$1.5440$	$1.5633$
micro-mass	log loss	$0.4759$	$0.5257$	$0.3358$	$0.4579$	$0.3478$	$0.3726$	$0.5579$	$0.4307$	$0.5137$	$0.3409$

Appendix

Table 23: Complete column-curation grid: mean error over 4 seeds, in each dataset’s own metric, so values compare across a row and not down a column; lower is better. gini denotes the backbone’s importance-based per-view sampler, which also uses LightGBM gain. The Importance and Random groups both keep

F=500

columns; pin gives all eight views the same set, and p.v. restores native subsampling within it. The last column adds importance selection with 200 columns fixed across eight views. Dashes denote unavailable 200-column results; regression retains the 500-column result in the main comparison.

Figure 11: Column-curation controls at a fixed 200-column selection budget with single-view TabPFN-3, separate from the eight-view comparison in Table 22 . Circles vary context rows at fixed width; squares vary width at fixed context size. The LightGBM ranking is fitted once per dataset and seed on the full training pool and held fixed through each sweep. Points are mean paired error reductions over four seeds, relative to using all available columns at that point; bars show one standard error. QSAR-TID-11 uses RMSE.

Family	Scope	Passes	Median	Example/control
Blind synthesis	51 dataset $\times$ operator	3	$-4.6$	none
Transduction	57 dataset $\times$ operator	14	$-1.8$	anneal $+12.8$ , airfoil $+1.2$
Learned rows	171 probe/dataset/dose	10	$-0.1$	concrete improves over placebo
Full-size joint rows	5 datasets	0	$-11.8$	no improvement observed
Self-stacking	19 datasets	1	$-3.0$	Marketing_Campaign only
OOF target encoding	9 datasets	2	$-0.2$	Marketing_Campaign $+9.4$

Appendix

Table 24: Context expansion by operator family, frozen TabPFN-3. Relative error reduction against the unmodified context, in per cent; positive is better, as in Tables 22 and 15 . The scope column names the unit being counted, which differs by family. Passes criterion counts units meeting that family’s own bar: an improvement over the unmodified context for every row except the learned-row program, where it is that program’s decision criterion.

Operator	Family	$n$	Median	IQR	Improves
Gaussian jitter	Blind synthesis	19	$-6.19$	$[-11.01,-3.99]$	2/19
Row interpolation	Blind synthesis	19	$-2.95$	$[-5.49,-1.84]$	1/19
Class-balanced interpolation	Blind synthesis	13	$-5.90$	$[-20.02,-3.39]$	0/13
Whole-query pseudo-labels	Transduction	19	$-12.66$	$[-44.80,-3.44]$	3/19
Cross-half pseudo-labels	Transduction	19	$-2.26$	$[-2.76,+0.04]$	5/19
Cross-half, confidence $\geq 0.9$	Transduction	14	$-0.59$	$[-1.41,-0.33]$	2/14

Appendix

Table 25: Expansion settings and controls over the 19-dataset evaluation. Relative error reduction against the unmodified context, in per cent; positive is better.

n

is the number of datasets on which the operator ran; some operators apply only to specific task types or class structures. Improves counts datasets with any reduction. For learned rows, this differs from the decision criterion in Table 24 .

M

is the number of added rows. Nearest-row curation selects 70% of the training rows nearest each query-cluster centroid as a curation reference.

Setting	Training / construction	Deployment	Labels / selection
Blind synthesis	Jitter, pair interpolation, or class-balanced interpolation of training rows; no optimization.	$\mathcal{D}+Z$ , with at most $n/2$ added rows.	Inherited training labels; interpolated targets for regression mixup.
Transduction	Predict the query batch from $\mathcal{D}$ . For cross-half expansion, split queries into two parts.	$\mathcal{D}$ plus pseudo-labeled rows from the other half; the whole-query control adds the whole batch.	Model predictions only; optional probability or quantile-width filter.
Row controls	Duplicate training rows or sample noise anchors; no optimization.	$\mathcal{D}$ plus the constructed rows.	Training labels or target tails for duplication; labels for noise anchors sampled from training class proportions or fixed to the majority class.
Fold-rotated rows	Optimize free rows using real training folds plus $Z$ as context; score a different training fold.	$\mathcal{D}+Z$ .	Fixed seed-row labels; training-side early stopping.
Free-row distillation	Optimize row features with $Z$ alone as context; predict real training queries.	$\mathcal{D}+Z$ ; $Z$ alone is a diagnostic arm.	Fixed seed-row labels; Nominal 10% training-side checkpoint slice; initialization details below.
MLP-generated rows	Same distillation objective; optimize a conditional MLP with a fixed latent bank.	$\mathcal{D}$ plus generated rows.	Fixed conditioning labels from training rows; training-side checkpoint selection.

Appendix

Table 26: Construction and use of expansion settings. All backbone weights are frozen.

\mathcal{D}

denotes the outer-training table and

Z

denotes constructed rows. Only transductive settings use query features to construct the conditioning data; query labels are reserved for evaluation.

Backbone	Method	Top-5 share	Datasets improved
TabFM	DiagScale	$70\%$	25/51
TabFM	full fine-tuning	$62\%$	31/51
TabICL v2	DiagScale	$46\%$	34/51
TabICL v2	full fine-tuning	$48\%$	35/51
TabPFN-3	DiagScale	$56\%$	31/51
TabPFN-3	aggregation	$68\%$	41/51

Appendix

Table 27: Concentration of positive per-dataset error reductions.

Outcome	$\rho_{32}$	$q_{21}$	$q_{147}$	$q_{21,8}$
TabFM / DiagScale	0.212	0.282	0.599	0.358
TabFM / full FT	0.284	0.906	0.528	0.941
TabICL v2 / DiagScale	0.426	0.039	0.130	0.123
TabICL v2 / full FT	0.412	0.056	0.130	0.138
TabPFN-3 / DiagScale	0.339	0.317	0.444	0.264
TabPFN-3 / aggregation	0.496	0.004	0.031	0.013

Appendix

Table 28: Native-view disagreement and intervention gains. Disagreement uses TabPFN-3 predictions for all outcomes.

\rho_{32}

is its Spearman correlation with per-dataset error reduction using 32 views;

q_{21}

and

q_{147}

are Benjamini–Hochberg adjusted

p

-values within each outcome and across all outcomes, respectively.

q_{21,8}

repeats the within-outcome correction using eight views, four from each of the two preprocessing pipelines.

TabPFN-3
Recipe	Elo	$\Delta$ Elo	Fit (h)	Predict (h)	Total (h)	$\times$ frozen
Frozen	1658	$+1$	$0.14$	$0.38$	$0.52$	$1.0$
32 native views	1675	$+21$	$0.19$	$1.47$	$1.66$	$3.2$
DiagScale	1682	$+26$	$6.30$	$0.31$	$6.61$	$12.7$
Full fine-tuning	1681	$+25$	$7.42$	$0.31$	$7.73$	$14.9$
Aggregation (96)	1721	$+67$	$177.71$	$69.79$	$247.50$	$476.4$

Appendix

Table 29: Measured runtime over the same 816 TabArena cells on single H100 GPUs. Fit includes adaptation or out-of-fold member evaluation and selection; predict covers the full test batches. Pool-based methods include predictions from all 96 configurations. Elo uses 68 fixed references and one candidate per fit;

\Delta

Elo uses the corresponding baseline within that fit. Frozen TabPFN-3 and TabICL v2 compare reproduced models with published defaults, so their deltas need not be zero. Frozen TabFM uses its rating in the TabFM full-FT fit. Runtime multiples use the reproduced frozen models.

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