Do Tabular Foundation Models Still Need Feature Engineering?

# Do Tabular Foundation Models Still Need Feature Engineering?
Source: [https://arxiv.org/html/2609.13202](https://arxiv.org/html/2609.13202)
###### Abstract

Feature engineering has long been a cornerstone of tabular machine learning\. Tabular foundation models \(TFMs\) are pretrained on a wide range of tabular datasets and applied via in\-context learning\. Their rise raises a natural question: does manual feature construction still matter as these models become more capable? To answer this, we perform a controlled study across several versions of two major TFM families, testing a wide range of existing feature engineering techniques on benchmark datasets from TabArena\. We find a consistent pattern: feature engineering gains are concentrated in earlier model generations and become negligible for the strongest models\. These results suggest that stronger TFMs depend less on explicitly engineered input representations\. In a complementary experiment, however, adding in\-context information from related datasets still improves performance\. Our findings indicate a shift in the source of performance gains for stronger TFMs: re\-representing existing inputs becomes less effective, while providing additional task\-relevant context remains beneficial\.

## Introduction

Feature engineering improves predictive performance by transforming raw variables into representations that better expose useful statistical structure\([24](https://arxiv.org/html/2609.13202#bib.bib2)\)\. Implicit in this practice is the assumption that such structure should be encoded into the input representation before learning, rather than inferred by the estimator itself\.

Tabular foundation models \(TFMs\) challenge this assumption\. Pre\-trained across many tabular tasks and applied through in\-context learning, TFMs may reduce the need for task\-specific feature engineering\. As these models become more capable, statistical structure that previously required explicit transformations may become increasingly accessible from the original input\. This raises a capability dependent question: does the marginal value of feature engineering decline as TFMs become stronger?

Recent work has shown that feature\-engineering pipelines can improve TFMs by explicitly exposing useful structure in the data\([21](https://arxiv.org/html/2609.13202#bib.bib12)\)\. However, it remains unclear whether these gains reflect a persistent limitation of TFMs in recovering structure from raw inputs, or whether they are concentrated in particular models and datasets and weaken as TFMs become more capable\. Existing evidence does not distinguish between these possibilities, as the value of feature engineering has not yet been systematically compared across model generations under controlled, within\-estimator settings\.

Answering this question requires evaluating feature engineering within each fixed estimator and then comparing its effect across successive TFM generations\. We therefore study whether engineered representations provide consistent gains across model versions, datasets, and tasks\. We further examine whether TFMs that benefit little from feature transformations can still exploit additional examples from related datasets\. Together, these analyses investigate whether stronger TFMs become broadly less responsive to additional intervention, or whether the value of intervention shifts from re\-representing existing inputs to providing additional task\-relevant context\.

To carry out this study, we evaluate successive versions of the TabPFN and TabICL families on datasets from TabArena\([6](https://arxiv.org/html/2609.13202#bib.bib11)\)\. For each dataset, split, and estimator, we use the model default configuration and native preprocessing while keeping the evaluation protocol fixed\. This paired comparison isolates how the effect of feature engineering changes across model versions\. In a separate experiment, we examine whether stronger TFMs can still benefit from additional source examples selected for compatibility with the target task\.

Across the evaluated TabArena tasks, generic feature engineering is not a reliable source of improvement for TFMs\. Most transformations are neutral or harmful, while positive gains are concentrated in particular datasets and earlier model versions\. For the strongest models, across dataset gains approach zero\. These models nevertheless remain responsive to additional examples from related datasets\. This contrast suggests that the declining value of generic feature transformations should not be interpreted as a general inability to exploit additional task\-relevant information\.

Our contribution is a controlled empirical reassessment of feature engineering for TFMs\. By isolating within\-estimator gains across successive TabPFN and TabICL versions, we show that the benefits of generic feature engineering are concentrated in earlier models and a small subset of datasets, while becoming negligible for the strongest models\. Our complementary context\-augmentation experiment provides evidence that these models can still exploit additional task\-relevant information, suggesting that the opportunity for improvement is shifting from re\-representing existing inputs toward enriching the available task context\.

## Related Work

Feature engineering transforms input variables to expose structures that may be easier for a particular estimator to use\. Common methods include numerical transformations, categorical encodings, discretization, and interaction construction\. Prior work shows that engineered features interact with the estimator: different model classes can respond differently to the same engineered structure\([10](https://arxiv.org/html/2609.13202#bib.bib1)\)\. Tree\-based and neural tabular models also differ in robustness to uninformative features, feature orientation, and irregular target functions\([9](https://arxiv.org/html/2609.13202#bib.bib3)\)\. Within neural models, transformations such as scaling and ranking can smooth irregular targets, but may also discard information or impair optimization, making their utility dependent on the feature and model setting\([3](https://arxiv.org/html/2609.13202#bib.bib4)\)\. These findings motivate evaluating feature transformations separately for each estimator\.

Tabular foundation models introduce a different setting\. TabPFN and TabICL are pretrained across tabular tasks and adapt to new datasets through in\-context learning, while successive versions differ in architecture, pretraining, context capacity, and the dataset sizes they can accommodate\([11](https://arxiv.org/html/2609.13202#bib.bib5);[12](https://arxiv.org/html/2609.13202#bib.bib6);[7](https://arxiv.org/html/2609.13202#bib.bib7);[8](https://arxiv.org/html/2609.13202#bib.bib8);[18](https://arxiv.org/html/2609.13202#bib.bib9);[19](https://arxiv.org/html/2609.13202#bib.bib10)\)\. Such changes may alter which structures can be recovered directly from raw inputs and which still benefit from explicit transformations\. Evidence obtained from one model version therefore does not establish whether the effect of feature engineering persists across later versions\.

TabPrep is closely related to our study\([21](https://arxiv.org/html/2609.13202#bib.bib12)\)\. It generates feature variants targeting numerical interactions, group\-conditional effects, and pseudo\-categorical numerical structure, and evaluates them within the TabArena training, tuning, and ensembling pipeline\. Its results show that engineered variants can improve performance within this broader pipeline, particularly when applied to TabPFN\-2\.5\. Our study asks a complementary question: how does the paired effect of feature engineering, measured within each estimator under a common evaluation protocol, change across successive versions of TabPFN and TabICL?

## Problem Setup and Estimand

### Notation

Let thedd\-th tabular prediction task be

𝒟d=\(Xd,yd\),\\mathcal\{D\}\_\{d\}=\(X\_\{d\},y\_\{d\}\),whereXdX\_\{d\}denotes the original predictors andydy\_\{d\}denotes the classification or regression target\. Letmmdenote a fixed tabular foundation model estimator, including its checkpoint, default configuration, ensemble procedure, and native preprocessing pipeline\.

Following the standard view of feature engineering as an explicit transformation of the input representation before prediction\([24](https://arxiv.org/html/2609.13202#bib.bib2)\), we represent each external feature engineering condition by a mapping

Tk:𝒳d→𝒵d,k\.T\_\{k\}:\\mathcal\{X\}\_\{d\}\\rightarrow\\mathcal\{Z\}\_\{d,k\}\.The identity condition isT0​\(X\)=XT\_\{0\}\(X\)=X, corresponding to no additional external feature engineering beyond the foundation model native preprocessing\. Eachk\>0k\>0denotes one pre\-specified intervention, and𝒦⁡\(d\)\\mathcal\{K\}\(d\)denotes the set of non\-identity interventions applicable to datasetdd\. Any data\-dependent component ofTkT\_\{k\}is fitted using only the corresponding training split\.

Letμd,s,m,k\\mu\_\{d,s,m,k\}denote the test metric obtained on datasetdd, evaluation splitss, estimatormm, and representation conditionkk\. Letσq∈\{−1,\+1\}\\sigma\_\{q\}\\in\\\{\-1,\+1\\\}denote the orientation of metricqq, withσq=\+1\\sigma\_\{q\}=\+1when larger values are better andσq=−1\\sigma\_\{q\}=\-1when smaller values are better\.

### Feature engineering gain

We define the direction normalized paired gain over the identity representation as

δd,s,m,k=σq​\(μd,s,m,k−μd,s,m,0\)\.\\delta\_\{d,s,m,k\}=\\sigma\_\{q\}\\left\(\\mu\_\{d,s,m,k\}\-\\mu\_\{d,s,m,0\}\\right\)\.Thus,δd,s,m,k\>0\\delta\_\{d,s,m,k\}\>0consistently indicates that interventionkkoutperforms the identity representation under the same split and estimator configuration\.

We summarize the repeated paired evaluations within each dataset by

Δd,m,k=medians​δd,s,m,k\.\\Delta\_\{d,m,k\}=\\mathrm\{median\}\_\{s\}\\;\\delta\_\{d,s,m,k\}\.Evaluation splits are treated as repeated measurements within a dataset, while datasets form the units of benchmark\-level analysis\.

To determine whether any evaluated intervention improves over identity, we define the best observed feature\-engineering gain as

Bd,m=maxk∈𝒦⁡\(d\)⁡Δd,m,k\.B\_\{d,m\}=\\max\_\{k\\in\\mathcal\{K\}\(d\)\}\\Delta\_\{d,m,k\}\.Accordingly,Bd,m≤0B\_\{d,m\}\\leq 0indicates that none of the evaluated interventions applicable to datasetddachieves a positive median paired gain, andBd,mB\_\{d,m\}is an oracle style observation, which reports the best observed condition without implying that this condition could be selected without a validation set\.

### Ordered hypothesis tests\.

For each version family, letDDdenote the number of benchmark datasets andGGthe number of estimator versions, ordered chronologically and indexed byg=1,…,Gg=1,\\ldots,G\. We useBd,gB\_\{d,g\}for the best\-observed gain introduced above, evaluated on datasetddat versiongg\. The candidate set𝒦⁡\(d\)\\mathcal\{K\}\(d\)is held fixed across versions, and datasets are the independent units of inference\.

For the TabPFN version families withG\>2G\>2, we use a one\-sided exact Page test for an ordered decline in best\-observed headroom\([17](https://arxiv.org/html/2609.13202#bib.bib22)\)\. Under the null, version labels are exchangeable within each dataset\. The alternative is that largerBd,gB\_\{d,g\}values tend to occur at earlier version positions\.

For each datasetdd, letrd,gr\_\{d,g\}denote the ascending midrank ofBd,gB\_\{d,g\}across theGGversions\. The Page statistic is

L=∑d=1D∑g=1G\(G\+1−g\)​rd,g\.L=\\sum\_\{d=1\}^\{D\}\\sum\_\{g=1\}^\{G\}\(G\+1\-g\)r\_\{d,g\}\.Since earlier versions receive larger weights, larger values ofLLprovide stronger evidence of an ordered decline\. We compute the exact one\-sided rawpp\-value by enumerating all within dataset permutations of the version labels\.

TabICL classification includes only two versions, so the ordered comparison reduces to a paired test\. For each dataset, let

Cd=Bd,v1−Bd,v2,C\_\{d\}=B\_\{d,\\mathrm\{v1\}\}\-B\_\{d,\\mathrm\{v2\}\},whereCd\>0C\_\{d\}\>0indicates a reduction in best\-observed headroom from v1 to v2\. We use

T=1D​∑d=1DCdT=\\frac\{1\}\{D\}\\sum\_\{d=1\}^\{D\}C\_\{d\}as the statistic in a one\-sided exact sign\-flip test\. Under the null, the paired differences are symmetric about zero\. The exact rawpp\-value is computed over all2D2^\{D\}sign assignments\.

The exact one\-sidedpp\-values from the three prespecified primary tests are adjusted jointly using the Benjamini–Hochberg procedure, withq<0\.05q<0\.05as the primary multiplicity\-adjusted significance criterion\([2](https://arxiv.org/html/2609.13202#bib.bib23)\)\. We additionally report Holm\-adjustedpp\-values to assess robustness under family\-wise error control\([13](https://arxiv.org/html/2609.13202#bib.bib24)\)\. As descriptive effect summaries, we report the median paired first\-to\-last difference

C~=mediand​\(Bd,1−Bd,G\)\\widetilde\{C\}=\\mathrm\{median\}\_\{d\}\\\!\\left\(B\_\{d,1\}\-B\_\{d,G\}\\right\)and

N↓=∑d=1D\{Bd,1\>Bd,G\},N\_\{\\downarrow\}=\\sum\_\{d=1\}^\{D\}\\mathbf\{1\}\\\!\\left\\\{B\_\{d,1\}\>B\_\{d,G\}\\right\\\},is the number of datasets with a positive first\-to\-last difference\.

## Experiments

We evaluate 12 estimator versions from the TabPFN and TabICL families on 13 TabArena datasets \(Table[1](https://arxiv.org/html/2609.13202#Sx4.T1)\): eight classification and five regression tasks\. The classification panel includes TabPFN v1, v2, v2\.5, v2\.6, v3, TabICL v1, and TabICL v2; all selected classification datasets satisfy the sample and feature limits of TabPFN v1 \(at most 1,024 training samples and 100 features\), ensuring that every generation is evaluated on the same datasets\. This restriction is deliberate: small data tasks are the intended operating regime of TFMs and provide a stringent setting for testing whether feature engineering still supplies useful inductive bias when task specific evidence is limited\. Regression experiments include TabPFN v2, v2\.5, v2\.6, v3, and TabICL v2, as both TabPFN v1 and TabICL v1 are classification only\. All experiments were run on a Ubuntu server with 32 GB NVIDIA Tesla V100 and AMD Ryzen 9700X processor\.

DatasetSamplesFeaturesClassesClassificationBlood transfusion74842Diabetes76882Anneal898385Credit\-g1,000202Maternal health1,01463QSAR biodeg1,054412Website phishing1,35393Fitness club1,50062RegressionQSAR fish toxicity9076—Concrete strength1,0308—Healthcare insurance1,3386—Airfoil noise1,5035—Used Fiat 5001,5387—Table 1:The 13 TabArena datasets used in this study, ordered by sample count within each task\.For each dataset and estimator, we compare the identity baseline against 26 feature engineering conditions drawn from seven families: scale and power transforms, categorical encodings, discretization, interaction features, selection methods, the TabPrep composite pipeline, and two prompt\-inspired conditions adapted from in\-context learning\. Each condition is a single atomic transformation; depending on column types, between 16 and 26 of these conditions apply to a given dataset\. Data dependent components are fitted on the corresponding training split only\.

Every condition is evaluated on the 30 official TabArena splits \(10 repeats×\\times3 folds\)\. For each dataset, estimator, and feature engineering combination, we compute the paired gain against identity on the same split and summarize it by the within cell medianΔd,m,k\\Delta\_\{d,m,k\}; the best observed gainBd,mB\_\{d,m\}is the maximum of these medians over applicable non\-identity conditions\. Following the TabArena protocol\([6](https://arxiv.org/html/2609.13202#bib.bib11)\), we adopt macro\-F1 for classification and sign reversed RMSE for regression, so that positive values consistently favor feature engineering\.

Table 2:The 26 feature engineering conditions grouped by family\. Applicability depends on dataset column types; the identity baseline is not shown\.The prompt\-inspired family adapts two forms of context augmentation from LLMs\. The first constructs a shared ICL context by retrieving training rows most similar to the test fold\([20](https://arxiv.org/html/2609.13202#bib.bib13)\)\. The second is a tabular analogue of generated knowledge prompting: predictions from the same estimator are added as auxiliary inputs to its final prediction\([14](https://arxiv.org/html/2609.13202#bib.bib15)\)\. These features are constructed using leakage safe three\-fold OOF predictions, making the implementation a form of stacked generalization\([22](https://arxiv.org/html/2609.13202#bib.bib14)\)\.

As an additional experiment, we examined whether providing task relevant context benefits the strongest TFMs\. Among the possible forms of context augmentation, we considered a simple setting in which samples from pre\-specified related datasets are added to the model in\-context examples\. Because related source datasets are typically distribution shifted relative to the target task, augmenting the context with the full source pool can introduce incompatible examples\. We therefore introduce Nearest\-Neighbor Reference Consistency \(NNRC\) screening to identify a target compatible source subset\. NNRC first filters source samples by proximity to the target covariate distribution and then ranks the remaining samples by label consistency with a reference model fitted only on the target training data\. The complete procedure is given in Algorithm[1](https://arxiv.org/html/2609.13202#alg1)\.

Algorithm 1NNRC Screening0:Source pool

𝒮=\(Xsrc,ysrc\)\\mathcal\{S\}=\(X^\{\\mathrm\{src\}\},y^\{\\mathrm\{src\}\}\); target training split

𝒟tr=\(Xtr,ytr\)\\mathcal\{D\}^\{\\mathrm\{tr\}\}=\(X^\{\\mathrm\{tr\}\},y^\{\\mathrm\{tr\}\}\); target test covariates

XteX^\{\\mathrm\{te\}\}; retention ratio

λ∈\(0,1\]\\lambda\\in\(0,1\]
0:Selected source subset

𝒮⋆\\mathcal\{S\}^\{\\star\}
1:Stage 1: proximity screening \(covariate space\)\.

2:Align the source and target schemas; impute each partition separately\.

3:For each source sample

xx, compute its mean Gower distance

d⁡\(x\)d\(x\)to its

kknearest neighbors in

XteX^\{\\mathrm\{te\}\}\.

4:Fit a two\-component Gaussian mixture on the scores

\{d⁡\(x\)\}\\\{d\(x\)\\\}and keep the lower\-mean component as the candidate set

𝒞\\mathcal\{C\}\.

5:Stage 2: reference\-consistency selection\.

6:Fit a reference model

ffon

𝒟tr\\mathcal\{D\}^\{\\mathrm\{tr\}\}\.

7:For each

\(xi,yi\)∈𝒞\(x\_\{i\},y\_\{i\}\)\\in\\mathcal\{C\}, compute the reference loss

8:

ℓi=\{\|yi−f⁡\(xi\)\|,regression−log⁡Pf​\(yi∣xi\),classification\.\\ell\_\{i\}=\\left\\\{\\begin\{array\}\[\]\{ll\}\|y\_\{i\}\-f\(x\_\{i\}\)\|,&\\mathrm\{regression\}\\\\ \-\\log P\_\{f\}\(y\_\{i\}\\mid x\_\{i\}\),&\\mathrm\{classification\}\.\\end\{array\}\\right\.
9:Set the budget

m←⌈λ​\|𝒞\|⌉m\\leftarrow\\lceil\\lambda\|\\mathcal\{C\}\|\\rceil\.

10:ifregressionthen

11:

𝒮⋆←\\mathcal\{S\}^\{\\star\}\\leftarrowthe

mmlowest loss candidates in

𝒞\\mathcal\{C\}\.

12:else

13:Allocate per\-class quotas

qcq\_\{c\}proportional to the

ytry^\{\\mathrm\{tr\}\}class frequencies via the largest remainder method, with

∑cqc=m\\sum\_\{c\}q\_\{c\}=m\.

14:Within each class

cc, select the

qcq\_\{c\}lowest loss candidates into

𝒮⋆\\mathcal\{S\}^\{\\star\}\.

15:Fill any remaining slots with the lowest loss unselected candidates\.

16:endif

17:return

𝒮⋆\\mathcal\{S\}^\{\\star\}

We restrict the context augmentation study to three target benchmarks: maternal health, concrete strength, and airfoil noise\. For each task, we identified a publicly available, task relevant source dataset whose predictors could be semantically aligned with the complete target predictor set\. No comparably matched public source was available for the remaining TabArena tasks\. The analysis is therefore a feasibility study conditioned on source availability and schema compatibility, rather than a benchmark wide evaluation\. The three source–target pairs exhibit different degrees of residual compatibility after predictor alignment\. We characterize this difficulty qualitatively from the correspondence between their data\-generating processes, the preservation of predictor and target semantics, and the extent of population or label shift\. These characterizations are based on dataset provenance rather than downstream augmentation results\. Table[3](https://arxiv.org/html/2609.13202#Sx4.T3)summarizes the resulting hierarchy\.

Table 3:Source–target compatibility in context augmentation\. Difficulty is residual mismatch after predictor alignment\.
## Results

### Feature engineering gains are smaller in later model versions\.

We distinguish the typical intervention effect, defined as the median gain across applicable interventions within each dataset, from the best observed effect, defined as the largest median paired gain among those interventions\. The latter is an oracle summary of available headroom rather than the performance of a deployable selection procedure\. Across datasets, the median best observed gain decreases from 1\.21 to 0\.25 macro\-F1 percentage points between TabPFN v1 and v3 classification, from 2\.06% to 0\.19% relative RMSE reduction between TabPFN v2 and v3 regression, and from 0\.73 to 0\.10 macro\-F1 points between TabICL v1 and v2 classification\. In contrast, the typical intervention effect remains non\-positive throughout\.

Exact ordered alternative tests support an aggregate decline in best observed feature engineering headroom \(Table[5](https://arxiv.org/html/2609.13202#Sx5.T5)\)\. Page tests provide evidence for the ordered decline in TabPFN classification \(L=389L=389, one\-sidedp=0\.0174p=0\.0174\) and regression \(L=139L=139,p=0\.0167p=0\.0167\)\. For TabICL classification, the exact paired sign\-flip test likewise supports lower headroom in v2 than in v1 \(T=0\.412T=0\.412macro\-F1 percentage points,p=0\.0234p=0\.0234\)\. All three comparisons remain significant after Benjamini–Hochberg false\-discovery\-rate correction \(q=0\.0234q=0\.0234\); the more conservative Holm\-adjusted value is borderline and lies just above 0\.05 \(pHolm=0\.0502p\_\{\\mathrm\{Holm\}\}=0\.0502\)\. The paired median first\-to\-last contraction is 1\.095 macro\-F1 percentage points for TabPFN classification, 1\.590 relative\-RMSE percentage points for TabPFN regression, and 0\.429 macro\-F1 percentage points for TabICL classification\. Headroom declines from the first to the last evaluated version on 5/8, 4/5, and 6/8 datasets, respectively\. Thus, the evidence concerns an aggregate ordered trend\.

Figure 1:Feature engineering response across model generations\. Per dataset and version, gains are medians over 30 paired splits; gray crosses and hollow circles show their median and maximum across interventions\. Orange and blue marks are the respective across\-dataset medians\. Positive favors feature engineering; the maximum is oracle, not validation\-selected\. Units are macro\-F1 points \(classification\) and relative RMSE reduction \(regression\)\.![Refer to caption](https://arxiv.org/html/2609.13202v1/figure2_intervention_heatmap.png)Figure 2:Across\-dataset median effects for all 26 interventions and 12 estimators; positive favors feature engineering\. Classification uses macro\-F1 points \(color limits±2\\pm 2\); regression uses relative RMSE reduction \(±10%\\pm 10\\%\)\. Open circles mark positive effects on at least half of applicable datasets; rules separate intervention families\.Table 4:Feature engineering family effects for the strongest evaluated model variants\. Each cell reports the median direction normalized effect across applicable \(dataset, intervention\) cells, followed by the number of positive cells over the number applicable\. Positive values favor feature engineering\.Table 5:Exact dataset\-level tests for declining best observed feature engineering headroom\. Rawppis one\-sided\. Joint adjustment givesqBH=0\.0234q\_\{\\mathrm\{BH\}\}=0\.0234andpHolm=0\.0502p\_\{\\mathrm\{Holm\}\}=0\.0502for every comparison\. Contraction is the median first\-to\-last difference; parentheses count declines across datasets\. Units are macro\-F1 points \(classification\) and relative RMSE points \(regression\)\.
### The remaining gains are sparse\.

Across dataset effects vary substantially by intervention\. Numerical transformations are generally concentrated near zero, whereas binning, supervised selection, and most TabPrep variants are predominantly negative\. Few interventions combine a positive across dataset median with improvements on at least half of their applicable datasets\. Positive gains therefore reflect particular dataset–intervention–estimator combinations rather than methods that transfer consistently across tasks\.

### Transfer benefit depends on source–target comparability\.

For each completed dataset–estimator cell, we compare target\-only inference with inference augmented by NNRC\-selected source samples under two target representations: the best\-observed feature\-engineering condition and the identity condition without external feature engineering\. The paired difference therefore estimates the incremental value of selected related observations within a fixed representation, not the value of feature engineering itself\. Each gain is the arithmetic mean of 30 paired split\-level gains \(10 repeats×\\times3 folds\)\. The best\-observed feature condition remains an oracle descriptive choice, and the NNRC settings were not selected by an independent validation procedure\. Airfoil benefits under both representations for TabPFN, whereas TabICL benefits only with numeric interactions\. Concrete and maternal effects are smaller and representation dependent, consistent with their residual compatibility \(Table[3](https://arxiv.org/html/2609.13202#Sx4.T3)\); complete NNRC values are retained in the supplementary artifact\.

### No universally effective transformations\.

For the latest evaluated models, all reported family\-level medians are non\-positive\. Binning has median effects of \-0\.88 and \-0\.96 macro\-F1 points for TabPFN v3 and TabICL v2 classification, and \-6\.70% and \-7\.40% relative RMSE reduction for regression\. TabPrep is also negative in all four settings, with median effects ranging from \-1\.47 macro\-F1 points to \-4\.13% relative RMSE reduction\. Numerical transformations are less disruptive, with medians close to zero, but their positive\-cell frequencies vary from 1/35 in TabICL classification to 18/25 in TabICL regression\. Thus, near\-zero aggregate effects do not imply invariance across datasets\. Overall, generic feature engineering offers less aggregate headroom in later model versions, but it is neither uniformly ineffective nor uniformly harmful\.

## Discussion

Our results indicate that the role of intervention is changing as tabular foundation models become stronger\. Across the examined generations, the best observed gain from feature engineering declines\. The typical intervention remains non positive\. For the latest models, no evaluated feature family produces a consistently positive aggregate effect\. The remaining gains occur only in specific combinations of datasets, transformations, and estimators\. Results from earlier model generations therefore do not fully predict the behavior of later models\. The small data regime is deliberate: it matches the intended use case of TFMs and provides a stringent test of whether feature engineering supplies useful inductive bias when task\-specific evidence is limited\. The observed decline in feature\-engineering headroom therefore occurs in a setting where such interventions have substantial opportunity to help\. We nevertheless scope our conclusions to the evaluated small\-data benchmarks, with datasets—not repeated splits—as the independent units of inference

A plausible explanation is that stronger TFMs extract more predictive structure directly from the original table\. This reduces the value of generic transformations\. The negative effects of binning, feature selection, and several composite pipelines show that later TFMs still respond to changes in representation\. However, these changes may remove useful variation or create inputs that are less compatible with pretrained inference\. Representation still matters, but generic re representation offers less benefit\. Task specific transformations may remain useful when they provide structure that the model cannot recover from the original inputs\.

The context augmentation results provide a complementary view\. Feature engineering reorganizes information already present in the target data\. Context augmentation can introduce new task relevant information\. Related source samples are one way to provide such information\. Their benefit is clearest for airfoil\. The effects are smaller or depend on the model for concrete and maternal health\. This variation shows that the value of additional context depends strongly on source target compatibility\. The key question is therefore not only how to transform the observed table, but also what additional information should be provided and how it should be organized\.

Taken together, our results point to a shift in the main source of improvement for stronger TFMs\. Across the evaluated generations, generic transformations of existing inputs provide progressively less aggregate headroom\. Compatible task relevant context can still produce measurable gains\. The improvement frontier may therefore be moving from representation engineering toward information augmentation\.

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## Exhaustive Raw\-Metric Tables

This appendix reports the full per\-dataset raw\-metric tables for every estimator and feature\-engineering condition evaluated in the paper\. Each table lists the condition mean and sample standard deviation across the 30 paired splits \(10 repeats×\\times3 folds\)\. Cells marked “—” indicate that the condition is not applicable to that dataset\.

Table 6:Complete raw metric results for Airfoil noise, metric r2\. Values are mean±\\mathbin\{\\pm\}sample standard deviation across the 30 paired splits\.ConditionPFN v2PFN v2\.5PFN v2\.6PFN v3ICL v2Identity0\.9737±0\.00460\.9737\\mathbin\{\\pm\}0\.00460\.9726±0\.00480\.9726\\mathbin\{\\pm\}0\.00480\.9751±0\.00480\.9751\\mathbin\{\\pm\}0\.00480\.9784±0\.00360\.9784\\mathbin\{\\pm\}0\.00360\.9756±0\.00390\.9756\\mathbin\{\\pm\}0\.0039Standard scaling0\.9731±0\.00500\.9731\\mathbin\{\\pm\}0\.00500\.9728±0\.00500\.9728\\mathbin\{\\pm\}0\.00500\.9731±0\.00420\.9731\\mathbin\{\\pm\}0\.00420\.9782±0\.00350\.9782\\mathbin\{\\pm\}0\.00350\.9756±0\.00390\.9756\\mathbin\{\\pm\}0\.0039Log transform0\.9730±0\.00460\.9730\\mathbin\{\\pm\}0\.00460\.9725±0\.00510\.9725\\mathbin\{\\pm\}0\.00510\.9722±0\.00460\.9722\\mathbin\{\\pm\}0\.00460\.9781±0\.00380\.9781\\mathbin\{\\pm\}0\.00380\.9763±0\.00400\.9763\\mathbin\{\\pm\}0\.0040Square\-root transform0\.9730±0\.00470\.9730\\mathbin\{\\pm\}0\.00470\.9727±0\.00500\.9727\\mathbin\{\\pm\}0\.00500\.9752±0\.00460\.9752\\mathbin\{\\pm\}0\.00460\.9778±0\.00390\.9778\\mathbin\{\\pm\}0\.00390\.9760±0\.00400\.9760\\mathbin\{\\pm\}0\.0040Box–Cox0\.9730±0\.00470\.9730\\mathbin\{\\pm\}0\.00470\.9726±0\.00500\.9726\\mathbin\{\\pm\}0\.00500\.9721±0\.00480\.9721\\mathbin\{\\pm\}0\.00480\.9785±0\.00340\.9785\\mathbin\{\\pm\}0\.00340\.9759±0\.00380\.9759\\mathbin\{\\pm\}0\.0038Min–max scaling0\.9733±0\.00470\.9733\\mathbin\{\\pm\}0\.00470\.9728±0\.00500\.9728\\mathbin\{\\pm\}0\.00500\.9733±0\.00490\.9733\\mathbin\{\\pm\}0\.00490\.9782±0\.00360\.9782\\mathbin\{\\pm\}0\.00360\.9756±0\.00390\.9756\\mathbin\{\\pm\}0\.0039One\-hot encoding0\.9728±0\.00420\.9728\\mathbin\{\\pm\}0\.00420\.9726±0\.00470\.9726\\mathbin\{\\pm\}0\.00470\.9724±0\.00430\.9724\\mathbin\{\\pm\}0\.00430\.9778±0\.00360\.9778\\mathbin\{\\pm\}0\.00360\.9731±0\.00420\.9731\\mathbin\{\\pm\}0\.0042Ordinal encoding0\.9731±0\.00490\.9731\\mathbin\{\\pm\}0\.00490\.9728±0\.00440\.9728\\mathbin\{\\pm\}0\.00440\.9750±0\.00460\.9750\\mathbin\{\\pm\}0\.00460\.9782±0\.00360\.9782\\mathbin\{\\pm\}0\.00360\.9754±0\.00410\.9754\\mathbin\{\\pm\}0\.0041Frequency encoding0\.9735±0\.00450\.9735\\mathbin\{\\pm\}0\.00450\.9726±0\.00480\.9726\\mathbin\{\\pm\}0\.00480\.9750±0\.00440\.9750\\mathbin\{\\pm\}0\.00440\.9783±0\.00350\.9783\\mathbin\{\\pm\}0\.00350\.9743±0\.00380\.9743\\mathbin\{\\pm\}0\.0038Target encoding0\.9713±0\.00490\.9713\\mathbin\{\\pm\}0\.00490\.9712±0\.00530\.9712\\mathbin\{\\pm\}0\.00530\.9736±0\.00490\.9736\\mathbin\{\\pm\}0\.00490\.9766±0\.00400\.9766\\mathbin\{\\pm\}0\.00400\.9675±0\.00530\.9675\\mathbin\{\\pm\}0\.0053Categorical crosses—————Equal\-width binning0\.7280±0\.02040\.7280\\mathbin\{\\pm\}0\.02040\.7261±0\.02010\.7261\\mathbin\{\\pm\}0\.02010\.7234±0\.02060\.7234\\mathbin\{\\pm\}0\.02060\.7374±0\.01960\.7374\\mathbin\{\\pm\}0\.01960\.7298±0\.02040\.7298\\mathbin\{\\pm\}0\.0204Equal\-frequency binning0\.8994±0\.00730\.8994\\mathbin\{\\pm\}0\.00730\.9002±0\.00740\.9002\\mathbin\{\\pm\}0\.00740\.8989±0\.00820\.8989\\mathbin\{\\pm\}0\.00820\.9072±0\.00810\.9072\\mathbin\{\\pm\}0\.00810\.9052±0\.00830\.9052\\mathbin\{\\pm\}0\.0083Numeric interactions0\.9732±0\.00490\.9732\\mathbin\{\\pm\}0\.00490\.9737±0\.00470\.9737\\mathbin\{\\pm\}0\.00470\.9734±0\.00500\.9734\\mathbin\{\\pm\}0\.00500\.9788±0\.00330\.9788\\mathbin\{\\pm\}0\.00330\.9764±0\.00410\.9764\\mathbin\{\\pm\}0\.0041Group aggregation0\.9733±0\.00420\.9733\\mathbin\{\\pm\}0\.00420\.9734±0\.00460\.9734\\mathbin\{\\pm\}0\.00460\.9731±0\.00440\.9731\\mathbin\{\\pm\}0\.00440\.9768±0\.00360\.9768\\mathbin\{\\pm\}0\.00360\.9745±0\.00390\.9745\\mathbin\{\\pm\}0\.0039Variance filter0\.8436±0\.01580\.8436\\mathbin\{\\pm\}0\.01580\.8404±0\.01610\.8404\\mathbin\{\\pm\}0\.01610\.8385±0\.01850\.8385\\mathbin\{\\pm\}0\.01850\.8491±0\.01580\.8491\\mathbin\{\\pm\}0\.01580\.8277±0\.03020\.8277\\mathbin\{\\pm\}0\.0302Collinearity filter0\.9737±0\.00460\.9737\\mathbin\{\\pm\}0\.00460\.9726±0\.00480\.9726\\mathbin\{\\pm\}0\.00480\.9751±0\.00480\.9751\\mathbin\{\\pm\}0\.00480\.9784±0\.00360\.9784\\mathbin\{\\pm\}0\.00360\.9756±0\.00390\.9756\\mathbin\{\\pm\}0\.0039PCA0\.9725±0\.00520\.9725\\mathbin\{\\pm\}0\.00520\.9716±0\.00530\.9716\\mathbin\{\\pm\}0\.00530\.9693±0\.00520\.9693\\mathbin\{\\pm\}0\.00520\.9766±0\.00400\.9766\\mathbin\{\\pm\}0\.00400\.9735±0\.00490\.9735\\mathbin\{\\pm\}0\.0049Supervised selection0\.8397±0\.02490\.8397\\mathbin\{\\pm\}0\.02490\.7971±0\.02310\.7971\\mathbin\{\\pm\}0\.02310\.8720±0\.02280\.8720\\mathbin\{\\pm\}0\.02280\.9163±0\.01280\.9163\\mathbin\{\\pm\}0\.01280\.7652±0\.03380\.7652\\mathbin\{\\pm\}0\.0338TabPrep full0\.9742±0\.00440\.9742\\mathbin\{\\pm\}0\.00440\.9775±0\.00380\.9775\\mathbin\{\\pm\}0\.00380\.9753±0\.00410\.9753\\mathbin\{\\pm\}0\.00410\.9779±0\.00340\.9779\\mathbin\{\\pm\}0\.00340\.9747±0\.00420\.9747\\mathbin\{\\pm\}0\.0042TabPrep w/o groupby0\.9745±0\.00440\.9745\\mathbin\{\\pm\}0\.00440\.9776±0\.00390\.9776\\mathbin\{\\pm\}0\.00390\.9749±0\.00410\.9749\\mathbin\{\\pm\}0\.00410\.9777±0\.00370\.9777\\mathbin\{\\pm\}0\.00370\.9746±0\.00430\.9746\\mathbin\{\\pm\}0\.0043TabPrep w/o RSFC0\.9742±0\.00460\.9742\\mathbin\{\\pm\}0\.00460\.9773±0\.00390\.9773\\mathbin\{\\pm\}0\.00390\.9752±0\.00410\.9752\\mathbin\{\\pm\}0\.00410\.9778±0\.00360\.9778\\mathbin\{\\pm\}0\.00360\.9746±0\.00440\.9746\\mathbin\{\\pm\}0\.0044TabPrep w/o arithmetic0\.9589±0\.00680\.9589\\mathbin\{\\pm\}0\.00680\.9613±0\.00680\.9613\\mathbin\{\\pm\}0\.00680\.9608±0\.00730\.9608\\mathbin\{\\pm\}0\.00730\.9522±0\.00790\.9522\\mathbin\{\\pm\}0\.00790\.9435±0\.00890\.9435\\mathbin\{\\pm\}0\.0089TabPrep w/o cat\. interact\.0\.9743±0\.00430\.9743\\mathbin\{\\pm\}0\.00430\.9778±0\.00370\.9778\\mathbin\{\\pm\}0\.00370\.9755±0\.00410\.9755\\mathbin\{\\pm\}0\.00410\.9778±0\.00380\.9778\\mathbin\{\\pm\}0\.00380\.9748±0\.00440\.9748\\mathbin\{\\pm\}0\.0044TabPrep w/o OOF\-TE0\.9743±0\.00430\.9743\\mathbin\{\\pm\}0\.00430\.9774±0\.00370\.9774\\mathbin\{\\pm\}0\.00370\.9750±0\.00430\.9750\\mathbin\{\\pm\}0\.00430\.9778±0\.00380\.9778\\mathbin\{\\pm\}0\.00380\.9747±0\.00430\.9747\\mathbin\{\\pm\}0\.0043Shared\-context kNN0\.9736±0\.00470\.9736\\mathbin\{\\pm\}0\.00470\.9726±0\.00480\.9726\\mathbin\{\\pm\}0\.00480\.9751±0\.00480\.9751\\mathbin\{\\pm\}0\.00480\.9784±0\.00360\.9784\\mathbin\{\\pm\}0\.00360\.9756±0\.00390\.9756\\mathbin\{\\pm\}0\.0039OOF prediction feature0\.9733±0\.00410\.9733\\mathbin\{\\pm\}0\.00410\.9719±0\.00510\.9719\\mathbin\{\\pm\}0\.00510\.9749±0\.00420\.9749\\mathbin\{\\pm\}0\.00420\.9777±0\.00340\.9777\\mathbin\{\\pm\}0\.00340\.9744±0\.00370\.9744\\mathbin\{\\pm\}0\.0037Table 7:Complete raw metric results for Airfoil noise, metric rmse\. Values are mean±\\mathbin\{\\pm\}sample standard deviation across the 30 paired splits\.ConditionPFN v2PFN v2\.5PFN v2\.6PFN v3ICL v2Identity1\.1122±0\.09251\.1122\\mathbin\{\\pm\}0\.09251\.1342±0\.09711\.1342\\mathbin\{\\pm\}0\.09711\.0820±0\.10021\.0820\\mathbin\{\\pm\}0\.10021\.0082±0\.07871\.0082\\mathbin\{\\pm\}0\.07871\.0729±0\.07871\.0729\\mathbin\{\\pm\}0\.0787Standard scaling1\.1233±0\.09631\.1233\\mathbin\{\\pm\}0\.09631\.1310±0\.09801\.1310\\mathbin\{\\pm\}0\.09801\.1256±0\.08191\.1256\\mathbin\{\\pm\}0\.08191\.0120±0\.07591\.0120\\mathbin\{\\pm\}0\.07591\.0729±0\.07871\.0729\\mathbin\{\\pm\}0\.0787Log transform1\.1277±0\.08891\.1277\\mathbin\{\\pm\}0\.08891\.1365±0\.10101\.1365\\mathbin\{\\pm\}0\.10101\.1448±0\.09381\.1448\\mathbin\{\\pm\}0\.09381\.0157±0\.08301\.0157\\mathbin\{\\pm\}0\.08301\.0572±0\.08321\.0572\\mathbin\{\\pm\}0\.0832Square\-root transform1\.1269±0\.09331\.1269\\mathbin\{\\pm\}0\.09331\.1334±0\.09811\.1334\\mathbin\{\\pm\}0\.09811\.0797±0\.09781\.0797\\mathbin\{\\pm\}0\.09781\.0218±0\.08371\.0218\\mathbin\{\\pm\}0\.08371\.0633±0\.08361\.0633\\mathbin\{\\pm\}0\.0836Box–Cox1\.1276±0\.08991\.1276\\mathbin\{\\pm\}0\.08991\.1342±0\.10031\.1342\\mathbin\{\\pm\}0\.10031\.1456±0\.09361\.1456\\mathbin\{\\pm\}0\.09361\.0062±0\.07501\.0062\\mathbin\{\\pm\}0\.07501\.0664±0\.07741\.0664\\mathbin\{\\pm\}0\.0774Min–max scaling1\.1213±0\.09161\.1213\\mathbin\{\\pm\}0\.09161\.1303±0\.09801\.1303\\mathbin\{\\pm\}0\.09801\.1208±0\.10511\.1208\\mathbin\{\\pm\}0\.10511\.0128±0\.07941\.0128\\mathbin\{\\pm\}0\.07941\.0729±0\.07871\.0729\\mathbin\{\\pm\}0\.0787One\-hot encoding1\.1324±0\.08381\.1324\\mathbin\{\\pm\}0\.08381\.1349±0\.09241\.1349\\mathbin\{\\pm\}0\.09241\.1393±0\.08321\.1393\\mathbin\{\\pm\}0\.08321\.0214±0\.08001\.0214\\mathbin\{\\pm\}0\.08001\.1265±0\.08261\.1265\\mathbin\{\\pm\}0\.0826Ordinal encoding1\.1237±0\.09491\.1237\\mathbin\{\\pm\}0\.09491\.1307±0\.08711\.1307\\mathbin\{\\pm\}0\.08711\.0833±0\.09891\.0833\\mathbin\{\\pm\}0\.09891\.0139±0\.07911\.0139\\mathbin\{\\pm\}0\.07911\.0751±0\.08481\.0751\\mathbin\{\\pm\}0\.0848Frequency encoding1\.1161±0\.08761\.1161\\mathbin\{\\pm\}0\.08761\.1357±0\.09501\.1357\\mathbin\{\\pm\}0\.09501\.0842±0\.09321\.0842\\mathbin\{\\pm\}0\.09321\.0119±0\.07711\.0119\\mathbin\{\\pm\}0\.07711\.0999±0\.07811\.0999\\mathbin\{\\pm\}0\.0781Target encoding1\.1628±0\.09301\.1628\\mathbin\{\\pm\}0\.09301\.1625±0\.10271\.1625\\mathbin\{\\pm\}0\.10271\.1139±0\.10131\.1139\\mathbin\{\\pm\}0\.10131\.0495±0\.09061\.0495\\mathbin\{\\pm\}0\.09061\.2367±0\.10111\.2367\\mathbin\{\\pm\}0\.1011Categorical crosses—————Equal\-width binning3\.5883±0\.11393\.5883\\mathbin\{\\pm\}0\.11393\.6009±0\.11033\.6009\\mathbin\{\\pm\}0\.11033\.6187±0\.10703\.6187\\mathbin\{\\pm\}0\.10703\.5257±0\.11273\.5257\\mathbin\{\\pm\}0\.11273\.5769±0\.11553\.5769\\mathbin\{\\pm\}0\.1155Equal\-frequency binning2\.1825±0\.08492\.1825\\mathbin\{\\pm\}0\.08492\.1740±0\.08542\.1740\\mathbin\{\\pm\}0\.08542\.1886±0\.09822\.1886\\mathbin\{\\pm\}0\.09822\.0962±0\.10232\.0962\\mathbin\{\\pm\}0\.10232\.1192±0\.10712\.1192\\mathbin\{\\pm\}0\.1071Numeric interactions1\.1214±0\.09481\.1214\\mathbin\{\\pm\}0\.09481\.1121±0\.09561\.1121\\mathbin\{\\pm\}0\.09561\.1185±0\.10221\.1185\\mathbin\{\\pm\}0\.10221\.0001±0\.07451\.0001\\mathbin\{\\pm\}0\.07451\.0535±0\.09011\.0535\\mathbin\{\\pm\}0\.0901Group aggregation1\.1214±0\.08461\.1214\\mathbin\{\\pm\}0\.08461\.1191±0\.09161\.1191\\mathbin\{\\pm\}0\.09161\.1265±0\.08741\.1265\\mathbin\{\\pm\}0\.08741\.0452±0\.07461\.0452\\mathbin\{\\pm\}0\.07461\.0968±0\.07771\.0968\\mathbin\{\\pm\}0\.0777Variance filter2\.7204±0\.13792\.7204\\mathbin\{\\pm\}0\.13792\.7480±0\.14272\.7480\\mathbin\{\\pm\}0\.14272\.7626±0\.15612\.7626\\mathbin\{\\pm\}0\.15612\.6716±0\.13512\.6716\\mathbin\{\\pm\}0\.13512\.8502±0\.27902\.8502\\mathbin\{\\pm\}0\.2790Collinearity filter1\.1122±0\.09251\.1122\\mathbin\{\\pm\}0\.09251\.1342±0\.09711\.1342\\mathbin\{\\pm\}0\.09711\.0820±0\.10021\.0820\\mathbin\{\\pm\}0\.10021\.0082±0\.07871\.0082\\mathbin\{\\pm\}0\.07871\.0729±0\.07871\.0729\\mathbin\{\\pm\}0\.0787PCA1\.1374±0\.10141\.1374\\mathbin\{\\pm\}0\.10141\.1541±0\.10421\.1541\\mathbin\{\\pm\}0\.10421\.2007±0\.09771\.2007\\mathbin\{\\pm\}0\.09771\.0485±0\.08801\.0485\\mathbin\{\\pm\}0\.08801\.1168±0\.10581\.1168\\mathbin\{\\pm\}0\.1058Supervised selection2\.7483±0\.19602\.7483\\mathbin\{\\pm\}0\.19603\.0952±0\.13643\.0952\\mathbin\{\\pm\}0\.13642\.4528±0\.17782\.4528\\mathbin\{\\pm\}0\.17781\.9860±0\.13931\.9860\\mathbin\{\\pm\}0\.13933\.3258±0\.21623\.3258\\mathbin\{\\pm\}0\.2162TabPrep full1\.1010±0\.08901\.1010\\mathbin\{\\pm\}0\.08901\.0300±0\.08921\.0300\\mathbin\{\\pm\}0\.08921\.0776±0\.08891\.0776\\mathbin\{\\pm\}0\.08891\.0218±0\.07841\.0218\\mathbin\{\\pm\}0\.07841\.0907±0\.08831\.0907\\mathbin\{\\pm\}0\.0883TabPrep w/o groupby1\.0960±0\.08871\.0960\\mathbin\{\\pm\}0\.08871\.0278±0\.09091\.0278\\mathbin\{\\pm\}0\.09091\.0882±0\.08931\.0882\\mathbin\{\\pm\}0\.08931\.0251±0\.08631\.0251\\mathbin\{\\pm\}0\.08631\.0937±0\.08881\.0937\\mathbin\{\\pm\}0\.0888TabPrep w/o RSFC1\.1019±0\.09161\.1019\\mathbin\{\\pm\}0\.09161\.0338±0\.09031\.0338\\mathbin\{\\pm\}0\.09031\.0810±0\.09051\.0810\\mathbin\{\\pm\}0\.09051\.0228±0\.08341\.0228\\mathbin\{\\pm\}0\.08341\.0935±0\.09171\.0935\\mathbin\{\\pm\}0\.0917TabPrep w/o arithmetic1\.3912±0\.10431\.3912\\mathbin\{\\pm\}0\.10431\.3485±0\.11471\.3485\\mathbin\{\\pm\}0\.11471\.3567±0\.12271\.3567\\mathbin\{\\pm\}0\.12271\.5009±0\.12051\.5009\\mathbin\{\\pm\}0\.12051\.6326±0\.12511\.6326\\mathbin\{\\pm\}0\.1251TabPrep w/o cat\. interact\.1\.1000±0\.08801\.1000\\mathbin\{\\pm\}0\.08801\.0226±0\.08531\.0226\\mathbin\{\\pm\}0\.08531\.0744±0\.08841\.0744\\mathbin\{\\pm\}0\.08841\.0224±0\.08551\.0224\\mathbin\{\\pm\}0\.08551\.0898±0\.09311\.0898\\mathbin\{\\pm\}0\.0931TabPrep w/o OOF\-TE1\.0998±0\.08781\.0998\\mathbin\{\\pm\}0\.08781\.0315±0\.08641\.0315\\mathbin\{\\pm\}0\.08641\.0836±0\.09341\.0836\\mathbin\{\\pm\}0\.09341\.0217±0\.08651\.0217\\mathbin\{\\pm\}0\.08651\.0903±0\.08881\.0903\\mathbin\{\\pm\}0\.0888Shared\-context kNN1\.1139±0\.09261\.1139\\mathbin\{\\pm\}0\.09261\.1342±0\.09711\.1342\\mathbin\{\\pm\}0\.09711\.0820±0\.10061\.0820\\mathbin\{\\pm\}0\.10061\.0075±0\.07861\.0075\\mathbin\{\\pm\}0\.07861\.0729±0\.07871\.0729\\mathbin\{\\pm\}0\.0787OOF prediction feature1\.1219±0\.08101\.1219\\mathbin\{\\pm\}0\.08101\.1487±0\.09961\.1487\\mathbin\{\\pm\}0\.09961\.0880±0\.08891\.0880\\mathbin\{\\pm\}0\.08891\.0264±0\.07291\.0264\\mathbin\{\\pm\}0\.07291\.0991±0\.07641\.0991\\mathbin\{\\pm\}0\.0764Table 8:Complete TabPFN and TabICL raw metric results for Anneal, metric accuracy\. Values are mean±\\mathbin\{\\pm\}sample standard deviation across the 30 paired splits\.ConditionPFN v1PFN v2PFN v2\.5PFN v2\.6PFN v3ICL v1ICL v2Identity0\.9709±0\.01060\.9709\\mathbin\{\\pm\}0\.01060\.9970±0\.00450\.9970\\mathbin\{\\pm\}0\.00450\.9969±0\.00440\.9969\\mathbin\{\\pm\}0\.00440\.9951±0\.00620\.9951\\mathbin\{\\pm\}0\.00620\.9968±0\.00420\.9968\\mathbin\{\\pm\}0\.00420\.9885±0\.00650\.9885\\mathbin\{\\pm\}0\.00650\.9952±0\.00520\.9952\\mathbin\{\\pm\}0\.0052Standard scaling0\.9703±0\.00990\.9703\\mathbin\{\\pm\}0\.00990\.9968±0\.00460\.9968\\mathbin\{\\pm\}0\.00460\.9967±0\.00440\.9967\\mathbin\{\\pm\}0\.00440\.9952±0\.00620\.9952\\mathbin\{\\pm\}0\.00620\.9968±0\.00380\.9968\\mathbin\{\\pm\}0\.00380\.9882±0\.00670\.9882\\mathbin\{\\pm\}0\.00670\.9952±0\.00520\.9952\\mathbin\{\\pm\}0\.0052Log transform0\.9619±0\.01230\.9619\\mathbin\{\\pm\}0\.01230\.9964±0\.00550\.9964\\mathbin\{\\pm\}0\.00550\.9970±0\.00380\.9970\\mathbin\{\\pm\}0\.00380\.9951±0\.00640\.9951\\mathbin\{\\pm\}0\.00640\.9941±0\.00670\.9941\\mathbin\{\\pm\}0\.00670\.9806±0\.00760\.9806\\mathbin\{\\pm\}0\.00760\.9952±0\.00560\.9952\\mathbin\{\\pm\}0\.0056Square\-root transform0\.9651±0\.01150\.9651\\mathbin\{\\pm\}0\.01150\.9969±0\.00460\.9969\\mathbin\{\\pm\}0\.00460\.9970±0\.00400\.9970\\mathbin\{\\pm\}0\.00400\.9950±0\.00640\.9950\\mathbin\{\\pm\}0\.00640\.9963±0\.00480\.9963\\mathbin\{\\pm\}0\.00480\.9866±0\.00600\.9866\\mathbin\{\\pm\}0\.00600\.9948±0\.00560\.9948\\mathbin\{\\pm\}0\.0056Box–Cox0\.9710±0\.01050\.9710\\mathbin\{\\pm\}0\.01050\.9967±0\.00450\.9967\\mathbin\{\\pm\}0\.00450\.9967±0\.00440\.9967\\mathbin\{\\pm\}0\.00440\.9953±0\.00670\.9953\\mathbin\{\\pm\}0\.00670\.9965±0\.00460\.9965\\mathbin\{\\pm\}0\.00460\.9883±0\.00590\.9883\\mathbin\{\\pm\}0\.00590\.9952±0\.00500\.9952\\mathbin\{\\pm\}0\.0050Min–max scaling0\.9703±0\.00990\.9703\\mathbin\{\\pm\}0\.00990\.9969±0\.00460\.9969\\mathbin\{\\pm\}0\.00460\.9967±0\.00440\.9967\\mathbin\{\\pm\}0\.00440\.9953±0\.00620\.9953\\mathbin\{\\pm\}0\.00620\.9969±0\.00370\.9969\\mathbin\{\\pm\}0\.00370\.9882±0\.00670\.9882\\mathbin\{\\pm\}0\.00670\.9952±0\.00520\.9952\\mathbin\{\\pm\}0\.0052One\-hot encoding0\.8939±0\.01150\.8939\\mathbin\{\\pm\}0\.01150\.9156±0\.00990\.9156\\mathbin\{\\pm\}0\.00990\.9174±0\.00990\.9174\\mathbin\{\\pm\}0\.00990\.9177±0\.00860\.9177\\mathbin\{\\pm\}0\.00860\.9130±0\.01160\.9130\\mathbin\{\\pm\}0\.01160\.9000±0\.01010\.9000\\mathbin\{\\pm\}0\.01010\.9223±0\.00890\.9223\\mathbin\{\\pm\}0\.0089Ordinal encoding0\.9706±0\.01110\.9706\\mathbin\{\\pm\}0\.01110\.9968±0\.00450\.9968\\mathbin\{\\pm\}0\.00450\.9970±0\.00450\.9970\\mathbin\{\\pm\}0\.00450\.9953±0\.00610\.9953\\mathbin\{\\pm\}0\.00610\.9967±0\.00470\.9967\\mathbin\{\\pm\}0\.00470\.9876±0\.00660\.9876\\mathbin\{\\pm\}0\.00660\.9952±0\.00550\.9952\\mathbin\{\\pm\}0\.0055Frequency encoding0\.9635±0\.01250\.9635\\mathbin\{\\pm\}0\.01250\.9970±0\.00460\.9970\\mathbin\{\\pm\}0\.00460\.9967±0\.00440\.9967\\mathbin\{\\pm\}0\.00440\.9958±0\.00610\.9958\\mathbin\{\\pm\}0\.00610\.9962±0\.00480\.9962\\mathbin\{\\pm\}0\.00480\.9876±0\.00720\.9876\\mathbin\{\\pm\}0\.00720\.9941±0\.00530\.9941\\mathbin\{\\pm\}0\.0053Target encoding0\.8586±0\.00930\.8586\\mathbin\{\\pm\}0\.00930\.8781±0\.01060\.8781\\mathbin\{\\pm\}0\.01060\.8822±0\.00970\.8822\\mathbin\{\\pm\}0\.00970\.8685±0\.01050\.8685\\mathbin\{\\pm\}0\.01050\.8716±0\.01290\.8716\\mathbin\{\\pm\}0\.01290\.8284±0\.01350\.8284\\mathbin\{\\pm\}0\.01350\.8457±0\.01150\.8457\\mathbin\{\\pm\}0\.0115Categorical crosses0\.9609±0\.01130\.9609\\mathbin\{\\pm\}0\.01130\.9964±0\.00470\.9964\\mathbin\{\\pm\}0\.00470\.9965±0\.00430\.9965\\mathbin\{\\pm\}0\.00430\.9943±0\.00690\.9943\\mathbin\{\\pm\}0\.00690\.9962±0\.00520\.9962\\mathbin\{\\pm\}0\.00520\.9714±0\.00860\.9714\\mathbin\{\\pm\}0\.00860\.9959±0\.00490\.9959\\mathbin\{\\pm\}0\.0049Equal\-width binning0\.9667±0\.01040\.9667\\mathbin\{\\pm\}0\.01040\.9953±0\.00380\.9953\\mathbin\{\\pm\}0\.00380\.9949±0\.00340\.9949\\mathbin\{\\pm\}0\.00340\.9941±0\.00570\.9941\\mathbin\{\\pm\}0\.00570\.9961±0\.00330\.9961\\mathbin\{\\pm\}0\.00330\.9792±0\.00890\.9792\\mathbin\{\\pm\}0\.00890\.9912±0\.00700\.9912\\mathbin\{\\pm\}0\.0070Equal\-frequency binning0\.9756±0\.00870\.9756\\mathbin\{\\pm\}0\.00870\.9968±0\.00460\.9968\\mathbin\{\\pm\}0\.00460\.9968±0\.00460\.9968\\mathbin\{\\pm\}0\.00460\.9937±0\.00790\.9937\\mathbin\{\\pm\}0\.00790\.9968±0\.00490\.9968\\mathbin\{\\pm\}0\.00490\.9857±0\.00730\.9857\\mathbin\{\\pm\}0\.00730\.9953±0\.00490\.9953\\mathbin\{\\pm\}0\.0049Numeric interactions0\.9685±0\.01060\.9685\\mathbin\{\\pm\}0\.01060\.9970±0\.00450\.9970\\mathbin\{\\pm\}0\.00450\.9964±0\.00460\.9964\\mathbin\{\\pm\}0\.00460\.9950±0\.00680\.9950\\mathbin\{\\pm\}0\.00680\.9957±0\.00540\.9957\\mathbin\{\\pm\}0\.00540\.9854±0\.00680\.9854\\mathbin\{\\pm\}0\.00680\.9947±0\.00570\.9947\\mathbin\{\\pm\}0\.0057Group aggregation0\.9684±0\.00980\.9684\\mathbin\{\\pm\}0\.00980\.9970±0\.00440\.9970\\mathbin\{\\pm\}0\.00440\.9969±0\.00440\.9969\\mathbin\{\\pm\}0\.00440\.9954±0\.00680\.9954\\mathbin\{\\pm\}0\.00680\.9968±0\.00470\.9968\\mathbin\{\\pm\}0\.00470\.9787±0\.00770\.9787\\mathbin\{\\pm\}0\.00770\.9954±0\.00560\.9954\\mathbin\{\\pm\}0\.0056Variance filter0\.9709±0\.01060\.9709\\mathbin\{\\pm\}0\.01060\.9970±0\.00450\.9970\\mathbin\{\\pm\}0\.00450\.9969±0\.00440\.9969\\mathbin\{\\pm\}0\.00440\.9951±0\.00620\.9951\\mathbin\{\\pm\}0\.00620\.9968±0\.00420\.9968\\mathbin\{\\pm\}0\.00420\.9885±0\.00650\.9885\\mathbin\{\\pm\}0\.00650\.9952±0\.00520\.9952\\mathbin\{\\pm\}0\.0052Collinearity filter0\.9709±0\.01060\.9709\\mathbin\{\\pm\}0\.01060\.9970±0\.00450\.9970\\mathbin\{\\pm\}0\.00450\.9969±0\.00440\.9969\\mathbin\{\\pm\}0\.00440\.9951±0\.00620\.9951\\mathbin\{\\pm\}0\.00620\.9968±0\.00420\.9968\\mathbin\{\\pm\}0\.00420\.9885±0\.00650\.9885\\mathbin\{\\pm\}0\.00650\.9952±0\.00520\.9952\\mathbin\{\\pm\}0\.0052PCA0\.9732±0\.00990\.9732\\mathbin\{\\pm\}0\.00990\.9959±0\.00420\.9959\\mathbin\{\\pm\}0\.00420\.9961±0\.00390\.9961\\mathbin\{\\pm\}0\.00390\.9942±0\.00550\.9942\\mathbin\{\\pm\}0\.00550\.9957±0\.00430\.9957\\mathbin\{\\pm\}0\.00430\.9869±0\.00790\.9869\\mathbin\{\\pm\}0\.00790\.9938±0\.00730\.9938\\mathbin\{\\pm\}0\.0073Supervised selection0\.9703±0\.01020\.9703\\mathbin\{\\pm\}0\.01020\.9921±0\.00760\.9921\\mathbin\{\\pm\}0\.00760\.9948±0\.00650\.9948\\mathbin\{\\pm\}0\.00650\.9921±0\.00790\.9921\\mathbin\{\\pm\}0\.00790\.9940±0\.00660\.9940\\mathbin\{\\pm\}0\.00660\.9883±0\.00730\.9883\\mathbin\{\\pm\}0\.00730\.9919±0\.00670\.9919\\mathbin\{\\pm\}0\.0067TabPrep full0\.7944±0\.00980\.7944\\mathbin\{\\pm\}0\.00980\.8791±0\.01390\.8791\\mathbin\{\\pm\}0\.01390\.8753±0\.01270\.8753\\mathbin\{\\pm\}0\.01270\.8747±0\.01520\.8747\\mathbin\{\\pm\}0\.01520\.8739±0\.01430\.8739\\mathbin\{\\pm\}0\.01430\.8309±0\.01650\.8309\\mathbin\{\\pm\}0\.01650\.8713±0\.01770\.8713\\mathbin\{\\pm\}0\.0177TabPrep w/o groupby0\.7944±0\.00960\.7944\\mathbin\{\\pm\}0\.00960\.8795±0\.01410\.8795\\mathbin\{\\pm\}0\.01410\.8736±0\.01240\.8736\\mathbin\{\\pm\}0\.01240\.8736±0\.01880\.8736\\mathbin\{\\pm\}0\.01880\.8717±0\.01310\.8717\\mathbin\{\\pm\}0\.01310\.8312±0\.01370\.8312\\mathbin\{\\pm\}0\.01370\.8701±0\.01630\.8701\\mathbin\{\\pm\}0\.0163TabPrep w/o RSFC0\.7951±0\.01060\.7951\\mathbin\{\\pm\}0\.01060\.8794±0\.01480\.8794\\mathbin\{\\pm\}0\.01480\.8737±0\.01440\.8737\\mathbin\{\\pm\}0\.01440\.8737±0\.01790\.8737\\mathbin\{\\pm\}0\.01790\.8735±0\.01440\.8735\\mathbin\{\\pm\}0\.01440\.8303±0\.01630\.8303\\mathbin\{\\pm\}0\.01630\.8698±0\.01720\.8698\\mathbin\{\\pm\}0\.0172TabPrep w/o arithmetic0\.9701±0\.01890\.9701\\mathbin\{\\pm\}0\.01890\.9755±0\.01650\.9755\\mathbin\{\\pm\}0\.01650\.9748±0\.01680\.9748\\mathbin\{\\pm\}0\.01680\.9751±0\.01760\.9751\\mathbin\{\\pm\}0\.01760\.9741±0\.01930\.9741\\mathbin\{\\pm\}0\.01930\.9735±0\.01930\.9735\\mathbin\{\\pm\}0\.01930\.9752±0\.01720\.9752\\mathbin\{\\pm\}0\.0172TabPrep w/o cat\. interact\.0\.7953±0\.00980\.7953\\mathbin\{\\pm\}0\.00980\.8786±0\.01420\.8786\\mathbin\{\\pm\}0\.01420\.8739±0\.01500\.8739\\mathbin\{\\pm\}0\.01500\.8741±0\.01900\.8741\\mathbin\{\\pm\}0\.01900\.8722±0\.01550\.8722\\mathbin\{\\pm\}0\.01550\.8291±0\.01360\.8291\\mathbin\{\\pm\}0\.01360\.8712±0\.01660\.8712\\mathbin\{\\pm\}0\.0166TabPrep w/o OOF\-TE0\.7938±0\.00850\.7938\\mathbin\{\\pm\}0\.00850\.8791±0\.01240\.8791\\mathbin\{\\pm\}0\.01240\.8756±0\.01230\.8756\\mathbin\{\\pm\}0\.01230\.8732±0\.01670\.8732\\mathbin\{\\pm\}0\.01670\.8746±0\.01330\.8746\\mathbin\{\\pm\}0\.01330\.8298±0\.01500\.8298\\mathbin\{\\pm\}0\.01500\.8711±0\.01660\.8711\\mathbin\{\\pm\}0\.0166Shared\-context kNN0\.9704±0\.01010\.9704\\mathbin\{\\pm\}0\.01010\.9970±0\.00430\.9970\\mathbin\{\\pm\}0\.00430\.9968±0\.00440\.9968\\mathbin\{\\pm\}0\.00440\.9950±0\.00670\.9950\\mathbin\{\\pm\}0\.00670\.9965±0\.00430\.9965\\mathbin\{\\pm\}0\.00430\.9872±0\.00610\.9872\\mathbin\{\\pm\}0\.00610\.9952±0\.00520\.9952\\mathbin\{\\pm\}0\.0052OOF prediction feature0\.9700±0\.00980\.9700\\mathbin\{\\pm\}0\.00980\.9957±0\.00550\.9957\\mathbin\{\\pm\}0\.00550\.9963±0\.00520\.9963\\mathbin\{\\pm\}0\.00520\.9936±0\.00700\.9936\\mathbin\{\\pm\}0\.00700\.9939±0\.00620\.9939\\mathbin\{\\pm\}0\.00620\.9835±0\.00680\.9835\\mathbin\{\\pm\}0\.00680\.9950±0\.00530\.9950\\mathbin\{\\pm\}0\.0053Table 9:Complete TabPFN and TabICL raw metric results for Anneal, metric macro f1\. Values are mean±\\mathbin\{\\pm\}sample standard deviation across the 30 paired splits\.ConditionPFN v1PFN v2PFN v2\.5PFN v2\.6PFN v3ICL v1ICL v2Identity0\.8755±0\.06880\.8755\\mathbin\{\\pm\}0\.06880\.9715±0\.04660\.9715\\mathbin\{\\pm\}0\.04660\.9714±0\.04650\.9714\\mathbin\{\\pm\}0\.04650\.9712±0\.04910\.9712\\mathbin\{\\pm\}0\.04910\.9771±0\.04260\.9771\\mathbin\{\\pm\}0\.04260\.9542±0\.04590\.9542\\mathbin\{\\pm\}0\.04590\.9721±0\.04730\.9721\\mathbin\{\\pm\}0\.0473Standard scaling0\.8663±0\.07260\.8663\\mathbin\{\\pm\}0\.07260\.9711±0\.04670\.9711\\mathbin\{\\pm\}0\.04670\.9672±0\.04840\.9672\\mathbin\{\\pm\}0\.04840\.9713±0\.04910\.9713\\mathbin\{\\pm\}0\.04910\.9773±0\.04120\.9773\\mathbin\{\\pm\}0\.04120\.9505±0\.04570\.9505\\mathbin\{\\pm\}0\.04570\.9721±0\.04730\.9721\\mathbin\{\\pm\}0\.0473Log transform0\.8682±0\.06410\.8682\\mathbin\{\\pm\}0\.06410\.9721±0\.04710\.9721\\mathbin\{\\pm\}0\.04710\.9731±0\.04280\.9731\\mathbin\{\\pm\}0\.04280\.9712±0\.04920\.9712\\mathbin\{\\pm\}0\.04920\.9713±0\.04570\.9713\\mathbin\{\\pm\}0\.04570\.9327±0\.04700\.9327\\mathbin\{\\pm\}0\.04700\.9720±0\.04780\.9720\\mathbin\{\\pm\}0\.0478Square\-root transform0\.8603±0\.07450\.8603\\mathbin\{\\pm\}0\.07450\.9714±0\.04660\.9714\\mathbin\{\\pm\}0\.04660\.9717±0\.04500\.9717\\mathbin\{\\pm\}0\.04500\.9711±0\.04920\.9711\\mathbin\{\\pm\}0\.04920\.9739±0\.04380\.9739\\mathbin\{\\pm\}0\.04380\.9470±0\.04340\.9470\\mathbin\{\\pm\}0\.04340\.9717±0\.04780\.9717\\mathbin\{\\pm\}0\.0478Box–Cox0\.8683±0\.07540\.8683\\mathbin\{\\pm\}0\.07540\.9699±0\.04630\.9699\\mathbin\{\\pm\}0\.04630\.9672±0\.04840\.9672\\mathbin\{\\pm\}0\.04840\.9709±0\.05060\.9709\\mathbin\{\\pm\}0\.05060\.9737±0\.04590\.9737\\mathbin\{\\pm\}0\.04590\.9475±0\.05340\.9475\\mathbin\{\\pm\}0\.05340\.9721±0\.04720\.9721\\mathbin\{\\pm\}0\.0472Min–max scaling0\.8663±0\.07260\.8663\\mathbin\{\\pm\}0\.07260\.9714±0\.04660\.9714\\mathbin\{\\pm\}0\.04660\.9672±0\.04840\.9672\\mathbin\{\\pm\}0\.04840\.9714±0\.04910\.9714\\mathbin\{\\pm\}0\.04910\.9774±0\.04120\.9774\\mathbin\{\\pm\}0\.04120\.9505±0\.04570\.9505\\mathbin\{\\pm\}0\.04570\.9721±0\.04730\.9721\\mathbin\{\\pm\}0\.0473One\-hot encoding0\.6766±0\.04980\.6766\\mathbin\{\\pm\}0\.04980\.7547±0\.05890\.7547\\mathbin\{\\pm\}0\.05890\.7596±0\.05820\.7596\\mathbin\{\\pm\}0\.05820\.7570±0\.05940\.7570\\mathbin\{\\pm\}0\.05940\.7484±0\.06010\.7484\\mathbin\{\\pm\}0\.06010\.7221±0\.05730\.7221\\mathbin\{\\pm\}0\.05730\.7646±0\.05760\.7646\\mathbin\{\\pm\}0\.0576Ordinal encoding0\.8825±0\.07330\.8825\\mathbin\{\\pm\}0\.07330\.9711±0\.04650\.9711\\mathbin\{\\pm\}0\.04650\.9713±0\.04650\.9713\\mathbin\{\\pm\}0\.04650\.9714±0\.04880\.9714\\mathbin\{\\pm\}0\.04880\.9739±0\.04650\.9739\\mathbin\{\\pm\}0\.04650\.9466±0\.04590\.9466\\mathbin\{\\pm\}0\.04590\.9721±0\.04750\.9721\\mathbin\{\\pm\}0\.0475Frequency encoding0\.8424±0\.08560\.8424\\mathbin\{\\pm\}0\.08560\.9740±0\.04700\.9740\\mathbin\{\\pm\}0\.04700\.9646±0\.04880\.9646\\mathbin\{\\pm\}0\.04880\.9719±0\.04890\.9719\\mathbin\{\\pm\}0\.04890\.9714±0\.04680\.9714\\mathbin\{\\pm\}0\.04680\.9548±0\.04700\.9548\\mathbin\{\\pm\}0\.04700\.9684±0\.04690\.9684\\mathbin\{\\pm\}0\.0469Target encoding0\.5533±0\.02390\.5533\\mathbin\{\\pm\}0\.02390\.6144±0\.02230\.6144\\mathbin\{\\pm\}0\.02230\.6554±0\.05440\.6554\\mathbin\{\\pm\}0\.05440\.5756±0\.02580\.5756\\mathbin\{\\pm\}0\.02580\.5982±0\.03060\.5982\\mathbin\{\\pm\}0\.03060\.4106±0\.05420\.4106\\mathbin\{\\pm\}0\.05420\.5817±0\.06430\.5817\\mathbin\{\\pm\}0\.0643Categorical crosses0\.8405±0\.07950\.8405\\mathbin\{\\pm\}0\.07950\.9626±0\.05600\.9626\\mathbin\{\\pm\}0\.05600\.9708±0\.04620\.9708\\mathbin\{\\pm\}0\.04620\.9691±0\.04970\.9691\\mathbin\{\\pm\}0\.04970\.9770±0\.02950\.9770\\mathbin\{\\pm\}0\.02950\.8880±0\.06370\.8880\\mathbin\{\\pm\}0\.06370\.9760±0\.04430\.9760\\mathbin\{\\pm\}0\.0443Equal\-width binning0\.8638±0\.07030\.8638\\mathbin\{\\pm\}0\.07030\.9642±0\.04660\.9642\\mathbin\{\\pm\}0\.04660\.9590±0\.04750\.9590\\mathbin\{\\pm\}0\.04750\.9678±0\.04530\.9678\\mathbin\{\\pm\}0\.04530\.9749±0\.03900\.9749\\mathbin\{\\pm\}0\.03900\.9269±0\.05310\.9269\\mathbin\{\\pm\}0\.05310\.9654±0\.04430\.9654\\mathbin\{\\pm\}0\.0443Equal\-frequency binning0\.9053±0\.06320\.9053\\mathbin\{\\pm\}0\.06320\.9706±0\.04850\.9706\\mathbin\{\\pm\}0\.04850\.9725±0\.04670\.9725\\mathbin\{\\pm\}0\.04670\.9688±0\.04900\.9688\\mathbin\{\\pm\}0\.04900\.9740±0\.04760\.9740\\mathbin\{\\pm\}0\.04760\.9431±0\.04740\.9431\\mathbin\{\\pm\}0\.04740\.9702±0\.04740\.9702\\mathbin\{\\pm\}0\.0474Numeric interactions0\.8674±0\.07960\.8674\\mathbin\{\\pm\}0\.07960\.9728±0\.04670\.9728\\mathbin\{\\pm\}0\.04670\.9667±0\.04830\.9667\\mathbin\{\\pm\}0\.04830\.9680±0\.05130\.9680\\mathbin\{\\pm\}0\.05130\.9726±0\.04740\.9726\\mathbin\{\\pm\}0\.04740\.9425±0\.05460\.9425\\mathbin\{\\pm\}0\.05460\.9703±0\.04780\.9703\\mathbin\{\\pm\}0\.0478Group aggregation0\.8774±0\.07570\.8774\\mathbin\{\\pm\}0\.07570\.9715±0\.04660\.9715\\mathbin\{\\pm\}0\.04660\.9714±0\.04650\.9714\\mathbin\{\\pm\}0\.04650\.9697±0\.05040\.9697\\mathbin\{\\pm\}0\.05040\.9757±0\.04440\.9757\\mathbin\{\\pm\}0\.04440\.9246±0\.04580\.9246\\mathbin\{\\pm\}0\.04580\.9724±0\.04760\.9724\\mathbin\{\\pm\}0\.0476Variance filter0\.8755±0\.06880\.8755\\mathbin\{\\pm\}0\.06880\.9715±0\.04660\.9715\\mathbin\{\\pm\}0\.04660\.9714±0\.04650\.9714\\mathbin\{\\pm\}0\.04650\.9712±0\.04910\.9712\\mathbin\{\\pm\}0\.04910\.9771±0\.04260\.9771\\mathbin\{\\pm\}0\.04260\.9542±0\.04590\.9542\\mathbin\{\\pm\}0\.04590\.9721±0\.04730\.9721\\mathbin\{\\pm\}0\.0473Collinearity filter0\.8755±0\.06880\.8755\\mathbin\{\\pm\}0\.06880\.9715±0\.04660\.9715\\mathbin\{\\pm\}0\.04660\.9714±0\.04650\.9714\\mathbin\{\\pm\}0\.04650\.9712±0\.04910\.9712\\mathbin\{\\pm\}0\.04910\.9771±0\.04260\.9771\\mathbin\{\\pm\}0\.04260\.9542±0\.04590\.9542\\mathbin\{\\pm\}0\.04590\.9721±0\.04730\.9721\\mathbin\{\\pm\}0\.0473PCA0\.8670±0\.07370\.8670\\mathbin\{\\pm\}0\.07370\.9599±0\.04660\.9599\\mathbin\{\\pm\}0\.04660\.9572±0\.04760\.9572\\mathbin\{\\pm\}0\.04760\.9565±0\.04860\.9565\\mathbin\{\\pm\}0\.04860\.9589±0\.04710\.9589\\mathbin\{\\pm\}0\.04710\.9276±0\.05820\.9276\\mathbin\{\\pm\}0\.05820\.9702±0\.04520\.9702\\mathbin\{\\pm\}0\.0452Supervised selection0\.8205±0\.07580\.8205\\mathbin\{\\pm\}0\.07580\.9639±0\.05150\.9639\\mathbin\{\\pm\}0\.05150\.9661±0\.05000\.9661\\mathbin\{\\pm\}0\.05000\.9583±0\.05480\.9583\\mathbin\{\\pm\}0\.05480\.9589±0\.05190\.9589\\mathbin\{\\pm\}0\.05190\.9497±0\.04740\.9497\\mathbin\{\\pm\}0\.04740\.9585±0\.05240\.9585\\mathbin\{\\pm\}0\.0524TabPrep full0\.3518±0\.03210\.3518\\mathbin\{\\pm\}0\.03210\.6218±0\.03040\.6218\\mathbin\{\\pm\}0\.03040\.6014±0\.02020\.6014\\mathbin\{\\pm\}0\.02020\.6202±0\.01950\.6202\\mathbin\{\\pm\}0\.01950\.6080±0\.02670\.6080\\mathbin\{\\pm\}0\.02670\.4812±0\.03610\.4812\\mathbin\{\\pm\}0\.03610\.5971±0\.02770\.5971\\mathbin\{\\pm\}0\.0277TabPrep w/o groupby0\.3547±0\.03030\.3547\\mathbin\{\\pm\}0\.03030\.6240±0\.02540\.6240\\mathbin\{\\pm\}0\.02540\.5992±0\.02130\.5992\\mathbin\{\\pm\}0\.02130\.6193±0\.02380\.6193\\mathbin\{\\pm\}0\.02380\.6057±0\.03310\.6057\\mathbin\{\\pm\}0\.03310\.4787±0\.03120\.4787\\mathbin\{\\pm\}0\.03120\.5964±0\.02690\.5964\\mathbin\{\\pm\}0\.0269TabPrep w/o RSFC0\.3541±0\.03330\.3541\\mathbin\{\\pm\}0\.03330\.6202±0\.02350\.6202\\mathbin\{\\pm\}0\.02350\.5992±0\.02520\.5992\\mathbin\{\\pm\}0\.02520\.6192±0\.02380\.6192\\mathbin\{\\pm\}0\.02380\.6053±0\.02320\.6053\\mathbin\{\\pm\}0\.02320\.4772±0\.03490\.4772\\mathbin\{\\pm\}0\.03490\.5970±0\.02930\.5970\\mathbin\{\\pm\}0\.0293TabPrep w/o arithmetic0\.8541±0\.08550\.8541\\mathbin\{\\pm\}0\.08550\.9076±0\.07320\.9076\\mathbin\{\\pm\}0\.07320\.8976±0\.07840\.8976\\mathbin\{\\pm\}0\.07840\.8937±0\.08980\.8937\\mathbin\{\\pm\}0\.08980\.9043±0\.07920\.9043\\mathbin\{\\pm\}0\.07920\.8899±0\.08580\.8899\\mathbin\{\\pm\}0\.08580\.9110±0\.06450\.9110\\mathbin\{\\pm\}0\.0645TabPrep w/o cat\. interact\.0\.3571±0\.03370\.3571\\mathbin\{\\pm\}0\.03370\.6196±0\.02010\.6196\\mathbin\{\\pm\}0\.02010\.5984±0\.02520\.5984\\mathbin\{\\pm\}0\.02520\.6199±0\.02310\.6199\\mathbin\{\\pm\}0\.02310\.6044±0\.02650\.6044\\mathbin\{\\pm\}0\.02650\.4743±0\.02990\.4743\\mathbin\{\\pm\}0\.02990\.5979±0\.02810\.5979\\mathbin\{\\pm\}0\.0281TabPrep w/o OOF\-TE0\.3534±0\.02970\.3534\\mathbin\{\\pm\}0\.02970\.6190±0\.02000\.6190\\mathbin\{\\pm\}0\.02000\.6021±0\.02190\.6021\\mathbin\{\\pm\}0\.02190\.6180±0\.02200\.6180\\mathbin\{\\pm\}0\.02200\.6121±0\.03400\.6121\\mathbin\{\\pm\}0\.03400\.4780±0\.03370\.4780\\mathbin\{\\pm\}0\.03370\.5978±0\.02780\.5978\\mathbin\{\\pm\}0\.0278Shared\-context kNN0\.8747±0\.06870\.8747\\mathbin\{\\pm\}0\.06870\.9703±0\.04630\.9703\\mathbin\{\\pm\}0\.04630\.9694±0\.04830\.9694\\mathbin\{\\pm\}0\.04830\.9711±0\.04940\.9711\\mathbin\{\\pm\}0\.04940\.9756±0\.04310\.9756\\mathbin\{\\pm\}0\.04310\.9508±0\.04500\.9508\\mathbin\{\\pm\}0\.04500\.9721±0\.04730\.9721\\mathbin\{\\pm\}0\.0473OOF prediction feature0\.8617±0\.08020\.8617\\mathbin\{\\pm\}0\.08020\.9644±0\.05620\.9644\\mathbin\{\\pm\}0\.05620\.9633±0\.05910\.9633\\mathbin\{\\pm\}0\.05910\.9555±0\.06070\.9555\\mathbin\{\\pm\}0\.06070\.9399±0\.07090\.9399\\mathbin\{\\pm\}0\.07090\.9345±0\.03400\.9345\\mathbin\{\\pm\}0\.03400\.9670±0\.04810\.9670\\mathbin\{\\pm\}0\.0481Table 10:Complete raw metric results for Used Fiat 500, metric r2\. Values are mean±\\mathbin\{\\pm\}sample standard deviation across the 30 paired splits\.ConditionPFN v2PFN v2\.5PFN v2\.6PFN v3ICL v2Identity0\.8587±0\.00990\.8587\\mathbin\{\\pm\}0\.00990\.8578±0\.01050\.8578\\mathbin\{\\pm\}0\.01050\.8589±0\.01100\.8589\\mathbin\{\\pm\}0\.01100\.8637±0\.01040\.8637\\mathbin\{\\pm\}0\.01040\.8632±0\.01020\.8632\\mathbin\{\\pm\}0\.0102Standard scaling0\.8587±0\.01010\.8587\\mathbin\{\\pm\}0\.01010\.8578±0\.01040\.8578\\mathbin\{\\pm\}0\.01040\.8601±0\.01090\.8601\\mathbin\{\\pm\}0\.01090\.8637±0\.01030\.8637\\mathbin\{\\pm\}0\.01030\.8632±0\.01020\.8632\\mathbin\{\\pm\}0\.0102Log transform0\.8583±0\.00960\.8583\\mathbin\{\\pm\}0\.00960\.8577±0\.01030\.8577\\mathbin\{\\pm\}0\.01030\.8587±0\.01100\.8587\\mathbin\{\\pm\}0\.01100\.8630±0\.01040\.8630\\mathbin\{\\pm\}0\.01040\.8634±0\.01010\.8634\\mathbin\{\\pm\}0\.0101Square\-root transform0\.8584±0\.00990\.8584\\mathbin\{\\pm\}0\.00990\.8576±0\.01040\.8576\\mathbin\{\\pm\}0\.01040\.8589±0\.01110\.8589\\mathbin\{\\pm\}0\.01110\.8631±0\.01050\.8631\\mathbin\{\\pm\}0\.01050\.8634±0\.01010\.8634\\mathbin\{\\pm\}0\.0101Box–Cox0\.8581±0\.01000\.8581\\mathbin\{\\pm\}0\.01000\.8571±0\.01040\.8571\\mathbin\{\\pm\}0\.01040\.8600±0\.01070\.8600\\mathbin\{\\pm\}0\.01070\.8630±0\.01040\.8630\\mathbin\{\\pm\}0\.01040\.8632±0\.01020\.8632\\mathbin\{\\pm\}0\.0102Min–max scaling0\.8592±0\.01010\.8592\\mathbin\{\\pm\}0\.01010\.8577±0\.01050\.8577\\mathbin\{\\pm\}0\.01050\.8608±0\.01110\.8608\\mathbin\{\\pm\}0\.01110\.8637±0\.01030\.8637\\mathbin\{\\pm\}0\.01030\.8632±0\.01020\.8632\\mathbin\{\\pm\}0\.0102One\-hot encoding0\.8587±0\.00990\.8587\\mathbin\{\\pm\}0\.00990\.8585±0\.01010\.8585\\mathbin\{\\pm\}0\.01010\.8599±0\.01070\.8599\\mathbin\{\\pm\}0\.01070\.8637±0\.01030\.8637\\mathbin\{\\pm\}0\.01030\.8633±0\.00980\.8633\\mathbin\{\\pm\}0\.0098Ordinal encoding0\.8587±0\.00990\.8587\\mathbin\{\\pm\}0\.00990\.8576±0\.01040\.8576\\mathbin\{\\pm\}0\.01040\.8589±0\.01100\.8589\\mathbin\{\\pm\}0\.01100\.8638±0\.01020\.8638\\mathbin\{\\pm\}0\.01020\.8632±0\.01020\.8632\\mathbin\{\\pm\}0\.0102Frequency encoding0\.8588±0\.01020\.8588\\mathbin\{\\pm\}0\.01020\.8575±0\.01050\.8575\\mathbin\{\\pm\}0\.01050\.8588±0\.01110\.8588\\mathbin\{\\pm\}0\.01110\.8638±0\.01020\.8638\\mathbin\{\\pm\}0\.01020\.8632±0\.01020\.8632\\mathbin\{\\pm\}0\.0102Target encoding0\.8579±0\.01030\.8579\\mathbin\{\\pm\}0\.01030\.8570±0\.01030\.8570\\mathbin\{\\pm\}0\.01030\.8578±0\.01130\.8578\\mathbin\{\\pm\}0\.01130\.8637±0\.01030\.8637\\mathbin\{\\pm\}0\.01030\.8607±0\.01050\.8607\\mathbin\{\\pm\}0\.0105Categorical crosses—————Equal\-width binning0\.8430±0\.01040\.8430\\mathbin\{\\pm\}0\.01040\.8437±0\.01060\.8437\\mathbin\{\\pm\}0\.01060\.8429±0\.01110\.8429\\mathbin\{\\pm\}0\.01110\.8446±0\.01110\.8446\\mathbin\{\\pm\}0\.01110\.8446±0\.01080\.8446\\mathbin\{\\pm\}0\.0108Equal\-frequency binning0\.8408±0\.01110\.8408\\mathbin\{\\pm\}0\.01110\.8410±0\.01140\.8410\\mathbin\{\\pm\}0\.01140\.8421±0\.01140\.8421\\mathbin\{\\pm\}0\.01140\.8414±0\.01160\.8414\\mathbin\{\\pm\}0\.01160\.8411±0\.01180\.8411\\mathbin\{\\pm\}0\.0118Numeric interactions0\.8591±0\.00960\.8591\\mathbin\{\\pm\}0\.00960\.8595±0\.01020\.8595\\mathbin\{\\pm\}0\.01020\.8608±0\.01050\.8608\\mathbin\{\\pm\}0\.01050\.8641±0\.01040\.8641\\mathbin\{\\pm\}0\.01040\.8641±0\.00960\.8641\\mathbin\{\\pm\}0\.0096Group aggregation0\.8585±0\.00990\.8585\\mathbin\{\\pm\}0\.00990\.8590±0\.01010\.8590\\mathbin\{\\pm\}0\.01010\.8603±0\.01040\.8603\\mathbin\{\\pm\}0\.01040\.8632±0\.01030\.8632\\mathbin\{\\pm\}0\.01030\.8627±0\.00930\.8627\\mathbin\{\\pm\}0\.0093Variance filter0\.8587±0\.00990\.8587\\mathbin\{\\pm\}0\.00990\.8578±0\.01050\.8578\\mathbin\{\\pm\}0\.01050\.8589±0\.01100\.8589\\mathbin\{\\pm\}0\.01100\.8637±0\.01040\.8637\\mathbin\{\\pm\}0\.01040\.8632±0\.01020\.8632\\mathbin\{\\pm\}0\.0102Collinearity filter0\.8587±0\.00990\.8587\\mathbin\{\\pm\}0\.00990\.8578±0\.01050\.8578\\mathbin\{\\pm\}0\.01050\.8589±0\.01100\.8589\\mathbin\{\\pm\}0\.01100\.8637±0\.01040\.8637\\mathbin\{\\pm\}0\.01040\.8632±0\.01020\.8632\\mathbin\{\\pm\}0\.0102PCA0\.8568±0\.01030\.8568\\mathbin\{\\pm\}0\.01030\.8560±0\.01130\.8560\\mathbin\{\\pm\}0\.01130\.8576±0\.01170\.8576\\mathbin\{\\pm\}0\.01170\.8622±0\.01090\.8622\\mathbin\{\\pm\}0\.01090\.8621±0\.00950\.8621\\mathbin\{\\pm\}0\.0095Supervised selection0\.8566±0\.01040\.8566\\mathbin\{\\pm\}0\.01040\.8554±0\.01060\.8554\\mathbin\{\\pm\}0\.01060\.8570±0\.01090\.8570\\mathbin\{\\pm\}0\.01090\.8603±0\.01060\.8603\\mathbin\{\\pm\}0\.01060\.8586±0\.01070\.8586\\mathbin\{\\pm\}0\.0107TabPrep full0\.8501±0\.01060\.8501\\mathbin\{\\pm\}0\.01060\.8511±0\.01100\.8511\\mathbin\{\\pm\}0\.01100\.8514±0\.01140\.8514\\mathbin\{\\pm\}0\.01140\.8556±0\.01130\.8556\\mathbin\{\\pm\}0\.01130\.8517±0\.01110\.8517\\mathbin\{\\pm\}0\.0111TabPrep w/o groupby0\.8503±0\.01060\.8503\\mathbin\{\\pm\}0\.01060\.8509±0\.01090\.8509\\mathbin\{\\pm\}0\.01090\.8515±0\.01160\.8515\\mathbin\{\\pm\}0\.01160\.8555±0\.01120\.8555\\mathbin\{\\pm\}0\.01120\.8517±0\.01120\.8517\\mathbin\{\\pm\}0\.0112TabPrep w/o RSFC0\.8500±0\.01070\.8500\\mathbin\{\\pm\}0\.01070\.8510±0\.01110\.8510\\mathbin\{\\pm\}0\.01110\.8515±0\.01160\.8515\\mathbin\{\\pm\}0\.01160\.8560±0\.01120\.8560\\mathbin\{\\pm\}0\.01120\.8518±0\.01120\.8518\\mathbin\{\\pm\}0\.0112TabPrep w/o arithmetic0\.8638±0\.01270\.8638\\mathbin\{\\pm\}0\.01270\.8623±0\.01340\.8623\\mathbin\{\\pm\}0\.01340\.8624±0\.01330\.8624\\mathbin\{\\pm\}0\.01330\.8630±0\.01360\.8630\\mathbin\{\\pm\}0\.01360\.8604±0\.01430\.8604\\mathbin\{\\pm\}0\.0143TabPrep w/o cat\. interact\.0\.8502±0\.01040\.8502\\mathbin\{\\pm\}0\.01040\.8510±0\.01130\.8510\\mathbin\{\\pm\}0\.01130\.8514±0\.01150\.8514\\mathbin\{\\pm\}0\.01150\.8557±0\.01110\.8557\\mathbin\{\\pm\}0\.01110\.8517±0\.01110\.8517\\mathbin\{\\pm\}0\.0111TabPrep w/o OOF\-TE0\.8500±0\.01080\.8500\\mathbin\{\\pm\}0\.01080\.8512±0\.01120\.8512\\mathbin\{\\pm\}0\.01120\.8514±0\.01170\.8514\\mathbin\{\\pm\}0\.01170\.8558±0\.01130\.8558\\mathbin\{\\pm\}0\.01130\.8516±0\.01130\.8516\\mathbin\{\\pm\}0\.0113Shared\-context kNN0\.8589±0\.00990\.8589\\mathbin\{\\pm\}0\.00990\.8577±0\.01060\.8577\\mathbin\{\\pm\}0\.01060\.8590±0\.01110\.8590\\mathbin\{\\pm\}0\.01110\.8638±0\.01040\.8638\\mathbin\{\\pm\}0\.01040\.8632±0\.01010\.8632\\mathbin\{\\pm\}0\.0101OOF prediction feature0\.8554±0\.01090\.8554\\mathbin\{\\pm\}0\.01090\.8540±0\.01030\.8540\\mathbin\{\\pm\}0\.01030\.8568±0\.01100\.8568\\mathbin\{\\pm\}0\.01100\.8591±0\.01110\.8591\\mathbin\{\\pm\}0\.01110\.8608±0\.00970\.8608\\mathbin\{\\pm\}0\.0097Table 11:Complete raw metric results for Used Fiat 500, metric rmse\. Values are mean±\\mathbin\{\\pm\}sample standard deviation across the 30 paired splits\.ConditionPFN v2PFN v2\.5PFN v2\.6PFN v3ICL v2Identity727\.4±23\.4727\.4\\mathbin\{\\pm\}23\.4729\.7±23\.8729\.7\\mathbin\{\\pm\}23\.8726\.8±24\.8726\.8\\mathbin\{\\pm\}24\.8714\.4±23\.2714\.4\\mathbin\{\\pm\}23\.2715\.7±23\.4715\.7\\mathbin\{\\pm\}23\.4Standard scaling727\.6±24\.0727\.6\\mathbin\{\\pm\}24\.0729\.9±23\.8729\.9\\mathbin\{\\pm\}23\.8723\.7±24\.9723\.7\\mathbin\{\\pm\}24\.9714\.5±23\.2714\.5\\mathbin\{\\pm\}23\.2715\.7±23\.4715\.7\\mathbin\{\\pm\}23\.4Log transform728\.6±23\.0728\.6\\mathbin\{\\pm\}23\.0730\.1±23\.5730\.1\\mathbin\{\\pm\}23\.5727\.5±24\.6727\.5\\mathbin\{\\pm\}24\.6716\.4±23\.4716\.4\\mathbin\{\\pm\}23\.4715\.4±23\.2715\.4\\mathbin\{\\pm\}23\.2Square\-root transform728\.2±23\.4728\.2\\mathbin\{\\pm\}23\.4730\.3±23\.6730\.3\\mathbin\{\\pm\}23\.6726\.8±25\.0726\.8\\mathbin\{\\pm\}25\.0716\.1±23\.4716\.1\\mathbin\{\\pm\}23\.4715\.2±23\.1715\.2\\mathbin\{\\pm\}23\.1Box–Cox729\.1±23\.8729\.1\\mathbin\{\\pm\}23\.8731\.7±23\.5731\.7\\mathbin\{\\pm\}23\.5724\.0±24\.5724\.0\\mathbin\{\\pm\}24\.5716\.4±23\.8716\.4\\mathbin\{\\pm\}23\.8715\.7±23\.6715\.7\\mathbin\{\\pm\}23\.6Min–max scaling726\.3±24\.1726\.3\\mathbin\{\\pm\}24\.1729\.9±23\.8729\.9\\mathbin\{\\pm\}23\.8722\.0±25\.0722\.0\\mathbin\{\\pm\}25\.0714\.3±23\.1714\.3\\mathbin\{\\pm\}23\.1715\.7±23\.4715\.7\\mathbin\{\\pm\}23\.4One\-hot encoding727\.6±23\.5727\.6\\mathbin\{\\pm\}23\.5728\.0±23\.2728\.0\\mathbin\{\\pm\}23\.2724\.2±24\.2724\.2\\mathbin\{\\pm\}24\.2714\.5±23\.0714\.5\\mathbin\{\\pm\}23\.0715\.4±22\.8715\.4\\mathbin\{\\pm\}22\.8Ordinal encoding727\.4±23\.4727\.4\\mathbin\{\\pm\}23\.4730\.2±23\.2730\.2\\mathbin\{\\pm\}23\.2726\.9±25\.0726\.9\\mathbin\{\\pm\}25\.0714\.2±23\.0714\.2\\mathbin\{\\pm\}23\.0715\.7±23\.2715\.7\\mathbin\{\\pm\}23\.2Frequency encoding727\.2±23\.8727\.2\\mathbin\{\\pm\}23\.8730\.6±24\.1730\.6\\mathbin\{\\pm\}24\.1727\.2±25\.1727\.2\\mathbin\{\\pm\}25\.1714\.2±22\.8714\.2\\mathbin\{\\pm\}22\.8715\.7±23\.0715\.7\\mathbin\{\\pm\}23\.0Target encoding729\.5±23\.9729\.5\\mathbin\{\\pm\}23\.9732\.0±23\.2732\.0\\mathbin\{\\pm\}23\.2729\.7±25\.4729\.7\\mathbin\{\\pm\}25\.4714\.5±23\.2714\.5\\mathbin\{\\pm\}23\.2722\.3±23\.8722\.3\\mathbin\{\\pm\}23\.8Categorical crosses—————Equal\-width binning767\.0±21\.7767\.0\\mathbin\{\\pm\}21\.7765\.0±21\.6765\.0\\mathbin\{\\pm\}21\.6767\.1±22\.9767\.1\\mathbin\{\\pm\}22\.9763\.0±23\.2763\.0\\mathbin\{\\pm\}23\.2762\.9±22\.2762\.9\\mathbin\{\\pm\}22\.2Equal\-frequency binning772\.2±23\.2772\.2\\mathbin\{\\pm\}23\.2771\.6±23\.8771\.6\\mathbin\{\\pm\}23\.8768\.9±23\.6768\.9\\mathbin\{\\pm\}23\.6770\.7±23\.5770\.7\\mathbin\{\\pm\}23\.5771\.3±24\.5771\.3\\mathbin\{\\pm\}24\.5Numeric interactions726\.5±21\.9726\.5\\mathbin\{\\pm\}21\.9725\.3±23\.0725\.3\\mathbin\{\\pm\}23\.0722\.0±24\.1722\.0\\mathbin\{\\pm\}24\.1713\.3±23\.3713\.3\\mathbin\{\\pm\}23\.3713\.4±21\.9713\.4\\mathbin\{\\pm\}21\.9Group aggregation727\.9±23\.5727\.9\\mathbin\{\\pm\}23\.5726\.7±23\.7726\.7\\mathbin\{\\pm\}23\.7723\.4±23\.4723\.4\\mathbin\{\\pm\}23\.4715\.8±22\.9715\.8\\mathbin\{\\pm\}22\.9717\.2±21\.3717\.2\\mathbin\{\\pm\}21\.3Variance filter727\.4±23\.4727\.4\\mathbin\{\\pm\}23\.4729\.7±23\.8729\.7\\mathbin\{\\pm\}23\.8726\.8±24\.8726\.8\\mathbin\{\\pm\}24\.8714\.4±23\.2714\.4\\mathbin\{\\pm\}23\.2715\.7±23\.4715\.7\\mathbin\{\\pm\}23\.4Collinearity filter727\.4±23\.4727\.4\\mathbin\{\\pm\}23\.4729\.7±23\.8729\.7\\mathbin\{\\pm\}23\.8726\.8±24\.8726\.8\\mathbin\{\\pm\}24\.8714\.4±23\.2714\.4\\mathbin\{\\pm\}23\.2715\.7±23\.4715\.7\\mathbin\{\\pm\}23\.4PCA732\.4±22\.4732\.4\\mathbin\{\\pm\}22\.4734\.4±23\.7734\.4\\mathbin\{\\pm\}23\.7730\.1±25\.5730\.1\\mathbin\{\\pm\}25\.5718\.3±23\.3718\.3\\mathbin\{\\pm\}23\.3718\.7±21\.1718\.7\\mathbin\{\\pm\}21\.1Supervised selection732\.7±24\.2732\.7\\mathbin\{\\pm\}24\.2736\.0±24\.1736\.0\\mathbin\{\\pm\}24\.1731\.7±24\.9731\.7\\mathbin\{\\pm\}24\.9723\.2±24\.5723\.2\\mathbin\{\\pm\}24\.5727\.7±24\.8727\.7\\mathbin\{\\pm\}24\.8TabPrep full749\.2±21\.9749\.2\\mathbin\{\\pm\}21\.9746\.8±23\.4746\.8\\mathbin\{\\pm\}23\.4745\.9±23\.8745\.9\\mathbin\{\\pm\}23\.8735\.2±23\.6735\.2\\mathbin\{\\pm\}23\.6745\.1±22\.3745\.1\\mathbin\{\\pm\}22\.3TabPrep w/o groupby748\.7±21\.8748\.7\\mathbin\{\\pm\}21\.8747\.3±22\.6747\.3\\mathbin\{\\pm\}22\.6745\.7±24\.4745\.7\\mathbin\{\\pm\}24\.4735\.6±23\.5735\.6\\mathbin\{\\pm\}23\.5745\.2±22\.5745\.2\\mathbin\{\\pm\}22\.5TabPrep w/o RSFC749\.6±22\.1749\.6\\mathbin\{\\pm\}22\.1747\.0±23\.3747\.0\\mathbin\{\\pm\}23\.3745\.6±24\.5745\.6\\mathbin\{\\pm\}24\.5734\.3±23\.5734\.3\\mathbin\{\\pm\}23\.5744\.9±22\.5744\.9\\mathbin\{\\pm\}22\.5TabPrep w/o arithmetic714\.0±34\.5714\.0\\mathbin\{\\pm\}34\.5718\.0±35\.9718\.0\\mathbin\{\\pm\}35\.9717\.6±34\.9717\.6\\mathbin\{\\pm\}34\.9716\.1±35\.9716\.1\\mathbin\{\\pm\}35\.9722\.8±37\.3722\.8\\mathbin\{\\pm\}37\.3TabPrep w/o cat\. interact\.749\.0±21\.6749\.0\\mathbin\{\\pm\}21\.6746\.9±23\.6746\.9\\mathbin\{\\pm\}23\.6746\.0±24\.3746\.0\\mathbin\{\\pm\}24\.3734\.9±23\.2734\.9\\mathbin\{\\pm\}23\.2745\.1±22\.3745\.1\\mathbin\{\\pm\}22\.3TabPrep w/o OOF\-TE749\.4±22\.4749\.4\\mathbin\{\\pm\}22\.4746\.6±23\.3746\.6\\mathbin\{\\pm\}23\.3745\.8±25\.0745\.8\\mathbin\{\\pm\}25\.0734\.8±23\.7734\.8\\mathbin\{\\pm\}23\.7745\.5±22\.4745\.5\\mathbin\{\\pm\}22\.4Shared\-context kNN726\.9±23\.3726\.9\\mathbin\{\\pm\}23\.3730\.1±24\.0730\.1\\mathbin\{\\pm\}24\.0726\.6±25\.0726\.6\\mathbin\{\\pm\}25\.0714\.0±23\.2714\.0\\mathbin\{\\pm\}23\.2715\.8±23\.4715\.8\\mathbin\{\\pm\}23\.4OOF prediction feature735\.9±25\.4735\.9\\mathbin\{\\pm\}25\.4739\.6±22\.9739\.6\\mathbin\{\\pm\}22\.9732\.4±25\.2732\.4\\mathbin\{\\pm\}25\.2726\.4±23\.4726\.4\\mathbin\{\\pm\}23\.4722\.3±23\.4722\.3\\mathbin\{\\pm\}23\.4Table 12:Complete TabPFN and TabICL raw metric results for Blood transfusion, metric accuracy\. Values are mean±\\mathbin\{\\pm\}sample standard deviation across the 30 paired splits\.ConditionPFN v1PFN v2PFN v2\.5PFN v2\.6PFN v3ICL v1ICL v2Identity0\.7925±0\.01130\.7925\\mathbin\{\\pm\}0\.01130\.7898±0\.00990\.7898\\mathbin\{\\pm\}0\.00990\.7932±0\.00900\.7932\\mathbin\{\\pm\}0\.00900\.7894±0\.01110\.7894\\mathbin\{\\pm\}0\.01110\.7904±0\.01020\.7904\\mathbin\{\\pm\}0\.01020\.7918±0\.00860\.7918\\mathbin\{\\pm\}0\.00860\.7913±0\.01070\.7913\\mathbin\{\\pm\}0\.0107Standard scaling0\.7925±0\.01130\.7925\\mathbin\{\\pm\}0\.01130\.7900±0\.00930\.7900\\mathbin\{\\pm\}0\.00930\.7928±0\.00960\.7928\\mathbin\{\\pm\}0\.00960\.7894±0\.01110\.7894\\mathbin\{\\pm\}0\.01110\.7901±0\.00960\.7901\\mathbin\{\\pm\}0\.00960\.7918±0\.00860\.7918\\mathbin\{\\pm\}0\.00860\.7913±0\.01070\.7913\\mathbin\{\\pm\}0\.0107Log transform0\.7901±0\.01170\.7901\\mathbin\{\\pm\}0\.01170\.7878±0\.01000\.7878\\mathbin\{\\pm\}0\.01000\.7885±0\.01050\.7885\\mathbin\{\\pm\}0\.01050\.7892±0\.00960\.7892\\mathbin\{\\pm\}0\.00960\.7877±0\.01270\.7877\\mathbin\{\\pm\}0\.01270\.7874±0\.01050\.7874\\mathbin\{\\pm\}0\.01050\.7913±0\.01050\.7913\\mathbin\{\\pm\}0\.0105Square\-root transform0\.7911±0\.01150\.7911\\mathbin\{\\pm\}0\.01150\.7886±0\.01030\.7886\\mathbin\{\\pm\}0\.01030\.7901±0\.01060\.7901\\mathbin\{\\pm\}0\.01060\.7878±0\.01210\.7878\\mathbin\{\\pm\}0\.01210\.7885±0\.01140\.7885\\mathbin\{\\pm\}0\.01140\.7889±0\.00810\.7889\\mathbin\{\\pm\}0\.00810\.7911±0\.00990\.7911\\mathbin\{\\pm\}0\.0099Box–Cox0\.7928±0\.01220\.7928\\mathbin\{\\pm\}0\.01220\.7870±0\.01070\.7870\\mathbin\{\\pm\}0\.01070\.7904±0\.00980\.7904\\mathbin\{\\pm\}0\.00980\.7893±0\.01120\.7893\\mathbin\{\\pm\}0\.01120\.7882±0\.01050\.7882\\mathbin\{\\pm\}0\.01050\.7888±0\.00980\.7888\\mathbin\{\\pm\}0\.00980\.7919±0\.01040\.7919\\mathbin\{\\pm\}0\.0104Min–max scaling0\.7925±0\.01130\.7925\\mathbin\{\\pm\}0\.01130\.7890±0\.00900\.7890\\mathbin\{\\pm\}0\.00900\.7933±0\.01070\.7933\\mathbin\{\\pm\}0\.01070\.7894±0\.01110\.7894\\mathbin\{\\pm\}0\.01110\.7897±0\.01130\.7897\\mathbin\{\\pm\}0\.01130\.7920±0\.00860\.7920\\mathbin\{\\pm\}0\.00860\.7913±0\.01070\.7913\\mathbin\{\\pm\}0\.0107One\-hot encoding———————Ordinal encoding———————Frequency encoding———————Target encoding———————Categorical crosses———————Equal\-width binning0\.7820±0\.01110\.7820\\mathbin\{\\pm\}0\.01110\.7763±0\.01070\.7763\\mathbin\{\\pm\}0\.01070\.7794±0\.01140\.7794\\mathbin\{\\pm\}0\.01140\.7778±0\.01250\.7778\\mathbin\{\\pm\}0\.01250\.7773±0\.00920\.7773\\mathbin\{\\pm\}0\.00920\.7808±0\.01200\.7808\\mathbin\{\\pm\}0\.01200\.7801±0\.01190\.7801\\mathbin\{\\pm\}0\.0119Equal\-frequency binning0\.7846±0\.01050\.7846\\mathbin\{\\pm\}0\.01050\.7800±0\.01150\.7800\\mathbin\{\\pm\}0\.01150\.7836±0\.01040\.7836\\mathbin\{\\pm\}0\.01040\.7870±0\.01410\.7870\\mathbin\{\\pm\}0\.01410\.7816±0\.01100\.7816\\mathbin\{\\pm\}0\.01100\.7790±0\.01270\.7790\\mathbin\{\\pm\}0\.01270\.7852±0\.01030\.7852\\mathbin\{\\pm\}0\.0103Numeric interactions0\.7925±0\.01130\.7925\\mathbin\{\\pm\}0\.01130\.7898±0\.00990\.7898\\mathbin\{\\pm\}0\.00990\.7932±0\.00900\.7932\\mathbin\{\\pm\}0\.00900\.7894±0\.01110\.7894\\mathbin\{\\pm\}0\.01110\.7904±0\.01020\.7904\\mathbin\{\\pm\}0\.01020\.7918±0\.00860\.7918\\mathbin\{\\pm\}0\.00860\.7913±0\.01070\.7913\\mathbin\{\\pm\}0\.0107Group aggregation———————Variance filter0\.7925±0\.01130\.7925\\mathbin\{\\pm\}0\.01130\.7898±0\.00990\.7898\\mathbin\{\\pm\}0\.00990\.7932±0\.00900\.7932\\mathbin\{\\pm\}0\.00900\.7894±0\.01110\.7894\\mathbin\{\\pm\}0\.01110\.7904±0\.01020\.7904\\mathbin\{\\pm\}0\.01020\.7918±0\.00860\.7918\\mathbin\{\\pm\}0\.00860\.7913±0\.01070\.7913\\mathbin\{\\pm\}0\.0107Collinearity filter0\.7933±0\.01310\.7933\\mathbin\{\\pm\}0\.01310\.7882±0\.01020\.7882\\mathbin\{\\pm\}0\.01020\.7910±0\.00710\.7910\\mathbin\{\\pm\}0\.00710\.7860±0\.01150\.7860\\mathbin\{\\pm\}0\.01150\.7884±0\.00970\.7884\\mathbin\{\\pm\}0\.00970\.7857±0\.00900\.7857\\mathbin\{\\pm\}0\.00900\.7935±0\.01170\.7935\\mathbin\{\\pm\}0\.0117PCA0\.7953±0\.01120\.7953\\mathbin\{\\pm\}0\.01120\.7927±0\.01100\.7927\\mathbin\{\\pm\}0\.01100\.7945±0\.01010\.7945\\mathbin\{\\pm\}0\.01010\.7913±0\.01520\.7913\\mathbin\{\\pm\}0\.01520\.7929±0\.01380\.7929\\mathbin\{\\pm\}0\.01380\.7928±0\.01200\.7928\\mathbin\{\\pm\}0\.01200\.7944±0\.01180\.7944\\mathbin\{\\pm\}0\.0118Supervised selection0\.7564±0\.01480\.7564\\mathbin\{\\pm\}0\.01480\.7644±0\.01250\.7644\\mathbin\{\\pm\}0\.01250\.7657±0\.01340\.7657\\mathbin\{\\pm\}0\.01340\.7584±0\.01460\.7584\\mathbin\{\\pm\}0\.01460\.7620±0\.01170\.7620\\mathbin\{\\pm\}0\.01170\.7616±0\.01580\.7616\\mathbin\{\\pm\}0\.01580\.7636±0\.01590\.7636\\mathbin\{\\pm\}0\.0159TabPrep full0\.7892±0\.00980\.7892\\mathbin\{\\pm\}0\.00980\.7868±0\.01090\.7868\\mathbin\{\\pm\}0\.01090\.7925±0\.00900\.7925\\mathbin\{\\pm\}0\.00900\.7912±0\.01370\.7912\\mathbin\{\\pm\}0\.01370\.7923±0\.00870\.7923\\mathbin\{\\pm\}0\.00870\.7927±0\.01180\.7927\\mathbin\{\\pm\}0\.01180\.7923±0\.01150\.7923\\mathbin\{\\pm\}0\.0115TabPrep w/o groupby0\.7886±0\.01050\.7886\\mathbin\{\\pm\}0\.01050\.7857±0\.00960\.7857\\mathbin\{\\pm\}0\.00960\.7924±0\.01000\.7924\\mathbin\{\\pm\}0\.01000\.7913±0\.01490\.7913\\mathbin\{\\pm\}0\.01490\.7928±0\.01040\.7928\\mathbin\{\\pm\}0\.01040\.7920±0\.01290\.7920\\mathbin\{\\pm\}0\.01290\.7928±0\.01060\.7928\\mathbin\{\\pm\}0\.0106TabPrep w/o RSFC0\.7889±0\.00960\.7889\\mathbin\{\\pm\}0\.00960\.7854±0\.00960\.7854\\mathbin\{\\pm\}0\.00960\.7935±0\.00940\.7935\\mathbin\{\\pm\}0\.00940\.7901±0\.01330\.7901\\mathbin\{\\pm\}0\.01330\.7925±0\.01090\.7925\\mathbin\{\\pm\}0\.01090\.7927±0\.01130\.7927\\mathbin\{\\pm\}0\.01130\.7919±0\.00890\.7919\\mathbin\{\\pm\}0\.0089TabPrep w/o arithmetic0\.7721±0\.01510\.7721\\mathbin\{\\pm\}0\.01510\.7743±0\.01580\.7743\\mathbin\{\\pm\}0\.01580\.7737±0\.01840\.7737\\mathbin\{\\pm\}0\.01840\.7743±0\.01780\.7743\\mathbin\{\\pm\}0\.01780\.7717±0\.01580\.7717\\mathbin\{\\pm\}0\.01580\.7691±0\.01620\.7691\\mathbin\{\\pm\}0\.01620\.7739±0\.01950\.7739\\mathbin\{\\pm\}0\.0195TabPrep w/o cat\. interact\.0\.7893±0\.01060\.7893\\mathbin\{\\pm\}0\.01060\.7869±0\.01100\.7869\\mathbin\{\\pm\}0\.01100\.7932±0\.01040\.7932\\mathbin\{\\pm\}0\.01040\.7913±0\.01270\.7913\\mathbin\{\\pm\}0\.01270\.7923±0\.01070\.7923\\mathbin\{\\pm\}0\.01070\.7919±0\.01170\.7919\\mathbin\{\\pm\}0\.01170\.7920±0\.00940\.7920\\mathbin\{\\pm\}0\.0094TabPrep w/o OOF\-TE0\.7897±0\.00950\.7897\\mathbin\{\\pm\}0\.00950\.7844±0\.01010\.7844\\mathbin\{\\pm\}0\.01010\.7919±0\.00980\.7919\\mathbin\{\\pm\}0\.00980\.7894±0\.01170\.7894\\mathbin\{\\pm\}0\.01170\.7920±0\.00980\.7920\\mathbin\{\\pm\}0\.00980\.7920±0\.01240\.7920\\mathbin\{\\pm\}0\.01240\.7928±0\.00990\.7928\\mathbin\{\\pm\}0\.0099Shared\-context kNN0\.7925±0\.01160\.7925\\mathbin\{\\pm\}0\.01160\.7897±0\.01110\.7897\\mathbin\{\\pm\}0\.01110\.7928±0\.00950\.7928\\mathbin\{\\pm\}0\.00950\.7890±0\.01000\.7890\\mathbin\{\\pm\}0\.01000\.7897±0\.01150\.7897\\mathbin\{\\pm\}0\.01150\.7916±0\.00820\.7916\\mathbin\{\\pm\}0\.00820\.7915±0\.01060\.7915\\mathbin\{\\pm\}0\.0106OOF prediction feature0\.7893±0\.01360\.7893\\mathbin\{\\pm\}0\.01360\.7914±0\.01000\.7914\\mathbin\{\\pm\}0\.01000\.7912±0\.00940\.7912\\mathbin\{\\pm\}0\.00940\.7868±0\.01170\.7868\\mathbin\{\\pm\}0\.01170\.7870±0\.01170\.7870\\mathbin\{\\pm\}0\.01170\.7924±0\.01390\.7924\\mathbin\{\\pm\}0\.01390\.7880±0\.01340\.7880\\mathbin\{\\pm\}0\.0134Table 13:Complete TabPFN and TabICL raw metric results for Blood transfusion, metric macro f1\. Values are mean±\\mathbin\{\\pm\}sample standard deviation across the 30 paired splits\.ConditionPFN v1PFN v2PFN v2\.5PFN v2\.6PFN v3ICL v1ICL v2Identity0\.6452±0\.03210\.6452\\mathbin\{\\pm\}0\.03210\.6232±0\.03620\.6232\\mathbin\{\\pm\}0\.03620\.6367±0\.03820\.6367\\mathbin\{\\pm\}0\.03820\.6359±0\.03350\.6359\\mathbin\{\\pm\}0\.03350\.6290±0\.03980\.6290\\mathbin\{\\pm\}0\.03980\.6368±0\.03610\.6368\\mathbin\{\\pm\}0\.03610\.6389±0\.03570\.6389\\mathbin\{\\pm\}0\.0357Standard scaling0\.6452±0\.03210\.6452\\mathbin\{\\pm\}0\.03210\.6217±0\.03700\.6217\\mathbin\{\\pm\}0\.03700\.6360±0\.03700\.6360\\mathbin\{\\pm\}0\.03700\.6359±0\.03350\.6359\\mathbin\{\\pm\}0\.03350\.6273±0\.04040\.6273\\mathbin\{\\pm\}0\.04040\.6368±0\.03610\.6368\\mathbin\{\\pm\}0\.03610\.6389±0\.03570\.6389\\mathbin\{\\pm\}0\.0357Log transform0\.6378±0\.03350\.6378\\mathbin\{\\pm\}0\.03350\.6208±0\.03860\.6208\\mathbin\{\\pm\}0\.03860\.6290±0\.03470\.6290\\mathbin\{\\pm\}0\.03470\.6359±0\.03230\.6359\\mathbin\{\\pm\}0\.03230\.6255±0\.03940\.6255\\mathbin\{\\pm\}0\.03940\.6226±0\.04150\.6226\\mathbin\{\\pm\}0\.04150\.6374±0\.03610\.6374\\mathbin\{\\pm\}0\.0361Square\-root transform0\.6402±0\.03260\.6402\\mathbin\{\\pm\}0\.03260\.6189±0\.03470\.6189\\mathbin\{\\pm\}0\.03470\.6315±0\.03040\.6315\\mathbin\{\\pm\}0\.03040\.6345±0\.03330\.6345\\mathbin\{\\pm\}0\.03330\.6271±0\.04010\.6271\\mathbin\{\\pm\}0\.04010\.6286±0\.03960\.6286\\mathbin\{\\pm\}0\.03960\.6378±0\.03420\.6378\\mathbin\{\\pm\}0\.0342Box–Cox0\.6465±0\.03290\.6465\\mathbin\{\\pm\}0\.03290\.6155±0\.04240\.6155\\mathbin\{\\pm\}0\.04240\.6321±0\.03440\.6321\\mathbin\{\\pm\}0\.03440\.6376±0\.03740\.6376\\mathbin\{\\pm\}0\.03740\.6237±0\.03980\.6237\\mathbin\{\\pm\}0\.03980\.6260±0\.04310\.6260\\mathbin\{\\pm\}0\.04310\.6397±0\.03530\.6397\\mathbin\{\\pm\}0\.0353Min–max scaling0\.6452±0\.03210\.6452\\mathbin\{\\pm\}0\.03210\.6203±0\.03950\.6203\\mathbin\{\\pm\}0\.03950\.6363±0\.03940\.6363\\mathbin\{\\pm\}0\.03940\.6359±0\.03350\.6359\\mathbin\{\\pm\}0\.03350\.6270±0\.04110\.6270\\mathbin\{\\pm\}0\.04110\.6371±0\.03580\.6371\\mathbin\{\\pm\}0\.03580\.6389±0\.03570\.6389\\mathbin\{\\pm\}0\.0357One\-hot encoding———————Ordinal encoding———————Frequency encoding———————Target encoding———————Categorical crosses———————Equal\-width binning0\.6145±0\.03780\.6145\\mathbin\{\\pm\}0\.03780\.5659±0\.05190\.5659\\mathbin\{\\pm\}0\.05190\.5858±0\.05280\.5858\\mathbin\{\\pm\}0\.05280\.5953±0\.04660\.5953\\mathbin\{\\pm\}0\.04660\.5853±0\.04600\.5853\\mathbin\{\\pm\}0\.04600\.6088±0\.03590\.6088\\mathbin\{\\pm\}0\.03590\.6016±0\.04330\.6016\\mathbin\{\\pm\}0\.0433Equal\-frequency binning0\.6163±0\.03080\.6163\\mathbin\{\\pm\}0\.03080\.5886±0\.03900\.5886\\mathbin\{\\pm\}0\.03900\.6024±0\.04100\.6024\\mathbin\{\\pm\}0\.04100\.6204±0\.04330\.6204\\mathbin\{\\pm\}0\.04330\.5984±0\.04640\.5984\\mathbin\{\\pm\}0\.04640\.5919±0\.04460\.5919\\mathbin\{\\pm\}0\.04460\.6091±0\.04120\.6091\\mathbin\{\\pm\}0\.0412Numeric interactions0\.6452±0\.03210\.6452\\mathbin\{\\pm\}0\.03210\.6232±0\.03620\.6232\\mathbin\{\\pm\}0\.03620\.6367±0\.03820\.6367\\mathbin\{\\pm\}0\.03820\.6359±0\.03350\.6359\\mathbin\{\\pm\}0\.03350\.6290±0\.03980\.6290\\mathbin\{\\pm\}0\.03980\.6368±0\.03610\.6368\\mathbin\{\\pm\}0\.03610\.6389±0\.03570\.6389\\mathbin\{\\pm\}0\.0357Group aggregation———————Variance filter0\.6452±0\.03210\.6452\\mathbin\{\\pm\}0\.03210\.6232±0\.03620\.6232\\mathbin\{\\pm\}0\.03620\.6367±0\.03820\.6367\\mathbin\{\\pm\}0\.03820\.6359±0\.03350\.6359\\mathbin\{\\pm\}0\.03350\.6290±0\.03980\.6290\\mathbin\{\\pm\}0\.03980\.6368±0\.03610\.6368\\mathbin\{\\pm\}0\.03610\.6389±0\.03570\.6389\\mathbin\{\\pm\}0\.0357Collinearity filter0\.6497±0\.02890\.6497\\mathbin\{\\pm\}0\.02890\.6188±0\.03950\.6188\\mathbin\{\\pm\}0\.03950\.6343±0\.03800\.6343\\mathbin\{\\pm\}0\.03800\.6301±0\.03170\.6301\\mathbin\{\\pm\}0\.03170\.6275±0\.03400\.6275\\mathbin\{\\pm\}0\.03400\.6201±0\.04260\.6201\\mathbin\{\\pm\}0\.04260\.6435±0\.03480\.6435\\mathbin\{\\pm\}0\.0348PCA0\.6529±0\.02860\.6529\\mathbin\{\\pm\}0\.02860\.6337±0\.03820\.6337\\mathbin\{\\pm\}0\.03820\.6423±0\.03440\.6423\\mathbin\{\\pm\}0\.03440\.6458±0\.03440\.6458\\mathbin\{\\pm\}0\.03440\.6387±0\.03370\.6387\\mathbin\{\\pm\}0\.03370\.6436±0\.02680\.6436\\mathbin\{\\pm\}0\.02680\.6456±0\.03060\.6456\\mathbin\{\\pm\}0\.0306Supervised selection0\.5014±0\.03870\.5014\\mathbin\{\\pm\}0\.03870\.5115±0\.03530\.5115\\mathbin\{\\pm\}0\.03530\.5222±0\.03490\.5222\\mathbin\{\\pm\}0\.03490\.5162±0\.04350\.5162\\mathbin\{\\pm\}0\.04350\.5054±0\.04070\.5054\\mathbin\{\\pm\}0\.04070\.4944±0\.03510\.4944\\mathbin\{\\pm\}0\.03510\.5257±0\.03650\.5257\\mathbin\{\\pm\}0\.0365TabPrep full0\.6192±0\.04330\.6192\\mathbin\{\\pm\}0\.04330\.6120±0\.03650\.6120\\mathbin\{\\pm\}0\.03650\.6369±0\.03240\.6369\\mathbin\{\\pm\}0\.03240\.6536±0\.02670\.6536\\mathbin\{\\pm\}0\.02670\.6358±0\.03200\.6358\\mathbin\{\\pm\}0\.03200\.6419±0\.02800\.6419\\mathbin\{\\pm\}0\.02800\.6398±0\.03400\.6398\\mathbin\{\\pm\}0\.0340TabPrep w/o groupby0\.6169±0\.04510\.6169\\mathbin\{\\pm\}0\.04510\.6121±0\.03790\.6121\\mathbin\{\\pm\}0\.03790\.6366±0\.03580\.6366\\mathbin\{\\pm\}0\.03580\.6523±0\.02780\.6523\\mathbin\{\\pm\}0\.02780\.6375±0\.03730\.6375\\mathbin\{\\pm\}0\.03730\.6411±0\.02900\.6411\\mathbin\{\\pm\}0\.02900\.6400±0\.03290\.6400\\mathbin\{\\pm\}0\.0329TabPrep w/o RSFC0\.6200±0\.04250\.6200\\mathbin\{\\pm\}0\.04250\.6092±0\.04590\.6092\\mathbin\{\\pm\}0\.04590\.6373±0\.03350\.6373\\mathbin\{\\pm\}0\.03350\.6515±0\.02550\.6515\\mathbin\{\\pm\}0\.02550\.6372±0\.03600\.6372\\mathbin\{\\pm\}0\.03600\.6425±0\.02990\.6425\\mathbin\{\\pm\}0\.02990\.6399±0\.02960\.6399\\mathbin\{\\pm\}0\.0296TabPrep w/o arithmetic0\.5850±0\.03410\.5850\\mathbin\{\\pm\}0\.03410\.5870±0\.04090\.5870\\mathbin\{\\pm\}0\.04090\.5957±0\.04400\.5957\\mathbin\{\\pm\}0\.04400\.6067±0\.03920\.6067\\mathbin\{\\pm\}0\.03920\.5925±0\.03980\.5925\\mathbin\{\\pm\}0\.03980\.5736±0\.04870\.5736\\mathbin\{\\pm\}0\.04870\.6018±0\.03860\.6018\\mathbin\{\\pm\}0\.0386TabPrep w/o cat\. interact\.0\.6186±0\.04200\.6186\\mathbin\{\\pm\}0\.04200\.6110±0\.04880\.6110\\mathbin\{\\pm\}0\.04880\.6394±0\.03250\.6394\\mathbin\{\\pm\}0\.03250\.6538±0\.02580\.6538\\mathbin\{\\pm\}0\.02580\.6365±0\.03460\.6365\\mathbin\{\\pm\}0\.03460\.6409±0\.02740\.6409\\mathbin\{\\pm\}0\.02740\.6395±0\.03220\.6395\\mathbin\{\\pm\}0\.0322TabPrep w/o OOF\-TE0\.6204±0\.04180\.6204\\mathbin\{\\pm\}0\.04180\.6062±0\.04770\.6062\\mathbin\{\\pm\}0\.04770\.6377±0\.03430\.6377\\mathbin\{\\pm\}0\.03430\.6496±0\.02860\.6496\\mathbin\{\\pm\}0\.02860\.6359±0\.03500\.6359\\mathbin\{\\pm\}0\.03500\.6407±0\.03150\.6407\\mathbin\{\\pm\}0\.03150\.6409±0\.03120\.6409\\mathbin\{\\pm\}0\.0312Shared\-context kNN0\.6451±0\.03160\.6451\\mathbin\{\\pm\}0\.03160\.6244±0\.03780\.6244\\mathbin\{\\pm\}0\.03780\.6362±0\.03670\.6362\\mathbin\{\\pm\}0\.03670\.6343±0\.02960\.6343\\mathbin\{\\pm\}0\.02960\.6292±0\.03880\.6292\\mathbin\{\\pm\}0\.03880\.6373±0\.03290\.6373\\mathbin\{\\pm\}0\.03290\.6394±0\.03420\.6394\\mathbin\{\\pm\}0\.0342OOF prediction feature0\.6374±0\.03270\.6374\\mathbin\{\\pm\}0\.03270\.6354±0\.03780\.6354\\mathbin\{\\pm\}0\.03780\.6307±0\.04700\.6307\\mathbin\{\\pm\}0\.04700\.6288±0\.03390\.6288\\mathbin\{\\pm\}0\.03390\.6274±0\.03270\.6274\\mathbin\{\\pm\}0\.03270\.6468±0\.03530\.6468\\mathbin\{\\pm\}0\.03530\.6378±0\.03100\.6378\\mathbin\{\\pm\}0\.0310Table 14:Complete raw metric results for Concrete strength, metric r2\. Values are mean±\\mathbin\{\\pm\}sample standard deviation across the 30 paired splits\.ConditionPFN v2PFN v2\.5PFN v2\.6PFN v3ICL v2Identity0\.9347±0\.01260\.9347\\mathbin\{\\pm\}0\.01260\.9394±0\.01240\.9394\\mathbin\{\\pm\}0\.01240\.9405±0\.01190\.9405\\mathbin\{\\pm\}0\.01190\.9411±0\.01250\.9411\\mathbin\{\\pm\}0\.01250\.9424±0\.01330\.9424\\mathbin\{\\pm\}0\.0133Standard scaling0\.9338±0\.01280\.9338\\mathbin\{\\pm\}0\.01280\.9393±0\.01240\.9393\\mathbin\{\\pm\}0\.01240\.9387±0\.01180\.9387\\mathbin\{\\pm\}0\.01180\.9411±0\.01250\.9411\\mathbin\{\\pm\}0\.01250\.9424±0\.01330\.9424\\mathbin\{\\pm\}0\.0133Log transform0\.9344±0\.01300\.9344\\mathbin\{\\pm\}0\.01300\.9400±0\.01240\.9400\\mathbin\{\\pm\}0\.01240\.9399±0\.01210\.9399\\mathbin\{\\pm\}0\.01210\.9427±0\.01240\.9427\\mathbin\{\\pm\}0\.01240\.9430±0\.01280\.9430\\mathbin\{\\pm\}0\.0128Square\-root transform0\.9347±0\.01270\.9347\\mathbin\{\\pm\}0\.01270\.9402±0\.01270\.9402\\mathbin\{\\pm\}0\.01270\.9402±0\.01200\.9402\\mathbin\{\\pm\}0\.01200\.9421±0\.01270\.9421\\mathbin\{\\pm\}0\.01270\.9425±0\.01320\.9425\\mathbin\{\\pm\}0\.0132Box–Cox0\.9352±0\.01250\.9352\\mathbin\{\\pm\}0\.01250\.9413±0\.01210\.9413\\mathbin\{\\pm\}0\.01210\.9409±0\.01240\.9409\\mathbin\{\\pm\}0\.01240\.9419±0\.01230\.9419\\mathbin\{\\pm\}0\.01230\.9433±0\.01290\.9433\\mathbin\{\\pm\}0\.0129Min–max scaling0\.9339±0\.01290\.9339\\mathbin\{\\pm\}0\.01290\.9394±0\.01250\.9394\\mathbin\{\\pm\}0\.01250\.9403±0\.01210\.9403\\mathbin\{\\pm\}0\.01210\.9412±0\.01250\.9412\\mathbin\{\\pm\}0\.01250\.9424±0\.01330\.9424\\mathbin\{\\pm\}0\.0133One\-hot encoding—————Ordinal encoding—————Frequency encoding—————Target encoding—————Categorical crosses—————Equal\-width binning0\.7327±0\.02520\.7327\\mathbin\{\\pm\}0\.02520\.7336±0\.02540\.7336\\mathbin\{\\pm\}0\.02540\.7336±0\.02700\.7336\\mathbin\{\\pm\}0\.02700\.7406±0\.02530\.7406\\mathbin\{\\pm\}0\.02530\.7477±0\.02400\.7477\\mathbin\{\\pm\}0\.0240Equal\-frequency binning0\.9269±0\.01230\.9269\\mathbin\{\\pm\}0\.01230\.9298±0\.01380\.9298\\mathbin\{\\pm\}0\.01380\.9309±0\.01280\.9309\\mathbin\{\\pm\}0\.01280\.9348±0\.01400\.9348\\mathbin\{\\pm\}0\.01400\.9304±0\.01420\.9304\\mathbin\{\\pm\}0\.0142Numeric interactions0\.9348±0\.01180\.9348\\mathbin\{\\pm\}0\.01180\.9381±0\.01130\.9381\\mathbin\{\\pm\}0\.01130\.9402±0\.01170\.9402\\mathbin\{\\pm\}0\.01170\.9380±0\.01270\.9380\\mathbin\{\\pm\}0\.01270\.9386±0\.01130\.9386\\mathbin\{\\pm\}0\.0113Group aggregation—————Variance filter0\.9347±0\.01260\.9347\\mathbin\{\\pm\}0\.01260\.9394±0\.01240\.9394\\mathbin\{\\pm\}0\.01240\.9405±0\.01190\.9405\\mathbin\{\\pm\}0\.01190\.9411±0\.01250\.9411\\mathbin\{\\pm\}0\.01250\.9424±0\.01330\.9424\\mathbin\{\\pm\}0\.0133Collinearity filter0\.9347±0\.01260\.9347\\mathbin\{\\pm\}0\.01260\.9394±0\.01240\.9394\\mathbin\{\\pm\}0\.01240\.9405±0\.01190\.9405\\mathbin\{\\pm\}0\.01190\.9411±0\.01250\.9411\\mathbin\{\\pm\}0\.01250\.9424±0\.01330\.9424\\mathbin\{\\pm\}0\.0133PCA0\.9180±0\.01110\.9180\\mathbin\{\\pm\}0\.01110\.9214±0\.01050\.9214\\mathbin\{\\pm\}0\.01050\.9156±0\.01150\.9156\\mathbin\{\\pm\}0\.01150\.9274±0\.01290\.9274\\mathbin\{\\pm\}0\.01290\.9294±0\.01180\.9294\\mathbin\{\\pm\}0\.0118Supervised selection0\.8752±0\.02560\.8752\\mathbin\{\\pm\}0\.02560\.8666±0\.02750\.8666\\mathbin\{\\pm\}0\.02750\.8887±0\.02270\.8887\\mathbin\{\\pm\}0\.02270\.8990±0\.02120\.8990\\mathbin\{\\pm\}0\.02120\.8880±0\.02230\.8880\\mathbin\{\\pm\}0\.0223TabPrep full0\.9294±0\.01260\.9294\\mathbin\{\\pm\}0\.01260\.9357±0\.01250\.9357\\mathbin\{\\pm\}0\.01250\.9365±0\.01350\.9365\\mathbin\{\\pm\}0\.01350\.9334±0\.01290\.9334\\mathbin\{\\pm\}0\.01290\.9321±0\.01210\.9321\\mathbin\{\\pm\}0\.0121TabPrep w/o groupby0\.9296±0\.01280\.9296\\mathbin\{\\pm\}0\.01280\.9358±0\.01280\.9358\\mathbin\{\\pm\}0\.01280\.9364±0\.01300\.9364\\mathbin\{\\pm\}0\.01300\.9337±0\.01250\.9337\\mathbin\{\\pm\}0\.01250\.9320±0\.01250\.9320\\mathbin\{\\pm\}0\.0125TabPrep w/o RSFC0\.9295±0\.01270\.9295\\mathbin\{\\pm\}0\.01270\.9359±0\.01250\.9359\\mathbin\{\\pm\}0\.01250\.9363±0\.01300\.9363\\mathbin\{\\pm\}0\.01300\.9337±0\.01240\.9337\\mathbin\{\\pm\}0\.01240\.9324±0\.01200\.9324\\mathbin\{\\pm\}0\.0120TabPrep w/o arithmetic0\.9163±0\.01430\.9163\\mathbin\{\\pm\}0\.01430\.9237±0\.01170\.9237\\mathbin\{\\pm\}0\.01170\.9202±0\.01350\.9202\\mathbin\{\\pm\}0\.01350\.9088±0\.01390\.9088\\mathbin\{\\pm\}0\.01390\.8947±0\.01830\.8947\\mathbin\{\\pm\}0\.0183TabPrep w/o cat\. interact\.0\.9293±0\.01260\.9293\\mathbin\{\\pm\}0\.01260\.9354±0\.01260\.9354\\mathbin\{\\pm\}0\.01260\.9363±0\.01300\.9363\\mathbin\{\\pm\}0\.01300\.9337±0\.01290\.9337\\mathbin\{\\pm\}0\.01290\.9316±0\.01200\.9316\\mathbin\{\\pm\}0\.0120TabPrep w/o OOF\-TE0\.9294±0\.01310\.9294\\mathbin\{\\pm\}0\.01310\.9357±0\.01270\.9357\\mathbin\{\\pm\}0\.01270\.9363±0\.01300\.9363\\mathbin\{\\pm\}0\.01300\.9334±0\.01310\.9334\\mathbin\{\\pm\}0\.01310\.9322±0\.01250\.9322\\mathbin\{\\pm\}0\.0125Shared\-context kNN0\.9349±0\.01250\.9349\\mathbin\{\\pm\}0\.01250\.9394±0\.01250\.9394\\mathbin\{\\pm\}0\.01250\.9405±0\.01180\.9405\\mathbin\{\\pm\}0\.01180\.9411±0\.01260\.9411\\mathbin\{\\pm\}0\.01260\.9425±0\.01320\.9425\\mathbin\{\\pm\}0\.0132OOF prediction feature0\.9319±0\.01300\.9319\\mathbin\{\\pm\}0\.01300\.9340±0\.01290\.9340\\mathbin\{\\pm\}0\.01290\.9371±0\.01280\.9371\\mathbin\{\\pm\}0\.01280\.9230±0\.01300\.9230\\mathbin\{\\pm\}0\.01300\.9372±0\.01270\.9372\\mathbin\{\\pm\}0\.0127Table 15:Complete raw metric results for Concrete strength, metric rmse\. Values are mean±\\mathbin\{\\pm\}sample standard deviation across the 30 paired splits\.ConditionPFN v2PFN v2\.5PFN v2\.6PFN v3ICL v2Identity4\.2382±0\.39264\.2382\\mathbin\{\\pm\}0\.39264\.0788±0\.37494\.0788\\mathbin\{\\pm\}0\.37494\.0434±0\.38264\.0434\\mathbin\{\\pm\}0\.38264\.0203±0\.40374\.0203\\mathbin\{\\pm\}0\.40373\.9739±0\.43783\.9739\\mathbin\{\\pm\}0\.4378Standard scaling4\.2664±0\.38564\.2664\\mathbin\{\\pm\}0\.38564\.0818±0\.37344\.0818\\mathbin\{\\pm\}0\.37344\.1077±0\.37354\.1077\\mathbin\{\\pm\}0\.37354\.0202±0\.40314\.0202\\mathbin\{\\pm\}0\.40313\.9739±0\.43783\.9739\\mathbin\{\\pm\}0\.4378Log transform4\.2486±0\.40004\.2486\\mathbin\{\\pm\}0\.40004\.0588±0\.37784\.0588\\mathbin\{\\pm\}0\.37784\.0637±0\.38544\.0637\\mathbin\{\\pm\}0\.38543\.9656±0\.40673\.9656\\mathbin\{\\pm\}0\.40673\.9543±0\.42533\.9543\\mathbin\{\\pm\}0\.4253Square\-root transform4\.2393±0\.39334\.2393\\mathbin\{\\pm\}0\.39334\.0500±0\.38534\.0500\\mathbin\{\\pm\}0\.38534\.0526±0\.38424\.0526\\mathbin\{\\pm\}0\.38423\.9848±0\.41273\.9848\\mathbin\{\\pm\}0\.41273\.9694±0\.43563\.9694\\mathbin\{\\pm\}0\.4356Box–Cox4\.2222±0\.38294\.2222\\mathbin\{\\pm\}0\.38294\.0160±0\.37514\.0160\\mathbin\{\\pm\}0\.37514\.0297±0\.40264\.0297\\mathbin\{\\pm\}0\.40263\.9920±0\.39793\.9920\\mathbin\{\\pm\}0\.39793\.9420±0\.42903\.9420\\mathbin\{\\pm\}0\.4290Min–max scaling4\.2651±0\.39344\.2651\\mathbin\{\\pm\}0\.39344\.0799±0\.37654\.0799\\mathbin\{\\pm\}0\.37654\.0495±0\.38264\.0495\\mathbin\{\\pm\}0\.38264\.0193±0\.40254\.0193\\mathbin\{\\pm\}0\.40253\.9739±0\.43783\.9739\\mathbin\{\\pm\}0\.4378One\-hot encoding—————Ordinal encoding—————Frequency encoding—————Target encoding—————Categorical crosses—————Equal\-width binning8\.6054±0\.39388\.6054\\mathbin\{\\pm\}0\.39388\.5900±0\.39098\.5900\\mathbin\{\\pm\}0\.39098\.5892±0\.40778\.5892\\mathbin\{\\pm\}0\.40778\.4761±0\.38958\.4761\\mathbin\{\\pm\}0\.38958\.3598±0\.38788\.3598\\mathbin\{\\pm\}0\.3878Equal\-frequency binning4\.4873±0\.34364\.4873\\mathbin\{\\pm\}0\.34364\.3910±0\.38274\.3910\\mathbin\{\\pm\}0\.38274\.3586±0\.36404\.3586\\mathbin\{\\pm\}0\.36404\.2308±0\.42684\.2308\\mathbin\{\\pm\}0\.42684\.3742±0\.43034\.3742\\mathbin\{\\pm\}0\.4303Numeric interactions4\.2355±0\.36544\.2355\\mathbin\{\\pm\}0\.36544\.1259±0\.34294\.1259\\mathbin\{\\pm\}0\.34294\.0528±0\.36704\.0528\\mathbin\{\\pm\}0\.36704\.1257±0\.38534\.1257\\mathbin\{\\pm\}0\.38534\.1130±0\.36004\.1130\\mathbin\{\\pm\}0\.3600Group aggregation—————Variance filter4\.2382±0\.39264\.2382\\mathbin\{\\pm\}0\.39264\.0788±0\.37494\.0788\\mathbin\{\\pm\}0\.37494\.0434±0\.38264\.0434\\mathbin\{\\pm\}0\.38264\.0203±0\.40374\.0203\\mathbin\{\\pm\}0\.40373\.9739±0\.43783\.9739\\mathbin\{\\pm\}0\.4378Collinearity filter4\.2382±0\.39264\.2382\\mathbin\{\\pm\}0\.39264\.0788±0\.37494\.0788\\mathbin\{\\pm\}0\.37494\.0434±0\.38264\.0434\\mathbin\{\\pm\}0\.38264\.0203±0\.40374\.0203\\mathbin\{\\pm\}0\.40373\.9739±0\.43783\.9739\\mathbin\{\\pm\}0\.4378PCA4\.7594±0\.29514\.7594\\mathbin\{\\pm\}0\.29514\.6608±0\.31274\.6608\\mathbin\{\\pm\}0\.31274\.8293±0\.32354\.8293\\mathbin\{\\pm\}0\.32354\.4717±0\.37954\.4717\\mathbin\{\\pm\}0\.37954\.4118±0\.36414\.4118\\mathbin\{\\pm\}0\.3641Supervised selection5\.8487±0\.60635\.8487\\mathbin\{\\pm\}0\.60636\.0465±0\.63976\.0465\\mathbin\{\\pm\}0\.63975\.5291±0\.58405\.5291\\mathbin\{\\pm\}0\.58405\.2634±0\.56055\.2634\\mathbin\{\\pm\}0\.56055\.5454±0\.56605\.5454\\mathbin\{\\pm\}0\.5660TabPrep full4\.4094±0\.37644\.4094\\mathbin\{\\pm\}0\.37644\.2053±0\.38344\.2053\\mathbin\{\\pm\}0\.38344\.1756±0\.41814\.1756\\mathbin\{\\pm\}0\.41814\.2795±0\.38254\.2795\\mathbin\{\\pm\}0\.38254\.3269±0\.39974\.3269\\mathbin\{\\pm\}0\.3997TabPrep w/o groupby4\.4044±0\.38774\.4044\\mathbin\{\\pm\}0\.38774\.2029±0\.39924\.2029\\mathbin\{\\pm\}0\.39924\.1811±0\.41194\.1811\\mathbin\{\\pm\}0\.41194\.2723±0\.37424\.2723\\mathbin\{\\pm\}0\.37424\.3283±0\.40164\.3283\\mathbin\{\\pm\}0\.4016TabPrep w/o RSFC4\.4063±0\.38034\.4063\\mathbin\{\\pm\}0\.38034\.2001±0\.38474\.2001\\mathbin\{\\pm\}0\.38474\.1816±0\.40054\.1816\\mathbin\{\\pm\}0\.40054\.2706±0\.36474\.2706\\mathbin\{\\pm\}0\.36474\.3157±0\.38754\.3157\\mathbin\{\\pm\}0\.3875TabPrep w/o arithmetic4\.7995±0\.34774\.7995\\mathbin\{\\pm\}0\.34774\.5890±0\.31154\.5890\\mathbin\{\\pm\}0\.31154\.6886±0\.35904\.6886\\mathbin\{\\pm\}0\.35905\.0171±0\.35725\.0171\\mathbin\{\\pm\}0\.35725\.3848±0\.41285\.3848\\mathbin\{\\pm\}0\.4128TabPrep w/o cat\. interact\.4\.4136±0\.38374\.4136\\mathbin\{\\pm\}0\.38374\.2154±0\.38704\.2154\\mathbin\{\\pm\}0\.38704\.1846±0\.40854\.1846\\mathbin\{\\pm\}0\.40854\.2695±0\.38074\.2695\\mathbin\{\\pm\}0\.38074\.3416±0\.39134\.3416\\mathbin\{\\pm\}0\.3913TabPrep w/o OOF\-TE4\.4093±0\.38634\.4093\\mathbin\{\\pm\}0\.38634\.2042±0\.39314\.2042\\mathbin\{\\pm\}0\.39314\.1843±0\.40344\.1843\\mathbin\{\\pm\}0\.40344\.2799±0\.38484\.2799\\mathbin\{\\pm\}0\.38484\.3221±0\.40214\.3221\\mathbin\{\\pm\}0\.4021Shared\-context kNN4\.2340±0\.38954\.2340\\mathbin\{\\pm\}0\.38954\.0798±0\.37554\.0798\\mathbin\{\\pm\}0\.37554\.0453±0\.37944\.0453\\mathbin\{\\pm\}0\.37944\.0210±0\.40624\.0210\\mathbin\{\\pm\}0\.40623\.9716±0\.43513\.9716\\mathbin\{\\pm\}0\.4351OOF prediction feature4\.3278±0\.40794\.3278\\mathbin\{\\pm\}0\.40794\.2597±0\.39204\.2597\\mathbin\{\\pm\}0\.39204\.1561±0\.39274\.1561\\mathbin\{\\pm\}0\.39274\.6059±0\.39834\.6059\\mathbin\{\\pm\}0\.39834\.1531±0\.39984\.1531\\mathbin\{\\pm\}0\.3998Table 16:Complete TabPFN and TabICL raw metric results for Credit\-g, metric accuracy\. Values are mean±\\mathbin\{\\pm\}sample standard deviation across the 30 paired splits\.ConditionPFN v1PFN v2PFN v2\.5PFN v2\.6PFN v3ICL v1ICL v2Identity0\.7332±0\.01240\.7332\\mathbin\{\\pm\}0\.01240\.7557±0\.02020\.7557\\mathbin\{\\pm\}0\.02020\.7584±0\.02060\.7584\\mathbin\{\\pm\}0\.02060\.7583±0\.01940\.7583\\mathbin\{\\pm\}0\.01940\.7583±0\.01890\.7583\\mathbin\{\\pm\}0\.01890\.7572±0\.01870\.7572\\mathbin\{\\pm\}0\.01870\.7596±0\.01850\.7596\\mathbin\{\\pm\}0\.0185Standard scaling0\.7348±0\.01300\.7348\\mathbin\{\\pm\}0\.01300\.7560±0\.02150\.7560\\mathbin\{\\pm\}0\.02150\.7582±0\.02120\.7582\\mathbin\{\\pm\}0\.02120\.7580±0\.01980\.7580\\mathbin\{\\pm\}0\.01980\.7590±0\.01930\.7590\\mathbin\{\\pm\}0\.01930\.7572±0\.01790\.7572\\mathbin\{\\pm\}0\.01790\.7596±0\.01850\.7596\\mathbin\{\\pm\}0\.0185Log transform0\.7342±0\.01380\.7342\\mathbin\{\\pm\}0\.01380\.7565±0\.02380\.7565\\mathbin\{\\pm\}0\.02380\.7582±0\.01970\.7582\\mathbin\{\\pm\}0\.01970\.7597±0\.02030\.7597\\mathbin\{\\pm\}0\.02030\.7604±0\.01810\.7604\\mathbin\{\\pm\}0\.01810\.7554±0\.01650\.7554\\mathbin\{\\pm\}0\.01650\.7584±0\.02110\.7584\\mathbin\{\\pm\}0\.0211Square\-root transform0\.7346±0\.01260\.7346\\mathbin\{\\pm\}0\.01260\.7560±0\.01980\.7560\\mathbin\{\\pm\}0\.01980\.7571±0\.01870\.7571\\mathbin\{\\pm\}0\.01870\.7593±0\.01980\.7593\\mathbin\{\\pm\}0\.01980\.7612±0\.01950\.7612\\mathbin\{\\pm\}0\.01950\.7566±0\.01760\.7566\\mathbin\{\\pm\}0\.01760\.7596±0\.01980\.7596\\mathbin\{\\pm\}0\.0198Box–Cox0\.7331±0\.01470\.7331\\mathbin\{\\pm\}0\.01470\.7547±0\.02570\.7547\\mathbin\{\\pm\}0\.02570\.7582±0\.02050\.7582\\mathbin\{\\pm\}0\.02050\.7588±0\.02100\.7588\\mathbin\{\\pm\}0\.02100\.7591±0\.01970\.7591\\mathbin\{\\pm\}0\.01970\.7557±0\.01720\.7557\\mathbin\{\\pm\}0\.01720\.7575±0\.01980\.7575\\mathbin\{\\pm\}0\.0198Min–max scaling0\.7348±0\.01300\.7348\\mathbin\{\\pm\}0\.01300\.7561±0\.02130\.7561\\mathbin\{\\pm\}0\.02130\.7582±0\.02060\.7582\\mathbin\{\\pm\}0\.02060\.7579±0\.01980\.7579\\mathbin\{\\pm\}0\.01980\.7607±0\.01940\.7607\\mathbin\{\\pm\}0\.01940\.7569±0\.01830\.7569\\mathbin\{\\pm\}0\.01830\.7596±0\.01850\.7596\\mathbin\{\\pm\}0\.0185One\-hot encoding0\.7579±0\.01950\.7579\\mathbin\{\\pm\}0\.01950\.7497±0\.01210\.7497\\mathbin\{\\pm\}0\.01210\.7558±0\.01530\.7558\\mathbin\{\\pm\}0\.01530\.7536±0\.01410\.7536\\mathbin\{\\pm\}0\.01410\.7591±0\.01710\.7591\\mathbin\{\\pm\}0\.01710\.7630±0\.01890\.7630\\mathbin\{\\pm\}0\.01890\.7571±0\.01880\.7571\\mathbin\{\\pm\}0\.0188Ordinal encoding0\.7341±0\.01340\.7341\\mathbin\{\\pm\}0\.01340\.7535±0\.01740\.7535\\mathbin\{\\pm\}0\.01740\.7579±0\.01800\.7579\\mathbin\{\\pm\}0\.01800\.7585±0\.01740\.7585\\mathbin\{\\pm\}0\.01740\.7599±0\.01890\.7599\\mathbin\{\\pm\}0\.01890\.7581±0\.01550\.7581\\mathbin\{\\pm\}0\.01550\.7595±0\.01870\.7595\\mathbin\{\\pm\}0\.0187Frequency encoding0\.7381±0\.01610\.7381\\mathbin\{\\pm\}0\.01610\.7551±0\.02120\.7551\\mathbin\{\\pm\}0\.02120\.7594±0\.02040\.7594\\mathbin\{\\pm\}0\.02040\.7588±0\.02100\.7588\\mathbin\{\\pm\}0\.02100\.7617±0\.01910\.7617\\mathbin\{\\pm\}0\.01910\.7565±0\.01670\.7565\\mathbin\{\\pm\}0\.01670\.7613±0\.01680\.7613\\mathbin\{\\pm\}0\.0168Target encoding0\.7487±0\.01860\.7487\\mathbin\{\\pm\}0\.01860\.7553±0\.02030\.7553\\mathbin\{\\pm\}0\.02030\.7560±0\.01980\.7560\\mathbin\{\\pm\}0\.01980\.7503±0\.02010\.7503\\mathbin\{\\pm\}0\.02010\.7551±0\.01970\.7551\\mathbin\{\\pm\}0\.01970\.7613±0\.02120\.7613\\mathbin\{\\pm\}0\.02120\.7481±0\.01750\.7481\\mathbin\{\\pm\}0\.0175Categorical crosses0\.7482±0\.02440\.7482\\mathbin\{\\pm\}0\.02440\.7534±0\.02210\.7534\\mathbin\{\\pm\}0\.02210\.7583±0\.01960\.7583\\mathbin\{\\pm\}0\.01960\.7561±0\.02370\.7561\\mathbin\{\\pm\}0\.02370\.7549±0\.02240\.7549\\mathbin\{\\pm\}0\.02240\.7483±0\.02270\.7483\\mathbin\{\\pm\}0\.02270\.7579±0\.02140\.7579\\mathbin\{\\pm\}0\.0214Equal\-width binning0\.7327±0\.01270\.7327\\mathbin\{\\pm\}0\.01270\.7522±0\.01790\.7522\\mathbin\{\\pm\}0\.01790\.7548±0\.01890\.7548\\mathbin\{\\pm\}0\.01890\.7534±0\.02090\.7534\\mathbin\{\\pm\}0\.02090\.7547±0\.01790\.7547\\mathbin\{\\pm\}0\.01790\.7544±0\.01840\.7544\\mathbin\{\\pm\}0\.01840\.7543±0\.01890\.7543\\mathbin\{\\pm\}0\.0189Equal\-frequency binning0\.7313±0\.01430\.7313\\mathbin\{\\pm\}0\.01430\.7499±0\.02210\.7499\\mathbin\{\\pm\}0\.02210\.7525±0\.01840\.7525\\mathbin\{\\pm\}0\.01840\.7569±0\.01950\.7569\\mathbin\{\\pm\}0\.01950\.7565±0\.02130\.7565\\mathbin\{\\pm\}0\.02130\.7527±0\.01770\.7527\\mathbin\{\\pm\}0\.01770\.7571±0\.01770\.7571\\mathbin\{\\pm\}0\.0177Numeric interactions0\.7332±0\.01240\.7332\\mathbin\{\\pm\}0\.01240\.7557±0\.02020\.7557\\mathbin\{\\pm\}0\.02020\.7584±0\.02060\.7584\\mathbin\{\\pm\}0\.02060\.7583±0\.01940\.7583\\mathbin\{\\pm\}0\.01940\.7583±0\.01890\.7583\\mathbin\{\\pm\}0\.01890\.7572±0\.01870\.7572\\mathbin\{\\pm\}0\.01870\.7596±0\.01850\.7596\\mathbin\{\\pm\}0\.0185Group aggregation0\.7470±0\.02140\.7470\\mathbin\{\\pm\}0\.02140\.7576±0\.01720\.7576\\mathbin\{\\pm\}0\.01720\.7621±0\.02110\.7621\\mathbin\{\\pm\}0\.02110\.7574±0\.02160\.7574\\mathbin\{\\pm\}0\.02160\.7571±0\.01850\.7571\\mathbin\{\\pm\}0\.01850\.7525±0\.01950\.7525\\mathbin\{\\pm\}0\.01950\.7526±0\.02100\.7526\\mathbin\{\\pm\}0\.0210Variance filter0\.7332±0\.01240\.7332\\mathbin\{\\pm\}0\.01240\.7557±0\.02020\.7557\\mathbin\{\\pm\}0\.02020\.7584±0\.02060\.7584\\mathbin\{\\pm\}0\.02060\.7583±0\.01940\.7583\\mathbin\{\\pm\}0\.01940\.7583±0\.01890\.7583\\mathbin\{\\pm\}0\.01890\.7572±0\.01870\.7572\\mathbin\{\\pm\}0\.01870\.7596±0\.01850\.7596\\mathbin\{\\pm\}0\.0185Collinearity filter0\.7332±0\.01240\.7332\\mathbin\{\\pm\}0\.01240\.7557±0\.02020\.7557\\mathbin\{\\pm\}0\.02020\.7584±0\.02060\.7584\\mathbin\{\\pm\}0\.02060\.7583±0\.01940\.7583\\mathbin\{\\pm\}0\.01940\.7583±0\.01890\.7583\\mathbin\{\\pm\}0\.01890\.7572±0\.01870\.7572\\mathbin\{\\pm\}0\.01870\.7596±0\.01850\.7596\\mathbin\{\\pm\}0\.0185PCA0\.7341±0\.01320\.7341\\mathbin\{\\pm\}0\.01320\.7598±0\.01910\.7598\\mathbin\{\\pm\}0\.01910\.7588±0\.01770\.7588\\mathbin\{\\pm\}0\.01770\.7646±0\.01820\.7646\\mathbin\{\\pm\}0\.01820\.7620±0\.01780\.7620\\mathbin\{\\pm\}0\.01780\.7569±0\.01740\.7569\\mathbin\{\\pm\}0\.01740\.7643±0\.01790\.7643\\mathbin\{\\pm\}0\.0179Supervised selection0\.7290±0\.01450\.7290\\mathbin\{\\pm\}0\.01450\.7590±0\.02180\.7590\\mathbin\{\\pm\}0\.02180\.7617±0\.01920\.7617\\mathbin\{\\pm\}0\.01920\.7626±0\.02060\.7626\\mathbin\{\\pm\}0\.02060\.7600±0\.01940\.7600\\mathbin\{\\pm\}0\.01940\.7603±0\.01650\.7603\\mathbin\{\\pm\}0\.01650\.7638±0\.02000\.7638\\mathbin\{\\pm\}0\.0200TabPrep full0\.6978±0\.00600\.6978\\mathbin\{\\pm\}0\.00600\.7069±0\.01190\.7069\\mathbin\{\\pm\}0\.01190\.7022±0\.01440\.7022\\mathbin\{\\pm\}0\.01440\.7016±0\.01420\.7016\\mathbin\{\\pm\}0\.01420\.7028±0\.01370\.7028\\mathbin\{\\pm\}0\.01370\.7000±0\.00970\.7000\\mathbin\{\\pm\}0\.00970\.7048±0\.01390\.7048\\mathbin\{\\pm\}0\.0139TabPrep w/o groupby0\.6979±0\.00700\.6979\\mathbin\{\\pm\}0\.00700\.7069±0\.00960\.7069\\mathbin\{\\pm\}0\.00960\.7033±0\.01470\.7033\\mathbin\{\\pm\}0\.01470\.7028±0\.01430\.7028\\mathbin\{\\pm\}0\.01430\.7034±0\.01420\.7034\\mathbin\{\\pm\}0\.01420\.7006±0\.01070\.7006\\mathbin\{\\pm\}0\.01070\.7048±0\.01290\.7048\\mathbin\{\\pm\}0\.0129TabPrep w/o RSFC0\.6979±0\.00630\.6979\\mathbin\{\\pm\}0\.00630\.7064±0\.01010\.7064\\mathbin\{\\pm\}0\.01010\.7034±0\.01380\.7034\\mathbin\{\\pm\}0\.01380\.7028±0\.01490\.7028\\mathbin\{\\pm\}0\.01490\.7047±0\.01340\.7047\\mathbin\{\\pm\}0\.01340\.6997±0\.01160\.6997\\mathbin\{\\pm\}0\.01160\.7055±0\.01210\.7055\\mathbin\{\\pm\}0\.0121TabPrep w/o arithmetic0\.7167±0\.02220\.7167\\mathbin\{\\pm\}0\.02220\.7205±0\.02030\.7205\\mathbin\{\\pm\}0\.02030\.7168±0\.01990\.7168\\mathbin\{\\pm\}0\.01990\.7187±0\.02160\.7187\\mathbin\{\\pm\}0\.02160\.7220±0\.01880\.7220\\mathbin\{\\pm\}0\.01880\.7151±0\.02090\.7151\\mathbin\{\\pm\}0\.02090\.7172±0\.02440\.7172\\mathbin\{\\pm\}0\.0244TabPrep w/o cat\. interact\.0\.6971±0\.00760\.6971\\mathbin\{\\pm\}0\.00760\.7075±0\.01190\.7075\\mathbin\{\\pm\}0\.01190\.7042±0\.01290\.7042\\mathbin\{\\pm\}0\.01290\.7037±0\.01550\.7037\\mathbin\{\\pm\}0\.01550\.7055±0\.01190\.7055\\mathbin\{\\pm\}0\.01190\.7008±0\.01260\.7008\\mathbin\{\\pm\}0\.01260\.7048±0\.01430\.7048\\mathbin\{\\pm\}0\.0143TabPrep w/o OOF\-TE0\.6970±0\.00720\.6970\\mathbin\{\\pm\}0\.00720\.7068±0\.01180\.7068\\mathbin\{\\pm\}0\.01180\.7047±0\.01210\.7047\\mathbin\{\\pm\}0\.01210\.7018±0\.01320\.7018\\mathbin\{\\pm\}0\.01320\.7030±0\.01400\.7030\\mathbin\{\\pm\}0\.01400\.7006±0\.01080\.7006\\mathbin\{\\pm\}0\.01080\.7061±0\.01300\.7061\\mathbin\{\\pm\}0\.0130Shared\-context kNN0\.7364±0\.01370\.7364\\mathbin\{\\pm\}0\.01370\.7557±0\.02090\.7557\\mathbin\{\\pm\}0\.02090\.7562±0\.01940\.7562\\mathbin\{\\pm\}0\.01940\.7568±0\.02060\.7568\\mathbin\{\\pm\}0\.02060\.7576±0\.01960\.7576\\mathbin\{\\pm\}0\.01960\.7577±0\.01850\.7577\\mathbin\{\\pm\}0\.01850\.7593±0\.01910\.7593\\mathbin\{\\pm\}0\.0191OOF prediction feature0\.7394±0\.01440\.7394\\mathbin\{\\pm\}0\.01440\.7574±0\.02170\.7574\\mathbin\{\\pm\}0\.02170\.7558±0\.01860\.7558\\mathbin\{\\pm\}0\.01860\.7504±0\.02190\.7504\\mathbin\{\\pm\}0\.02190\.7567±0\.02080\.7567\\mathbin\{\\pm\}0\.02080\.7545±0\.01630\.7545\\mathbin\{\\pm\}0\.01630\.7539±0\.01970\.7539\\mathbin\{\\pm\}0\.0197Table 17:Complete TabPFN and TabICL raw metric results for Credit\-g, metric macro f1\. Values are mean±\\mathbin\{\\pm\}sample standard deviation across the 30 paired splits\.ConditionPFN v1PFN v2PFN v2\.5PFN v2\.6PFN v3ICL v1ICL v2Identity0\.6167±0\.02560\.6167\\mathbin\{\\pm\}0\.02560\.6719±0\.02410\.6719\\mathbin\{\\pm\}0\.02410\.6751±0\.02600\.6751\\mathbin\{\\pm\}0\.02600\.6808±0\.02670\.6808\\mathbin\{\\pm\}0\.02670\.6839±0\.02210\.6839\\mathbin\{\\pm\}0\.02210\.6763±0\.02360\.6763\\mathbin\{\\pm\}0\.02360\.6820±0\.02370\.6820\\mathbin\{\\pm\}0\.0237Standard scaling0\.6195±0\.02490\.6195\\mathbin\{\\pm\}0\.02490\.6716±0\.02710\.6716\\mathbin\{\\pm\}0\.02710\.6751±0\.02730\.6751\\mathbin\{\\pm\}0\.02730\.6804±0\.02750\.6804\\mathbin\{\\pm\}0\.02750\.6847±0\.02260\.6847\\mathbin\{\\pm\}0\.02260\.6779±0\.02240\.6779\\mathbin\{\\pm\}0\.02240\.6820±0\.02370\.6820\\mathbin\{\\pm\}0\.0237Log transform0\.6204±0\.02300\.6204\\mathbin\{\\pm\}0\.02300\.6746±0\.02950\.6746\\mathbin\{\\pm\}0\.02950\.6763±0\.02560\.6763\\mathbin\{\\pm\}0\.02560\.6827±0\.02750\.6827\\mathbin\{\\pm\}0\.02750\.6865±0\.02160\.6865\\mathbin\{\\pm\}0\.02160\.6745±0\.02130\.6745\\mathbin\{\\pm\}0\.02130\.6805±0\.02630\.6805\\mathbin\{\\pm\}0\.0263Square\-root transform0\.6207±0\.02340\.6207\\mathbin\{\\pm\}0\.02340\.6729±0\.02560\.6729\\mathbin\{\\pm\}0\.02560\.6745±0\.02400\.6745\\mathbin\{\\pm\}0\.02400\.6819±0\.02640\.6819\\mathbin\{\\pm\}0\.02640\.6878±0\.02370\.6878\\mathbin\{\\pm\}0\.02370\.6778±0\.02280\.6778\\mathbin\{\\pm\}0\.02280\.6825±0\.02480\.6825\\mathbin\{\\pm\}0\.0248Box–Cox0\.6187±0\.02480\.6187\\mathbin\{\\pm\}0\.02480\.6727±0\.03180\.6727\\mathbin\{\\pm\}0\.03180\.6753±0\.02640\.6753\\mathbin\{\\pm\}0\.02640\.6816±0\.02880\.6816\\mathbin\{\\pm\}0\.02880\.6855±0\.02280\.6855\\mathbin\{\\pm\}0\.02280\.6734±0\.02250\.6734\\mathbin\{\\pm\}0\.02250\.6803±0\.02430\.6803\\mathbin\{\\pm\}0\.0243Min–max scaling0\.6195±0\.02490\.6195\\mathbin\{\\pm\}0\.02490\.6718±0\.02630\.6718\\mathbin\{\\pm\}0\.02630\.6748±0\.02760\.6748\\mathbin\{\\pm\}0\.02760\.6801±0\.02770\.6801\\mathbin\{\\pm\}0\.02770\.6871±0\.02250\.6871\\mathbin\{\\pm\}0\.02250\.6775±0\.02300\.6775\\mathbin\{\\pm\}0\.02300\.6820±0\.02370\.6820\\mathbin\{\\pm\}0\.0237One\-hot encoding0\.6830±0\.02340\.6830\\mathbin\{\\pm\}0\.02340\.6642±0\.01570\.6642\\mathbin\{\\pm\}0\.01570\.6767±0\.02070\.6767\\mathbin\{\\pm\}0\.02070\.6782±0\.01850\.6782\\mathbin\{\\pm\}0\.01850\.6837±0\.01960\.6837\\mathbin\{\\pm\}0\.01960\.6903±0\.02400\.6903\\mathbin\{\\pm\}0\.02400\.6785±0\.02440\.6785\\mathbin\{\\pm\}0\.0244Ordinal encoding0\.6173±0\.02650\.6173\\mathbin\{\\pm\}0\.02650\.6677±0\.02280\.6677\\mathbin\{\\pm\}0\.02280\.6749±0\.02340\.6749\\mathbin\{\\pm\}0\.02340\.6811±0\.02270\.6811\\mathbin\{\\pm\}0\.02270\.6862±0\.02290\.6862\\mathbin\{\\pm\}0\.02290\.6797±0\.02060\.6797\\mathbin\{\\pm\}0\.02060\.6818±0\.02240\.6818\\mathbin\{\\pm\}0\.0224Frequency encoding0\.6252±0\.02530\.6252\\mathbin\{\\pm\}0\.02530\.6700±0\.02660\.6700\\mathbin\{\\pm\}0\.02660\.6762±0\.02810\.6762\\mathbin\{\\pm\}0\.02810\.6811±0\.02810\.6811\\mathbin\{\\pm\}0\.02810\.6902±0\.02430\.6902\\mathbin\{\\pm\}0\.02430\.6785±0\.02070\.6785\\mathbin\{\\pm\}0\.02070\.6852±0\.02020\.6852\\mathbin\{\\pm\}0\.0202Target encoding0\.6655±0\.02040\.6655\\mathbin\{\\pm\}0\.02040\.6734±0\.02720\.6734\\mathbin\{\\pm\}0\.02720\.6749±0\.02520\.6749\\mathbin\{\\pm\}0\.02520\.6703±0\.02590\.6703\\mathbin\{\\pm\}0\.02590\.6769±0\.02340\.6769\\mathbin\{\\pm\}0\.02340\.6853±0\.02700\.6853\\mathbin\{\\pm\}0\.02700\.6359±0\.04080\.6359\\mathbin\{\\pm\}0\.0408Categorical crosses0\.6655±0\.03300\.6655\\mathbin\{\\pm\}0\.03300\.6703±0\.03150\.6703\\mathbin\{\\pm\}0\.03150\.6759±0\.02480\.6759\\mathbin\{\\pm\}0\.02480\.6748±0\.03490\.6748\\mathbin\{\\pm\}0\.03490\.6735±0\.02890\.6735\\mathbin\{\\pm\}0\.02890\.6616±0\.02950\.6616\\mathbin\{\\pm\}0\.02950\.6790±0\.02750\.6790\\mathbin\{\\pm\}0\.0275Equal\-width binning0\.6162±0\.02520\.6162\\mathbin\{\\pm\}0\.02520\.6642±0\.02330\.6642\\mathbin\{\\pm\}0\.02330\.6683±0\.02440\.6683\\mathbin\{\\pm\}0\.02440\.6739±0\.02720\.6739\\mathbin\{\\pm\}0\.02720\.6758±0\.02280\.6758\\mathbin\{\\pm\}0\.02280\.6676±0\.02300\.6676\\mathbin\{\\pm\}0\.02300\.6745±0\.02470\.6745\\mathbin\{\\pm\}0\.0247Equal\-frequency binning0\.6185±0\.02280\.6185\\mathbin\{\\pm\}0\.02280\.6651±0\.02650\.6651\\mathbin\{\\pm\}0\.02650\.6680±0\.02440\.6680\\mathbin\{\\pm\}0\.02440\.6803±0\.02430\.6803\\mathbin\{\\pm\}0\.02430\.6806±0\.02630\.6806\\mathbin\{\\pm\}0\.02630\.6690±0\.02090\.6690\\mathbin\{\\pm\}0\.02090\.6790±0\.02160\.6790\\mathbin\{\\pm\}0\.0216Numeric interactions0\.6167±0\.02560\.6167\\mathbin\{\\pm\}0\.02560\.6719±0\.02410\.6719\\mathbin\{\\pm\}0\.02410\.6751±0\.02600\.6751\\mathbin\{\\pm\}0\.02600\.6808±0\.02670\.6808\\mathbin\{\\pm\}0\.02670\.6839±0\.02210\.6839\\mathbin\{\\pm\}0\.02210\.6763±0\.02360\.6763\\mathbin\{\\pm\}0\.02360\.6820±0\.02370\.6820\\mathbin\{\\pm\}0\.0237Group aggregation0\.6674±0\.02450\.6674\\mathbin\{\\pm\}0\.02450\.6683±0\.02400\.6683\\mathbin\{\\pm\}0\.02400\.6824±0\.02770\.6824\\mathbin\{\\pm\}0\.02770\.6773±0\.02810\.6773\\mathbin\{\\pm\}0\.02810\.6710±0\.02620\.6710\\mathbin\{\\pm\}0\.02620\.6685±0\.02230\.6685\\mathbin\{\\pm\}0\.02230\.6711±0\.02770\.6711\\mathbin\{\\pm\}0\.0277Variance filter0\.6167±0\.02560\.6167\\mathbin\{\\pm\}0\.02560\.6719±0\.02410\.6719\\mathbin\{\\pm\}0\.02410\.6751±0\.02600\.6751\\mathbin\{\\pm\}0\.02600\.6808±0\.02670\.6808\\mathbin\{\\pm\}0\.02670\.6839±0\.02210\.6839\\mathbin\{\\pm\}0\.02210\.6763±0\.02360\.6763\\mathbin\{\\pm\}0\.02360\.6820±0\.02370\.6820\\mathbin\{\\pm\}0\.0237Collinearity filter0\.6167±0\.02560\.6167\\mathbin\{\\pm\}0\.02560\.6719±0\.02410\.6719\\mathbin\{\\pm\}0\.02410\.6751±0\.02600\.6751\\mathbin\{\\pm\}0\.02600\.6808±0\.02670\.6808\\mathbin\{\\pm\}0\.02670\.6839±0\.02210\.6839\\mathbin\{\\pm\}0\.02210\.6763±0\.02360\.6763\\mathbin\{\\pm\}0\.02360\.6820±0\.02370\.6820\\mathbin\{\\pm\}0\.0237PCA0\.6162±0\.02410\.6162\\mathbin\{\\pm\}0\.02410\.6766±0\.02510\.6766\\mathbin\{\\pm\}0\.02510\.6760±0\.02650\.6760\\mathbin\{\\pm\}0\.02650\.6861±0\.02540\.6861\\mathbin\{\\pm\}0\.02540\.6876±0\.02300\.6876\\mathbin\{\\pm\}0\.02300\.6772±0\.02220\.6772\\mathbin\{\\pm\}0\.02220\.6887±0\.02350\.6887\\mathbin\{\\pm\}0\.0235Supervised selection0\.6090±0\.02980\.6090\\mathbin\{\\pm\}0\.02980\.6760±0\.02990\.6760\\mathbin\{\\pm\}0\.02990\.6789±0\.02710\.6789\\mathbin\{\\pm\}0\.02710\.6854±0\.02880\.6854\\mathbin\{\\pm\}0\.02880\.6831±0\.02610\.6831\\mathbin\{\\pm\}0\.02610\.6807±0\.02380\.6807\\mathbin\{\\pm\}0\.02380\.6882±0\.02840\.6882\\mathbin\{\\pm\}0\.0284TabPrep full0\.4312±0\.02590\.4312\\mathbin\{\\pm\}0\.02590\.4977±0\.02850\.4977\\mathbin\{\\pm\}0\.02850\.4894±0\.02870\.4894\\mathbin\{\\pm\}0\.02870\.5094±0\.02060\.5094\\mathbin\{\\pm\}0\.02060\.4985±0\.02620\.4985\\mathbin\{\\pm\}0\.02620\.4763±0\.03890\.4763\\mathbin\{\\pm\}0\.03890\.5109±0\.02480\.5109\\mathbin\{\\pm\}0\.0248TabPrep w/o groupby0\.4344±0\.02620\.4344\\mathbin\{\\pm\}0\.02620\.4939±0\.02490\.4939\\mathbin\{\\pm\}0\.02490\.4944±0\.02840\.4944\\mathbin\{\\pm\}0\.02840\.5114±0\.02700\.5114\\mathbin\{\\pm\}0\.02700\.4974±0\.02730\.4974\\mathbin\{\\pm\}0\.02730\.4748±0\.03800\.4748\\mathbin\{\\pm\}0\.03800\.5103±0\.02540\.5103\\mathbin\{\\pm\}0\.0254TabPrep w/o RSFC0\.4339±0\.02960\.4339\\mathbin\{\\pm\}0\.02960\.4925±0\.02470\.4925\\mathbin\{\\pm\}0\.02470\.4929±0\.03000\.4929\\mathbin\{\\pm\}0\.03000\.5091±0\.02180\.5091\\mathbin\{\\pm\}0\.02180\.5005±0\.02640\.5005\\mathbin\{\\pm\}0\.02640\.4773±0\.03890\.4773\\mathbin\{\\pm\}0\.03890\.5098±0\.02510\.5098\\mathbin\{\\pm\}0\.0251TabPrep w/o arithmetic0\.5870±0\.06090\.5870\\mathbin\{\\pm\}0\.06090\.5957±0\.04800\.5957\\mathbin\{\\pm\}0\.04800\.5965±0\.04210\.5965\\mathbin\{\\pm\}0\.04210\.5883±0\.05500\.5883\\mathbin\{\\pm\}0\.05500\.6064±0\.04510\.6064\\mathbin\{\\pm\}0\.04510\.5845±0\.05570\.5845\\mathbin\{\\pm\}0\.05570\.6002±0\.03990\.6002\\mathbin\{\\pm\}0\.0399TabPrep w/o cat\. interact\.0\.4297±0\.02380\.4297\\mathbin\{\\pm\}0\.02380\.4960±0\.02640\.4960\\mathbin\{\\pm\}0\.02640\.4953±0\.03040\.4953\\mathbin\{\\pm\}0\.03040\.5118±0\.02300\.5118\\mathbin\{\\pm\}0\.02300\.5015±0\.02560\.5015\\mathbin\{\\pm\}0\.02560\.4794±0\.04140\.4794\\mathbin\{\\pm\}0\.04140\.5104±0\.02440\.5104\\mathbin\{\\pm\}0\.0244TabPrep w/o OOF\-TE0\.4292±0\.02730\.4292\\mathbin\{\\pm\}0\.02730\.4947±0\.02570\.4947\\mathbin\{\\pm\}0\.02570\.4927±0\.03270\.4927\\mathbin\{\\pm\}0\.03270\.5110±0\.02310\.5110\\mathbin\{\\pm\}0\.02310\.4980±0\.02620\.4980\\mathbin\{\\pm\}0\.02620\.4747±0\.04020\.4747\\mathbin\{\\pm\}0\.04020\.5127±0\.02300\.5127\\mathbin\{\\pm\}0\.0230Shared\-context kNN0\.6257±0\.02590\.6257\\mathbin\{\\pm\}0\.02590\.6720±0\.02510\.6720\\mathbin\{\\pm\}0\.02510\.6718±0\.02650\.6718\\mathbin\{\\pm\}0\.02650\.6788±0\.02830\.6788\\mathbin\{\\pm\}0\.02830\.6829±0\.02320\.6829\\mathbin\{\\pm\}0\.02320\.6774±0\.02300\.6774\\mathbin\{\\pm\}0\.02300\.6817±0\.02420\.6817\\mathbin\{\\pm\}0\.0242OOF prediction feature0\.6290±0\.02700\.6290\\mathbin\{\\pm\}0\.02700\.6817±0\.02610\.6817\\mathbin\{\\pm\}0\.02610\.6777±0\.02820\.6777\\mathbin\{\\pm\}0\.02820\.6712±0\.03090\.6712\\mathbin\{\\pm\}0\.03090\.6800±0\.02770\.6800\\mathbin\{\\pm\}0\.02770\.6734±0\.02250\.6734\\mathbin\{\\pm\}0\.02250\.6749±0\.02490\.6749\\mathbin\{\\pm\}0\.0249Table 18:Complete TabPFN and TabICL raw metric results for Diabetes, metric accuracy\. Values are mean±\\mathbin\{\\pm\}sample standard deviation across the 30 paired splits\.ConditionPFN v1PFN v2PFN v2\.5PFN v2\.6PFN v3ICL v1ICL v2Identity0\.7680±0\.02440\.7680\\mathbin\{\\pm\}0\.02440\.7638±0\.02330\.7638\\mathbin\{\\pm\}0\.02330\.7676±0\.02280\.7676\\mathbin\{\\pm\}0\.02280\.7633±0\.02350\.7633\\mathbin\{\\pm\}0\.02350\.7645±0\.02400\.7645\\mathbin\{\\pm\}0\.02400\.7682±0\.02360\.7682\\mathbin\{\\pm\}0\.02360\.7658±0\.02460\.7658\\mathbin\{\\pm\}0\.0246Standard scaling0\.7678±0\.02460\.7678\\mathbin\{\\pm\}0\.02460\.7652±0\.02460\.7652\\mathbin\{\\pm\}0\.02460\.7673±0\.02510\.7673\\mathbin\{\\pm\}0\.02510\.7634±0\.02330\.7634\\mathbin\{\\pm\}0\.02330\.7652±0\.02420\.7652\\mathbin\{\\pm\}0\.02420\.7681±0\.02360\.7681\\mathbin\{\\pm\}0\.02360\.7658±0\.02460\.7658\\mathbin\{\\pm\}0\.0246Log transform0\.7635±0\.02670\.7635\\mathbin\{\\pm\}0\.02670\.7701±0\.02370\.7701\\mathbin\{\\pm\}0\.02370\.7665±0\.02310\.7665\\mathbin\{\\pm\}0\.02310\.7643±0\.02200\.7643\\mathbin\{\\pm\}0\.02200\.7632±0\.02540\.7632\\mathbin\{\\pm\}0\.02540\.7689±0\.02520\.7689\\mathbin\{\\pm\}0\.02520\.7661±0\.02450\.7661\\mathbin\{\\pm\}0\.0245Square\-root transform0\.7643±0\.02610\.7643\\mathbin\{\\pm\}0\.02610\.7678±0\.02210\.7678\\mathbin\{\\pm\}0\.02210\.7658±0\.02380\.7658\\mathbin\{\\pm\}0\.02380\.7635±0\.02260\.7635\\mathbin\{\\pm\}0\.02260\.7661±0\.02390\.7661\\mathbin\{\\pm\}0\.02390\.7673±0\.02590\.7673\\mathbin\{\\pm\}0\.02590\.7652±0\.02470\.7652\\mathbin\{\\pm\}0\.0247Box–Cox0\.7685±0\.02560\.7685\\mathbin\{\\pm\}0\.02560\.7668±0\.02310\.7668\\mathbin\{\\pm\}0\.02310\.7656±0\.02340\.7656\\mathbin\{\\pm\}0\.02340\.7634±0\.02350\.7634\\mathbin\{\\pm\}0\.02350\.7654±0\.02360\.7654\\mathbin\{\\pm\}0\.02360\.7656±0\.02480\.7656\\mathbin\{\\pm\}0\.02480\.7652±0\.02490\.7652\\mathbin\{\\pm\}0\.0249Min–max scaling0\.7678±0\.02460\.7678\\mathbin\{\\pm\}0\.02460\.7652±0\.02340\.7652\\mathbin\{\\pm\}0\.02340\.7671±0\.02470\.7671\\mathbin\{\\pm\}0\.02470\.7630±0\.02340\.7630\\mathbin\{\\pm\}0\.02340\.7648±0\.02490\.7648\\mathbin\{\\pm\}0\.02490\.7681±0\.02360\.7681\\mathbin\{\\pm\}0\.02360\.7658±0\.02460\.7658\\mathbin\{\\pm\}0\.0246One\-hot encoding———————Ordinal encoding———————Frequency encoding———————Target encoding———————Categorical crosses———————Equal\-width binning0\.7652±0\.02530\.7652\\mathbin\{\\pm\}0\.02530\.7673±0\.02610\.7673\\mathbin\{\\pm\}0\.02610\.7681±0\.02410\.7681\\mathbin\{\\pm\}0\.02410\.7642±0\.02730\.7642\\mathbin\{\\pm\}0\.02730\.7669±0\.02680\.7669\\mathbin\{\\pm\}0\.02680\.7669±0\.02810\.7669\\mathbin\{\\pm\}0\.02810\.7661±0\.02750\.7661\\mathbin\{\\pm\}0\.0275Equal\-frequency binning0\.7612±0\.02560\.7612\\mathbin\{\\pm\}0\.02560\.7645±0\.02190\.7645\\mathbin\{\\pm\}0\.02190\.7661±0\.02510\.7661\\mathbin\{\\pm\}0\.02510\.7667±0\.02380\.7667\\mathbin\{\\pm\}0\.02380\.7645±0\.02490\.7645\\mathbin\{\\pm\}0\.02490\.7617±0\.02180\.7617\\mathbin\{\\pm\}0\.02180\.7624±0\.02450\.7624\\mathbin\{\\pm\}0\.0245Numeric interactions0\.7688±0\.02450\.7688\\mathbin\{\\pm\}0\.02450\.7682±0\.02290\.7682\\mathbin\{\\pm\}0\.02290\.7689±0\.02340\.7689\\mathbin\{\\pm\}0\.02340\.7674±0\.02420\.7674\\mathbin\{\\pm\}0\.02420\.7646±0\.02260\.7646\\mathbin\{\\pm\}0\.02260\.7664±0\.02460\.7664\\mathbin\{\\pm\}0\.02460\.7625±0\.02430\.7625\\mathbin\{\\pm\}0\.0243Group aggregation———————Variance filter0\.7680±0\.02440\.7680\\mathbin\{\\pm\}0\.02440\.7638±0\.02330\.7638\\mathbin\{\\pm\}0\.02330\.7676±0\.02280\.7676\\mathbin\{\\pm\}0\.02280\.7633±0\.02350\.7633\\mathbin\{\\pm\}0\.02350\.7645±0\.02400\.7645\\mathbin\{\\pm\}0\.02400\.7682±0\.02360\.7682\\mathbin\{\\pm\}0\.02360\.7658±0\.02460\.7658\\mathbin\{\\pm\}0\.0246Collinearity filter0\.7680±0\.02440\.7680\\mathbin\{\\pm\}0\.02440\.7638±0\.02330\.7638\\mathbin\{\\pm\}0\.02330\.7676±0\.02280\.7676\\mathbin\{\\pm\}0\.02280\.7633±0\.02350\.7633\\mathbin\{\\pm\}0\.02350\.7645±0\.02400\.7645\\mathbin\{\\pm\}0\.02400\.7682±0\.02360\.7682\\mathbin\{\\pm\}0\.02360\.7658±0\.02460\.7658\\mathbin\{\\pm\}0\.0246PCA0\.7607±0\.02500\.7607\\mathbin\{\\pm\}0\.02500\.7688±0\.02660\.7688\\mathbin\{\\pm\}0\.02660\.7721±0\.02300\.7721\\mathbin\{\\pm\}0\.02300\.7707±0\.02550\.7707\\mathbin\{\\pm\}0\.02550\.7716±0\.02460\.7716\\mathbin\{\\pm\}0\.02460\.7600±0\.02340\.7600\\mathbin\{\\pm\}0\.02340\.7655±0\.02620\.7655\\mathbin\{\\pm\}0\.0262Supervised selection0\.7605±0\.02020\.7605\\mathbin\{\\pm\}0\.02020\.7669±0\.02110\.7669\\mathbin\{\\pm\}0\.02110\.7663±0\.01890\.7663\\mathbin\{\\pm\}0\.01890\.7684±0\.02050\.7684\\mathbin\{\\pm\}0\.02050\.7655±0\.02100\.7655\\mathbin\{\\pm\}0\.02100\.7639±0\.02240\.7639\\mathbin\{\\pm\}0\.02240\.7673±0\.02060\.7673\\mathbin\{\\pm\}0\.0206TabPrep full0\.7578±0\.02570\.7578\\mathbin\{\\pm\}0\.02570\.7633±0\.02330\.7633\\mathbin\{\\pm\}0\.02330\.7646±0\.02250\.7646\\mathbin\{\\pm\}0\.02250\.7652±0\.02480\.7652\\mathbin\{\\pm\}0\.02480\.7658±0\.02250\.7658\\mathbin\{\\pm\}0\.02250\.7607±0\.02060\.7607\\mathbin\{\\pm\}0\.02060\.7651±0\.02380\.7651\\mathbin\{\\pm\}0\.0238TabPrep w/o groupby0\.7552±0\.02630\.7552\\mathbin\{\\pm\}0\.02630\.7648±0\.02140\.7648\\mathbin\{\\pm\}0\.02140\.7646±0\.02340\.7646\\mathbin\{\\pm\}0\.02340\.7621±0\.02370\.7621\\mathbin\{\\pm\}0\.02370\.7659±0\.02270\.7659\\mathbin\{\\pm\}0\.02270\.7617±0\.02210\.7617\\mathbin\{\\pm\}0\.02210\.7638±0\.02270\.7638\\mathbin\{\\pm\}0\.0227TabPrep w/o RSFC0\.7551±0\.02740\.7551\\mathbin\{\\pm\}0\.02740\.7668±0\.02310\.7668\\mathbin\{\\pm\}0\.02310\.7634±0\.02320\.7634\\mathbin\{\\pm\}0\.02320\.7637±0\.02240\.7637\\mathbin\{\\pm\}0\.02240\.7682±0\.02300\.7682\\mathbin\{\\pm\}0\.02300\.7613±0\.02330\.7613\\mathbin\{\\pm\}0\.02330\.7659±0\.02290\.7659\\mathbin\{\\pm\}0\.0229TabPrep w/o arithmetic0\.7577±0\.02660\.7577\\mathbin\{\\pm\}0\.02660\.7672±0\.02560\.7672\\mathbin\{\\pm\}0\.02560\.7665±0\.02570\.7665\\mathbin\{\\pm\}0\.02570\.7676±0\.02500\.7676\\mathbin\{\\pm\}0\.02500\.7629±0\.02550\.7629\\mathbin\{\\pm\}0\.02550\.7605±0\.02460\.7605\\mathbin\{\\pm\}0\.02460\.7634±0\.02290\.7634\\mathbin\{\\pm\}0\.0229TabPrep w/o cat\. interact\.0\.7581±0\.02710\.7581\\mathbin\{\\pm\}0\.02710\.7647±0\.02340\.7647\\mathbin\{\\pm\}0\.02340\.7643±0\.02240\.7643\\mathbin\{\\pm\}0\.02240\.7633±0\.02490\.7633\\mathbin\{\\pm\}0\.02490\.7661±0\.02240\.7661\\mathbin\{\\pm\}0\.02240\.7624±0\.02150\.7624\\mathbin\{\\pm\}0\.02150\.7658±0\.02160\.7658\\mathbin\{\\pm\}0\.0216TabPrep w/o OOF\-TE0\.7568±0\.02730\.7568\\mathbin\{\\pm\}0\.02730\.7656±0\.02480\.7656\\mathbin\{\\pm\}0\.02480\.7660±0\.02260\.7660\\mathbin\{\\pm\}0\.02260\.7661±0\.02330\.7661\\mathbin\{\\pm\}0\.02330\.7655±0\.02330\.7655\\mathbin\{\\pm\}0\.02330\.7630±0\.02280\.7630\\mathbin\{\\pm\}0\.02280\.7663±0\.02410\.7663\\mathbin\{\\pm\}0\.0241Shared\-context kNN0\.7685±0\.02580\.7685\\mathbin\{\\pm\}0\.02580\.7660±0\.02260\.7660\\mathbin\{\\pm\}0\.02260\.7681±0\.02300\.7681\\mathbin\{\\pm\}0\.02300\.7639±0\.02220\.7639\\mathbin\{\\pm\}0\.02220\.7648±0\.02350\.7648\\mathbin\{\\pm\}0\.02350\.7694±0\.02320\.7694\\mathbin\{\\pm\}0\.02320\.7655±0\.02460\.7655\\mathbin\{\\pm\}0\.0246OOF prediction feature0\.7678±0\.02290\.7678\\mathbin\{\\pm\}0\.02290\.7684±0\.02030\.7684\\mathbin\{\\pm\}0\.02030\.7708±0\.02480\.7708\\mathbin\{\\pm\}0\.02480\.7641±0\.02360\.7641\\mathbin\{\\pm\}0\.02360\.7673±0\.02460\.7673\\mathbin\{\\pm\}0\.02460\.7652±0\.02750\.7652\\mathbin\{\\pm\}0\.02750\.7663±0\.02540\.7663\\mathbin\{\\pm\}0\.0254Table 19:Complete TabPFN and TabICL raw metric results for Diabetes, metric macro f1\. Values are mean±\\mathbin\{\\pm\}sample standard deviation across the 30 paired splits\.ConditionPFN v1PFN v2PFN v2\.5PFN v2\.6PFN v3ICL v1ICL v2Identity0\.7331±0\.02680\.7331\\mathbin\{\\pm\}0\.02680\.7299±0\.02570\.7299\\mathbin\{\\pm\}0\.02570\.7337±0\.02490\.7337\\mathbin\{\\pm\}0\.02490\.7293±0\.02650\.7293\\mathbin\{\\pm\}0\.02650\.7301±0\.02630\.7301\\mathbin\{\\pm\}0\.02630\.7333±0\.02520\.7333\\mathbin\{\\pm\}0\.02520\.7303±0\.02780\.7303\\mathbin\{\\pm\}0\.0278Standard scaling0\.7330±0\.02690\.7330\\mathbin\{\\pm\}0\.02690\.7312±0\.02710\.7312\\mathbin\{\\pm\}0\.02710\.7333±0\.02760\.7333\\mathbin\{\\pm\}0\.02760\.7295±0\.02610\.7295\\mathbin\{\\pm\}0\.02610\.7313±0\.02660\.7313\\mathbin\{\\pm\}0\.02660\.7332±0\.02530\.7332\\mathbin\{\\pm\}0\.02530\.7303±0\.02780\.7303\\mathbin\{\\pm\}0\.0278Log transform0\.7285±0\.02940\.7285\\mathbin\{\\pm\}0\.02940\.7381±0\.02590\.7381\\mathbin\{\\pm\}0\.02590\.7333±0\.02470\.7333\\mathbin\{\\pm\}0\.02470\.7304±0\.02450\.7304\\mathbin\{\\pm\}0\.02450\.7300±0\.02800\.7300\\mathbin\{\\pm\}0\.02800\.7345±0\.02840\.7345\\mathbin\{\\pm\}0\.02840\.7308±0\.02790\.7308\\mathbin\{\\pm\}0\.0279Square\-root transform0\.7288±0\.02870\.7288\\mathbin\{\\pm\}0\.02870\.7350±0\.02420\.7350\\mathbin\{\\pm\}0\.02420\.7320±0\.02630\.7320\\mathbin\{\\pm\}0\.02630\.7296±0\.02490\.7296\\mathbin\{\\pm\}0\.02490\.7327±0\.02640\.7327\\mathbin\{\\pm\}0\.02640\.7322±0\.02860\.7322\\mathbin\{\\pm\}0\.02860\.7295±0\.02800\.7295\\mathbin\{\\pm\}0\.0280Box–Cox0\.7346±0\.02810\.7346\\mathbin\{\\pm\}0\.02810\.7326±0\.02590\.7326\\mathbin\{\\pm\}0\.02590\.7309±0\.02570\.7309\\mathbin\{\\pm\}0\.02570\.7293±0\.02620\.7293\\mathbin\{\\pm\}0\.02620\.7313±0\.02600\.7313\\mathbin\{\\pm\}0\.02600\.7301±0\.02780\.7301\\mathbin\{\\pm\}0\.02780\.7300±0\.02830\.7300\\mathbin\{\\pm\}0\.0283Min–max scaling0\.7330±0\.02690\.7330\\mathbin\{\\pm\}0\.02690\.7315±0\.02580\.7315\\mathbin\{\\pm\}0\.02580\.7328±0\.02660\.7328\\mathbin\{\\pm\}0\.02660\.7290±0\.02640\.7290\\mathbin\{\\pm\}0\.02640\.7308±0\.02750\.7308\\mathbin\{\\pm\}0\.02750\.7332±0\.02530\.7332\\mathbin\{\\pm\}0\.02530\.7303±0\.02780\.7303\\mathbin\{\\pm\}0\.0278One\-hot encoding———————Ordinal encoding———————Frequency encoding———————Target encoding———————Categorical crosses———————Equal\-width binning0\.7311±0\.02800\.7311\\mathbin\{\\pm\}0\.02800\.7329±0\.02880\.7329\\mathbin\{\\pm\}0\.02880\.7337±0\.02660\.7337\\mathbin\{\\pm\}0\.02660\.7300±0\.02990\.7300\\mathbin\{\\pm\}0\.02990\.7338±0\.02900\.7338\\mathbin\{\\pm\}0\.02900\.7333±0\.03090\.7333\\mathbin\{\\pm\}0\.03090\.7325±0\.03010\.7325\\mathbin\{\\pm\}0\.0301Equal\-frequency binning0\.7268±0\.02910\.7268\\mathbin\{\\pm\}0\.02910\.7301±0\.02520\.7301\\mathbin\{\\pm\}0\.02520\.7322±0\.02840\.7322\\mathbin\{\\pm\}0\.02840\.7326±0\.02700\.7326\\mathbin\{\\pm\}0\.02700\.7308±0\.02800\.7308\\mathbin\{\\pm\}0\.02800\.7267±0\.02490\.7267\\mathbin\{\\pm\}0\.02490\.7298±0\.02730\.7298\\mathbin\{\\pm\}0\.0273Numeric interactions0\.7340±0\.02710\.7340\\mathbin\{\\pm\}0\.02710\.7354±0\.02510\.7354\\mathbin\{\\pm\}0\.02510\.7349±0\.02580\.7349\\mathbin\{\\pm\}0\.02580\.7345±0\.02590\.7345\\mathbin\{\\pm\}0\.02590\.7311±0\.02510\.7311\\mathbin\{\\pm\}0\.02510\.7316±0\.02690\.7316\\mathbin\{\\pm\}0\.02690\.7273±0\.02760\.7273\\mathbin\{\\pm\}0\.0276Group aggregation———————Variance filter0\.7331±0\.02680\.7331\\mathbin\{\\pm\}0\.02680\.7299±0\.02570\.7299\\mathbin\{\\pm\}0\.02570\.7337±0\.02490\.7337\\mathbin\{\\pm\}0\.02490\.7293±0\.02650\.7293\\mathbin\{\\pm\}0\.02650\.7301±0\.02630\.7301\\mathbin\{\\pm\}0\.02630\.7333±0\.02520\.7333\\mathbin\{\\pm\}0\.02520\.7303±0\.02780\.7303\\mathbin\{\\pm\}0\.0278Collinearity filter0\.7331±0\.02680\.7331\\mathbin\{\\pm\}0\.02680\.7299±0\.02570\.7299\\mathbin\{\\pm\}0\.02570\.7337±0\.02490\.7337\\mathbin\{\\pm\}0\.02490\.7293±0\.02650\.7293\\mathbin\{\\pm\}0\.02650\.7301±0\.02630\.7301\\mathbin\{\\pm\}0\.02630\.7333±0\.02520\.7333\\mathbin\{\\pm\}0\.02520\.7303±0\.02780\.7303\\mathbin\{\\pm\}0\.0278PCA0\.7236±0\.02740\.7236\\mathbin\{\\pm\}0\.02740\.7348±0\.02910\.7348\\mathbin\{\\pm\}0\.02910\.7391±0\.02500\.7391\\mathbin\{\\pm\}0\.02500\.7390±0\.02680\.7390\\mathbin\{\\pm\}0\.02680\.7390±0\.02710\.7390\\mathbin\{\\pm\}0\.02710\.7241±0\.02580\.7241\\mathbin\{\\pm\}0\.02580\.7317±0\.02800\.7317\\mathbin\{\\pm\}0\.0280Supervised selection0\.7236±0\.02290\.7236\\mathbin\{\\pm\}0\.02290\.7313±0\.02430\.7313\\mathbin\{\\pm\}0\.02430\.7306±0\.02150\.7306\\mathbin\{\\pm\}0\.02150\.7332±0\.02340\.7332\\mathbin\{\\pm\}0\.02340\.7306±0\.02440\.7306\\mathbin\{\\pm\}0\.02440\.7275±0\.02560\.7275\\mathbin\{\\pm\}0\.02560\.7317±0\.02340\.7317\\mathbin\{\\pm\}0\.0234TabPrep full0\.7247±0\.02850\.7247\\mathbin\{\\pm\}0\.02850\.7286±0\.02640\.7286\\mathbin\{\\pm\}0\.02640\.7300±0\.02550\.7300\\mathbin\{\\pm\}0\.02550\.7319±0\.02760\.7319\\mathbin\{\\pm\}0\.02760\.7326±0\.02450\.7326\\mathbin\{\\pm\}0\.02450\.7257±0\.02190\.7257\\mathbin\{\\pm\}0\.02190\.7307±0\.02680\.7307\\mathbin\{\\pm\}0\.0268TabPrep w/o groupby0\.7219±0\.02910\.7219\\mathbin\{\\pm\}0\.02910\.7308±0\.02540\.7308\\mathbin\{\\pm\}0\.02540\.7301±0\.02660\.7301\\mathbin\{\\pm\}0\.02660\.7279±0\.02650\.7279\\mathbin\{\\pm\}0\.02650\.7327±0\.02510\.7327\\mathbin\{\\pm\}0\.02510\.7273±0\.02320\.7273\\mathbin\{\\pm\}0\.02320\.7291±0\.02530\.7291\\mathbin\{\\pm\}0\.0253TabPrep w/o RSFC0\.7215±0\.03020\.7215\\mathbin\{\\pm\}0\.03020\.7333±0\.02620\.7333\\mathbin\{\\pm\}0\.02620\.7295±0\.02600\.7295\\mathbin\{\\pm\}0\.02600\.7306±0\.02510\.7306\\mathbin\{\\pm\}0\.02510\.7356±0\.02540\.7356\\mathbin\{\\pm\}0\.02540\.7264±0\.02530\.7264\\mathbin\{\\pm\}0\.02530\.7316±0\.02540\.7316\\mathbin\{\\pm\}0\.0254TabPrep w/o arithmetic0\.7214±0\.03010\.7214\\mathbin\{\\pm\}0\.03010\.7328±0\.02790\.7328\\mathbin\{\\pm\}0\.02790\.7316±0\.02780\.7316\\mathbin\{\\pm\}0\.02780\.7324±0\.02650\.7324\\mathbin\{\\pm\}0\.02650\.7263±0\.02740\.7263\\mathbin\{\\pm\}0\.02740\.7219±0\.02670\.7219\\mathbin\{\\pm\}0\.02670\.7267±0\.02750\.7267\\mathbin\{\\pm\}0\.0275TabPrep w/o cat\. interact\.0\.7250±0\.02970\.7250\\mathbin\{\\pm\}0\.02970\.7305±0\.02670\.7305\\mathbin\{\\pm\}0\.02670\.7294±0\.02520\.7294\\mathbin\{\\pm\}0\.02520\.7297±0\.02770\.7297\\mathbin\{\\pm\}0\.02770\.7328±0\.02470\.7328\\mathbin\{\\pm\}0\.02470\.7277±0\.02260\.7277\\mathbin\{\\pm\}0\.02260\.7309±0\.02450\.7309\\mathbin\{\\pm\}0\.0245TabPrep w/o OOF\-TE0\.7233±0\.02970\.7233\\mathbin\{\\pm\}0\.02970\.7311±0\.02840\.7311\\mathbin\{\\pm\}0\.02840\.7323±0\.02510\.7323\\mathbin\{\\pm\}0\.02510\.7333±0\.02620\.7333\\mathbin\{\\pm\}0\.02620\.7323±0\.02600\.7323\\mathbin\{\\pm\}0\.02600\.7287±0\.02470\.7287\\mathbin\{\\pm\}0\.02470\.7317±0\.02710\.7317\\mathbin\{\\pm\}0\.0271Shared\-context kNN0\.7334±0\.02860\.7334\\mathbin\{\\pm\}0\.02860\.7321±0\.02500\.7321\\mathbin\{\\pm\}0\.02500\.7341±0\.02500\.7341\\mathbin\{\\pm\}0\.02500\.7296±0\.02490\.7296\\mathbin\{\\pm\}0\.02490\.7303±0\.02580\.7303\\mathbin\{\\pm\}0\.02580\.7349±0\.02520\.7349\\mathbin\{\\pm\}0\.02520\.7296±0\.02840\.7296\\mathbin\{\\pm\}0\.0284OOF prediction feature0\.7324±0\.02660\.7324\\mathbin\{\\pm\}0\.02660\.7328±0\.02220\.7328\\mathbin\{\\pm\}0\.02220\.7367±0\.02710\.7367\\mathbin\{\\pm\}0\.02710\.7299±0\.02670\.7299\\mathbin\{\\pm\}0\.02670\.7350±0\.02770\.7350\\mathbin\{\\pm\}0\.02770\.7290±0\.02990\.7290\\mathbin\{\\pm\}0\.02990\.7315±0\.02940\.7315\\mathbin\{\\pm\}0\.0294Table 20:Complete TabPFN and TabICL raw metric results for Fitness club, metric accuracy\. Values are mean±\\mathbin\{\\pm\}sample standard deviation across the 30 paired splits\.ConditionPFN v1PFN v2PFN v2\.5PFN v2\.6PFN v3ICL v1ICL v2Identity0\.7776±0\.01390\.7776\\mathbin\{\\pm\}0\.01390\.7809±0\.01080\.7809\\mathbin\{\\pm\}0\.01080\.7791±0\.01090\.7791\\mathbin\{\\pm\}0\.01090\.7805±0\.01100\.7805\\mathbin\{\\pm\}0\.01100\.7815±0\.01070\.7815\\mathbin\{\\pm\}0\.01070\.7774±0\.01190\.7774\\mathbin\{\\pm\}0\.01190\.7817±0\.01130\.7817\\mathbin\{\\pm\}0\.0113Standard scaling0\.7774±0\.01350\.7774\\mathbin\{\\pm\}0\.01350\.7815±0\.01040\.7815\\mathbin\{\\pm\}0\.01040\.7799±0\.01090\.7799\\mathbin\{\\pm\}0\.01090\.7805±0\.01090\.7805\\mathbin\{\\pm\}0\.01090\.7811±0\.01080\.7811\\mathbin\{\\pm\}0\.01080\.7773±0\.01200\.7773\\mathbin\{\\pm\}0\.01200\.7817±0\.01130\.7817\\mathbin\{\\pm\}0\.0113Log transform0\.7771±0\.01440\.7771\\mathbin\{\\pm\}0\.01440\.7819±0\.01120\.7819\\mathbin\{\\pm\}0\.01120\.7807±0\.01170\.7807\\mathbin\{\\pm\}0\.01170\.7797±0\.01110\.7797\\mathbin\{\\pm\}0\.01110\.7810±0\.01130\.7810\\mathbin\{\\pm\}0\.01130\.7777±0\.01250\.7777\\mathbin\{\\pm\}0\.01250\.7817±0\.01140\.7817\\mathbin\{\\pm\}0\.0114Square\-root transform0\.7769±0\.01400\.7769\\mathbin\{\\pm\}0\.01400\.7814±0\.01100\.7814\\mathbin\{\\pm\}0\.01100\.7803±0\.01140\.7803\\mathbin\{\\pm\}0\.01140\.7805±0\.01130\.7805\\mathbin\{\\pm\}0\.01130\.7818±0\.01190\.7818\\mathbin\{\\pm\}0\.01190\.7777±0\.01260\.7777\\mathbin\{\\pm\}0\.01260\.7815±0\.01110\.7815\\mathbin\{\\pm\}0\.0111Box–Cox0\.7773±0\.01410\.7773\\mathbin\{\\pm\}0\.01410\.7813±0\.01120\.7813\\mathbin\{\\pm\}0\.01120\.7808±0\.01260\.7808\\mathbin\{\\pm\}0\.01260\.7811±0\.01070\.7811\\mathbin\{\\pm\}0\.01070\.7817±0\.01060\.7817\\mathbin\{\\pm\}0\.01060\.7773±0\.01280\.7773\\mathbin\{\\pm\}0\.01280\.7817±0\.01140\.7817\\mathbin\{\\pm\}0\.0114Min–max scaling0\.7774±0\.01350\.7774\\mathbin\{\\pm\}0\.01350\.7814±0\.01060\.7814\\mathbin\{\\pm\}0\.01060\.7797±0\.01140\.7797\\mathbin\{\\pm\}0\.01140\.7804±0\.01090\.7804\\mathbin\{\\pm\}0\.01090\.7814±0\.01070\.7814\\mathbin\{\\pm\}0\.01070\.7774±0\.01210\.7774\\mathbin\{\\pm\}0\.01210\.7817±0\.01130\.7817\\mathbin\{\\pm\}0\.0113One\-hot encoding0\.7720±0\.01490\.7720\\mathbin\{\\pm\}0\.01490\.7808±0\.01120\.7808\\mathbin\{\\pm\}0\.01120\.7797±0\.01070\.7797\\mathbin\{\\pm\}0\.01070\.7809±0\.01060\.7809\\mathbin\{\\pm\}0\.01060\.7807±0\.01060\.7807\\mathbin\{\\pm\}0\.01060\.7777±0\.01280\.7777\\mathbin\{\\pm\}0\.01280\.7815±0\.01100\.7815\\mathbin\{\\pm\}0\.0110Ordinal encoding0\.7776±0\.01390\.7776\\mathbin\{\\pm\}0\.01390\.7811±0\.01100\.7811\\mathbin\{\\pm\}0\.01100\.7803±0\.01150\.7803\\mathbin\{\\pm\}0\.01150\.7804±0\.01100\.7804\\mathbin\{\\pm\}0\.01100\.7808±0\.01140\.7808\\mathbin\{\\pm\}0\.01140\.7774±0\.01190\.7774\\mathbin\{\\pm\}0\.01190\.7819±0\.01110\.7819\\mathbin\{\\pm\}0\.0111Frequency encoding0\.7777±0\.01300\.7777\\mathbin\{\\pm\}0\.01300\.7805±0\.01070\.7805\\mathbin\{\\pm\}0\.01070\.7805±0\.01050\.7805\\mathbin\{\\pm\}0\.01050\.7809±0\.01070\.7809\\mathbin\{\\pm\}0\.01070\.7816±0\.01040\.7816\\mathbin\{\\pm\}0\.01040\.7781±0\.01270\.7781\\mathbin\{\\pm\}0\.01270\.7817±0\.01120\.7817\\mathbin\{\\pm\}0\.0112Target encoding0\.7783±0\.01100\.7783\\mathbin\{\\pm\}0\.01100\.7816±0\.01060\.7816\\mathbin\{\\pm\}0\.01060\.7807±0\.01130\.7807\\mathbin\{\\pm\}0\.01130\.7821±0\.01110\.7821\\mathbin\{\\pm\}0\.01110\.7817±0\.01130\.7817\\mathbin\{\\pm\}0\.01130\.7792±0\.01170\.7792\\mathbin\{\\pm\}0\.01170\.7815±0\.01040\.7815\\mathbin\{\\pm\}0\.0104Categorical crosses0\.7742±0\.01390\.7742\\mathbin\{\\pm\}0\.01390\.7803±0\.01110\.7803\\mathbin\{\\pm\}0\.01110\.7791±0\.01120\.7791\\mathbin\{\\pm\}0\.01120\.7801±0\.01040\.7801\\mathbin\{\\pm\}0\.01040\.7794±0\.01080\.7794\\mathbin\{\\pm\}0\.01080\.7759±0\.01550\.7759\\mathbin\{\\pm\}0\.01550\.7821±0\.01080\.7821\\mathbin\{\\pm\}0\.0108Equal\-width binning0\.7694±0\.01670\.7694\\mathbin\{\\pm\}0\.01670\.7683±0\.01570\.7683\\mathbin\{\\pm\}0\.01570\.7687±0\.01650\.7687\\mathbin\{\\pm\}0\.01650\.7688±0\.01570\.7688\\mathbin\{\\pm\}0\.01570\.7707±0\.01550\.7707\\mathbin\{\\pm\}0\.01550\.7685±0\.01630\.7685\\mathbin\{\\pm\}0\.01630\.7703±0\.01530\.7703\\mathbin\{\\pm\}0\.0153Equal\-frequency binning0\.7788±0\.01440\.7788\\mathbin\{\\pm\}0\.01440\.7809±0\.01150\.7809\\mathbin\{\\pm\}0\.01150\.7806±0\.01150\.7806\\mathbin\{\\pm\}0\.01150\.7805±0\.01140\.7805\\mathbin\{\\pm\}0\.01140\.7789±0\.01150\.7789\\mathbin\{\\pm\}0\.01150\.7779±0\.01390\.7779\\mathbin\{\\pm\}0\.01390\.7799±0\.01220\.7799\\mathbin\{\\pm\}0\.0122Numeric interactions0\.7776±0\.01390\.7776\\mathbin\{\\pm\}0\.01390\.7809±0\.01080\.7809\\mathbin\{\\pm\}0\.01080\.7791±0\.01090\.7791\\mathbin\{\\pm\}0\.01090\.7805±0\.01100\.7805\\mathbin\{\\pm\}0\.01100\.7815±0\.01070\.7815\\mathbin\{\\pm\}0\.01070\.7774±0\.01190\.7774\\mathbin\{\\pm\}0\.01190\.7817±0\.01130\.7817\\mathbin\{\\pm\}0\.0113Group aggregation0\.7718±0\.01680\.7718\\mathbin\{\\pm\}0\.01680\.7793±0\.01040\.7793\\mathbin\{\\pm\}0\.01040\.7795±0\.01130\.7795\\mathbin\{\\pm\}0\.01130\.7808±0\.01030\.7808\\mathbin\{\\pm\}0\.01030\.7811±0\.01080\.7811\\mathbin\{\\pm\}0\.01080\.7757±0\.01500\.7757\\mathbin\{\\pm\}0\.01500\.7822±0\.01150\.7822\\mathbin\{\\pm\}0\.0115Variance filter0\.7776±0\.01390\.7776\\mathbin\{\\pm\}0\.01390\.7809±0\.01080\.7809\\mathbin\{\\pm\}0\.01080\.7791±0\.01090\.7791\\mathbin\{\\pm\}0\.01090\.7805±0\.01100\.7805\\mathbin\{\\pm\}0\.01100\.7815±0\.01070\.7815\\mathbin\{\\pm\}0\.01070\.7774±0\.01190\.7774\\mathbin\{\\pm\}0\.01190\.7817±0\.01130\.7817\\mathbin\{\\pm\}0\.0113Collinearity filter0\.7776±0\.01390\.7776\\mathbin\{\\pm\}0\.01390\.7809±0\.01080\.7809\\mathbin\{\\pm\}0\.01080\.7791±0\.01090\.7791\\mathbin\{\\pm\}0\.01090\.7805±0\.01100\.7805\\mathbin\{\\pm\}0\.01100\.7815±0\.01070\.7815\\mathbin\{\\pm\}0\.01070\.7774±0\.01190\.7774\\mathbin\{\\pm\}0\.01190\.7817±0\.01130\.7817\\mathbin\{\\pm\}0\.0113PCA0\.7782±0\.01350\.7782\\mathbin\{\\pm\}0\.01350\.7803±0\.01100\.7803\\mathbin\{\\pm\}0\.01100\.7806±0\.01100\.7806\\mathbin\{\\pm\}0\.01100\.7792±0\.01160\.7792\\mathbin\{\\pm\}0\.01160\.7808±0\.01150\.7808\\mathbin\{\\pm\}0\.01150\.7770±0\.01420\.7770\\mathbin\{\\pm\}0\.01420\.7809±0\.01300\.7809\\mathbin\{\\pm\}0\.0130Supervised selection0\.7749±0\.01400\.7749\\mathbin\{\\pm\}0\.01400\.7803±0\.01200\.7803\\mathbin\{\\pm\}0\.01200\.7799±0\.01150\.7799\\mathbin\{\\pm\}0\.01150\.7802±0\.01180\.7802\\mathbin\{\\pm\}0\.01180\.7815±0\.01160\.7815\\mathbin\{\\pm\}0\.01160\.7775±0\.01290\.7775\\mathbin\{\\pm\}0\.01290\.7805±0\.01190\.7805\\mathbin\{\\pm\}0\.0119TabPrep full0\.7754±0\.01520\.7754\\mathbin\{\\pm\}0\.01520\.7799±0\.01470\.7799\\mathbin\{\\pm\}0\.01470\.7775±0\.01360\.7775\\mathbin\{\\pm\}0\.01360\.7774±0\.01600\.7774\\mathbin\{\\pm\}0\.01600\.7798±0\.01420\.7798\\mathbin\{\\pm\}0\.01420\.7774±0\.01420\.7774\\mathbin\{\\pm\}0\.01420\.7811±0\.01360\.7811\\mathbin\{\\pm\}0\.0136TabPrep w/o groupby0\.7759±0\.01430\.7759\\mathbin\{\\pm\}0\.01430\.7762±0\.01380\.7762\\mathbin\{\\pm\}0\.01380\.7775±0\.01470\.7775\\mathbin\{\\pm\}0\.01470\.7764±0\.01560\.7764\\mathbin\{\\pm\}0\.01560\.7802±0\.01450\.7802\\mathbin\{\\pm\}0\.01450\.7765±0\.01420\.7765\\mathbin\{\\pm\}0\.01420\.7795±0\.01480\.7795\\mathbin\{\\pm\}0\.0148TabPrep w/o RSFC0\.7766±0\.01210\.7766\\mathbin\{\\pm\}0\.01210\.7779±0\.01380\.7779\\mathbin\{\\pm\}0\.01380\.7758±0\.01280\.7758\\mathbin\{\\pm\}0\.01280\.7773±0\.01350\.7773\\mathbin\{\\pm\}0\.01350\.7802±0\.01230\.7802\\mathbin\{\\pm\}0\.01230\.7762±0\.01440\.7762\\mathbin\{\\pm\}0\.01440\.7805±0\.01370\.7805\\mathbin\{\\pm\}0\.0137TabPrep w/o arithmetic0\.7476±0\.01540\.7476\\mathbin\{\\pm\}0\.01540\.7561±0\.01550\.7561\\mathbin\{\\pm\}0\.01550\.7590±0\.01340\.7590\\mathbin\{\\pm\}0\.01340\.7557±0\.01530\.7557\\mathbin\{\\pm\}0\.01530\.7571±0\.01440\.7571\\mathbin\{\\pm\}0\.01440\.7519±0\.01680\.7519\\mathbin\{\\pm\}0\.01680\.7525±0\.01700\.7525\\mathbin\{\\pm\}0\.0170TabPrep w/o cat\. interact\.0\.7760±0\.01330\.7760\\mathbin\{\\pm\}0\.01330\.7777±0\.01410\.7777\\mathbin\{\\pm\}0\.01410\.7781±0\.01270\.7781\\mathbin\{\\pm\}0\.01270\.7757±0\.01200\.7757\\mathbin\{\\pm\}0\.01200\.7810±0\.01380\.7810\\mathbin\{\\pm\}0\.01380\.7761±0\.01210\.7761\\mathbin\{\\pm\}0\.01210\.7805±0\.01370\.7805\\mathbin\{\\pm\}0\.0137TabPrep w/o OOF\-TE0\.7752±0\.01550\.7752\\mathbin\{\\pm\}0\.01550\.7787±0\.01340\.7787\\mathbin\{\\pm\}0\.01340\.7777±0\.01490\.7777\\mathbin\{\\pm\}0\.01490\.7762±0\.01300\.7762\\mathbin\{\\pm\}0\.01300\.7810±0\.01530\.7810\\mathbin\{\\pm\}0\.01530\.7761±0\.01500\.7761\\mathbin\{\\pm\}0\.01500\.7803±0\.01390\.7803\\mathbin\{\\pm\}0\.0139Shared\-context kNN0\.7781±0\.01420\.7781\\mathbin\{\\pm\}0\.01420\.7810±0\.01150\.7810\\mathbin\{\\pm\}0\.01150\.7799±0\.01110\.7799\\mathbin\{\\pm\}0\.01110\.7807±0\.01110\.7807\\mathbin\{\\pm\}0\.01110\.7810±0\.01080\.7810\\mathbin\{\\pm\}0\.01080\.7779±0\.01220\.7779\\mathbin\{\\pm\}0\.01220\.7815±0\.01160\.7815\\mathbin\{\\pm\}0\.0116OOF prediction feature0\.7769±0\.01390\.7769\\mathbin\{\\pm\}0\.01390\.7808±0\.01190\.7808\\mathbin\{\\pm\}0\.01190\.7795±0\.01200\.7795\\mathbin\{\\pm\}0\.01200\.7806±0\.01190\.7806\\mathbin\{\\pm\}0\.01190\.7799±0\.01240\.7799\\mathbin\{\\pm\}0\.01240\.7770±0\.01250\.7770\\mathbin\{\\pm\}0\.01250\.7817±0\.01100\.7817\\mathbin\{\\pm\}0\.0110Table 21:Complete TabPFN and TabICL raw metric results for Fitness club, metric macro f1\. Values are mean±\\mathbin\{\\pm\}sample standard deviation across the 30 paired splits\.ConditionPFN v1PFN v2PFN v2\.5PFN v2\.6PFN v3ICL v1ICL v2Identity0\.7104±0\.02110\.7104\\mathbin\{\\pm\}0\.02110\.7162±0\.01780\.7162\\mathbin\{\\pm\}0\.01780\.7141±0\.01880\.7141\\mathbin\{\\pm\}0\.01880\.7181±0\.01810\.7181\\mathbin\{\\pm\}0\.01810\.7177±0\.01750\.7177\\mathbin\{\\pm\}0\.01750\.7115±0\.01900\.7115\\mathbin\{\\pm\}0\.01900\.7156±0\.01900\.7156\\mathbin\{\\pm\}0\.0190Standard scaling0\.7102±0\.02070\.7102\\mathbin\{\\pm\}0\.02070\.7173±0\.01710\.7173\\mathbin\{\\pm\}0\.01710\.7154±0\.01900\.7154\\mathbin\{\\pm\}0\.01900\.7182±0\.01800\.7182\\mathbin\{\\pm\}0\.01800\.7169±0\.01770\.7169\\mathbin\{\\pm\}0\.01770\.7117±0\.01890\.7117\\mathbin\{\\pm\}0\.01890\.7156±0\.01900\.7156\\mathbin\{\\pm\}0\.0190Log transform0\.7091±0\.02190\.7091\\mathbin\{\\pm\}0\.02190\.7158±0\.01780\.7158\\mathbin\{\\pm\}0\.01780\.7157±0\.01870\.7157\\mathbin\{\\pm\}0\.01870\.7170±0\.01750\.7170\\mathbin\{\\pm\}0\.01750\.7169±0\.01830\.7169\\mathbin\{\\pm\}0\.01830\.7112±0\.01940\.7112\\mathbin\{\\pm\}0\.01940\.7156±0\.01870\.7156\\mathbin\{\\pm\}0\.0187Square\-root transform0\.7085±0\.02150\.7085\\mathbin\{\\pm\}0\.02150\.7153±0\.01780\.7153\\mathbin\{\\pm\}0\.01780\.7142±0\.01920\.7142\\mathbin\{\\pm\}0\.01920\.7180±0\.01840\.7180\\mathbin\{\\pm\}0\.01840\.7171±0\.01910\.7171\\mathbin\{\\pm\}0\.01910\.7111±0\.01950\.7111\\mathbin\{\\pm\}0\.01950\.7151±0\.01860\.7151\\mathbin\{\\pm\}0\.0186Box–Cox0\.7095±0\.02190\.7095\\mathbin\{\\pm\}0\.02190\.7153±0\.01830\.7153\\mathbin\{\\pm\}0\.01830\.7165±0\.01950\.7165\\mathbin\{\\pm\}0\.01950\.7186±0\.01760\.7186\\mathbin\{\\pm\}0\.01760\.7180±0\.01690\.7180\\mathbin\{\\pm\}0\.01690\.7106±0\.01990\.7106\\mathbin\{\\pm\}0\.01990\.7156±0\.01880\.7156\\mathbin\{\\pm\}0\.0188Min–max scaling0\.7102±0\.02070\.7102\\mathbin\{\\pm\}0\.02070\.7166±0\.01770\.7166\\mathbin\{\\pm\}0\.01770\.7148±0\.01920\.7148\\mathbin\{\\pm\}0\.01920\.7180±0\.01800\.7180\\mathbin\{\\pm\}0\.01800\.7173±0\.01740\.7173\\mathbin\{\\pm\}0\.01740\.7118±0\.01900\.7118\\mathbin\{\\pm\}0\.01900\.7156±0\.01900\.7156\\mathbin\{\\pm\}0\.0190One\-hot encoding0\.7049±0\.02100\.7049\\mathbin\{\\pm\}0\.02100\.7157±0\.01850\.7157\\mathbin\{\\pm\}0\.01850\.7155±0\.01770\.7155\\mathbin\{\\pm\}0\.01770\.7190±0\.01720\.7190\\mathbin\{\\pm\}0\.01720\.7166±0\.01640\.7166\\mathbin\{\\pm\}0\.01640\.7144±0\.02090\.7144\\mathbin\{\\pm\}0\.02090\.7156±0\.01850\.7156\\mathbin\{\\pm\}0\.0185Ordinal encoding0\.7104±0\.02110\.7104\\mathbin\{\\pm\}0\.02110\.7168±0\.01750\.7168\\mathbin\{\\pm\}0\.01750\.7163±0\.01830\.7163\\mathbin\{\\pm\}0\.01830\.7178±0\.01800\.7178\\mathbin\{\\pm\}0\.01800\.7170±0\.01810\.7170\\mathbin\{\\pm\}0\.01810\.7115±0\.01900\.7115\\mathbin\{\\pm\}0\.01900\.7160±0\.01920\.7160\\mathbin\{\\pm\}0\.0192Frequency encoding0\.7111±0\.02030\.7111\\mathbin\{\\pm\}0\.02030\.7157±0\.01780\.7157\\mathbin\{\\pm\}0\.01780\.7165±0\.01790\.7165\\mathbin\{\\pm\}0\.01790\.7190±0\.01790\.7190\\mathbin\{\\pm\}0\.01790\.7180±0\.01690\.7180\\mathbin\{\\pm\}0\.01690\.7122±0\.02040\.7122\\mathbin\{\\pm\}0\.02040\.7173±0\.01800\.7173\\mathbin\{\\pm\}0\.0180Target encoding0\.7112±0\.01900\.7112\\mathbin\{\\pm\}0\.01900\.7172±0\.01760\.7172\\mathbin\{\\pm\}0\.01760\.7166±0\.01890\.7166\\mathbin\{\\pm\}0\.01890\.7198±0\.01800\.7198\\mathbin\{\\pm\}0\.01800\.7174±0\.01850\.7174\\mathbin\{\\pm\}0\.01850\.7138±0\.02010\.7138\\mathbin\{\\pm\}0\.02010\.7169±0\.01790\.7169\\mathbin\{\\pm\}0\.0179Categorical crosses0\.7058±0\.02060\.7058\\mathbin\{\\pm\}0\.02060\.7150±0\.01870\.7150\\mathbin\{\\pm\}0\.01870\.7148±0\.01780\.7148\\mathbin\{\\pm\}0\.01780\.7170±0\.01730\.7170\\mathbin\{\\pm\}0\.01730\.7155±0\.01750\.7155\\mathbin\{\\pm\}0\.01750\.7122±0\.02250\.7122\\mathbin\{\\pm\}0\.02250\.7162±0\.01820\.7162\\mathbin\{\\pm\}0\.0182Equal\-width binning0\.7067±0\.02370\.7067\\mathbin\{\\pm\}0\.02370\.7115±0\.02300\.7115\\mathbin\{\\pm\}0\.02300\.7116±0\.02460\.7116\\mathbin\{\\pm\}0\.02460\.7138±0\.02380\.7138\\mathbin\{\\pm\}0\.02380\.7132±0\.02260\.7132\\mathbin\{\\pm\}0\.02260\.7122±0\.02450\.7122\\mathbin\{\\pm\}0\.02450\.7116±0\.02200\.7116\\mathbin\{\\pm\}0\.0220Equal\-frequency binning0\.7184±0\.02040\.7184\\mathbin\{\\pm\}0\.02040\.7140±0\.01900\.7140\\mathbin\{\\pm\}0\.01900\.7133±0\.01840\.7133\\mathbin\{\\pm\}0\.01840\.7136±0\.01760\.7136\\mathbin\{\\pm\}0\.01760\.7125±0\.01840\.7125\\mathbin\{\\pm\}0\.01840\.7134±0\.01970\.7134\\mathbin\{\\pm\}0\.01970\.7143±0\.01880\.7143\\mathbin\{\\pm\}0\.0188Numeric interactions0\.7104±0\.02110\.7104\\mathbin\{\\pm\}0\.02110\.7162±0\.01780\.7162\\mathbin\{\\pm\}0\.01780\.7141±0\.01880\.7141\\mathbin\{\\pm\}0\.01880\.7181±0\.01810\.7181\\mathbin\{\\pm\}0\.01810\.7177±0\.01750\.7177\\mathbin\{\\pm\}0\.01750\.7115±0\.01900\.7115\\mathbin\{\\pm\}0\.01900\.7156±0\.01900\.7156\\mathbin\{\\pm\}0\.0190Group aggregation0\.7008±0\.02510\.7008\\mathbin\{\\pm\}0\.02510\.7148±0\.01810\.7148\\mathbin\{\\pm\}0\.01810\.7156±0\.01920\.7156\\mathbin\{\\pm\}0\.01920\.7184±0\.01750\.7184\\mathbin\{\\pm\}0\.01750\.7174±0\.01760\.7174\\mathbin\{\\pm\}0\.01760\.7117±0\.02320\.7117\\mathbin\{\\pm\}0\.02320\.7157±0\.01880\.7157\\mathbin\{\\pm\}0\.0188Variance filter0\.7104±0\.02110\.7104\\mathbin\{\\pm\}0\.02110\.7162±0\.01780\.7162\\mathbin\{\\pm\}0\.01780\.7141±0\.01880\.7141\\mathbin\{\\pm\}0\.01880\.7181±0\.01810\.7181\\mathbin\{\\pm\}0\.01810\.7177±0\.01750\.7177\\mathbin\{\\pm\}0\.01750\.7115±0\.01900\.7115\\mathbin\{\\pm\}0\.01900\.7156±0\.01900\.7156\\mathbin\{\\pm\}0\.0190Collinearity filter0\.7104±0\.02110\.7104\\mathbin\{\\pm\}0\.02110\.7162±0\.01780\.7162\\mathbin\{\\pm\}0\.01780\.7141±0\.01880\.7141\\mathbin\{\\pm\}0\.01880\.7181±0\.01810\.7181\\mathbin\{\\pm\}0\.01810\.7177±0\.01750\.7177\\mathbin\{\\pm\}0\.01750\.7115±0\.01900\.7115\\mathbin\{\\pm\}0\.01900\.7156±0\.01900\.7156\\mathbin\{\\pm\}0\.0190PCA0\.7108±0\.02090\.7108\\mathbin\{\\pm\}0\.02090\.7149±0\.01790\.7149\\mathbin\{\\pm\}0\.01790\.7155±0\.01740\.7155\\mathbin\{\\pm\}0\.01740\.7132±0\.01840\.7132\\mathbin\{\\pm\}0\.01840\.7144±0\.01900\.7144\\mathbin\{\\pm\}0\.01900\.7086±0\.02210\.7086\\mathbin\{\\pm\}0\.02210\.7124±0\.02120\.7124\\mathbin\{\\pm\}0\.0212Supervised selection0\.7072±0\.02140\.7072\\mathbin\{\\pm\}0\.02140\.7169±0\.01940\.7169\\mathbin\{\\pm\}0\.01940\.7158±0\.01890\.7158\\mathbin\{\\pm\}0\.01890\.7177±0\.01850\.7177\\mathbin\{\\pm\}0\.01850\.7177±0\.01870\.7177\\mathbin\{\\pm\}0\.01870\.7128±0\.02040\.7128\\mathbin\{\\pm\}0\.02040\.7139±0\.01960\.7139\\mathbin\{\\pm\}0\.0196TabPrep full0\.7045±0\.02390\.7045\\mathbin\{\\pm\}0\.02390\.7146±0\.02190\.7146\\mathbin\{\\pm\}0\.02190\.7098±0\.02210\.7098\\mathbin\{\\pm\}0\.02210\.7110±0\.02410\.7110\\mathbin\{\\pm\}0\.02410\.7106±0\.02250\.7106\\mathbin\{\\pm\}0\.02250\.7080±0\.02290\.7080\\mathbin\{\\pm\}0\.02290\.7119±0\.02210\.7119\\mathbin\{\\pm\}0\.0221TabPrep w/o groupby0\.7061±0\.02210\.7061\\mathbin\{\\pm\}0\.02210\.7089±0\.02160\.7089\\mathbin\{\\pm\}0\.02160\.7093±0\.02430\.7093\\mathbin\{\\pm\}0\.02430\.7091±0\.02620\.7091\\mathbin\{\\pm\}0\.02620\.7103±0\.02420\.7103\\mathbin\{\\pm\}0\.02420\.7068±0\.02270\.7068\\mathbin\{\\pm\}0\.02270\.7110±0\.02370\.7110\\mathbin\{\\pm\}0\.0237TabPrep w/o RSFC0\.7099±0\.02050\.7099\\mathbin\{\\pm\}0\.02050\.7125±0\.02150\.7125\\mathbin\{\\pm\}0\.02150\.7075±0\.02180\.7075\\mathbin\{\\pm\}0\.02180\.7126±0\.02120\.7126\\mathbin\{\\pm\}0\.02120\.7125±0\.02060\.7125\\mathbin\{\\pm\}0\.02060\.7078±0\.02390\.7078\\mathbin\{\\pm\}0\.02390\.7121±0\.02190\.7121\\mathbin\{\\pm\}0\.0219TabPrep w/o arithmetic0\.6656±0\.02390\.6656\\mathbin\{\\pm\}0\.02390\.6807±0\.02500\.6807\\mathbin\{\\pm\}0\.02500\.6855±0\.02150\.6855\\mathbin\{\\pm\}0\.02150\.6739±0\.03160\.6739\\mathbin\{\\pm\}0\.03160\.6745±0\.02940\.6745\\mathbin\{\\pm\}0\.02940\.6773±0\.02430\.6773\\mathbin\{\\pm\}0\.02430\.6496±0\.03960\.6496\\mathbin\{\\pm\}0\.0396TabPrep w/o cat\. interact\.0\.7065±0\.02130\.7065\\mathbin\{\\pm\}0\.02130\.7115±0\.02120\.7115\\mathbin\{\\pm\}0\.02120\.7105±0\.02040\.7105\\mathbin\{\\pm\}0\.02040\.7092±0\.01970\.7092\\mathbin\{\\pm\}0\.01970\.7125±0\.02270\.7125\\mathbin\{\\pm\}0\.02270\.7059±0\.02090\.7059\\mathbin\{\\pm\}0\.02090\.7119±0\.02200\.7119\\mathbin\{\\pm\}0\.0220TabPrep w/o OOF\-TE0\.7053±0\.02210\.7053\\mathbin\{\\pm\}0\.02210\.7129±0\.02150\.7129\\mathbin\{\\pm\}0\.02150\.7102±0\.02360\.7102\\mathbin\{\\pm\}0\.02360\.7110±0\.01970\.7110\\mathbin\{\\pm\}0\.01970\.7133±0\.02390\.7133\\mathbin\{\\pm\}0\.02390\.7068±0\.02360\.7068\\mathbin\{\\pm\}0\.02360\.7119±0\.02390\.7119\\mathbin\{\\pm\}0\.0239Shared\-context kNN0\.7108±0\.02180\.7108\\mathbin\{\\pm\}0\.02180\.7160±0\.01880\.7160\\mathbin\{\\pm\}0\.01880\.7155±0\.01830\.7155\\mathbin\{\\pm\}0\.01830\.7184±0\.01820\.7184\\mathbin\{\\pm\}0\.01820\.7168±0\.01760\.7168\\mathbin\{\\pm\}0\.01760\.7121±0\.01910\.7121\\mathbin\{\\pm\}0\.01910\.7155±0\.01910\.7155\\mathbin\{\\pm\}0\.0191OOF prediction feature0\.7051±0\.02280\.7051\\mathbin\{\\pm\}0\.02280\.7152±0\.02000\.7152\\mathbin\{\\pm\}0\.02000\.7146±0\.01930\.7146\\mathbin\{\\pm\}0\.01930\.7172±0\.01980\.7172\\mathbin\{\\pm\}0\.01980\.7163±0\.01850\.7163\\mathbin\{\\pm\}0\.01850\.7142±0\.02030\.7142\\mathbin\{\\pm\}0\.02030\.7174±0\.01840\.7174\\mathbin\{\\pm\}0\.0184Table 22:Complete raw metric results for Healthcare insurance, metric r2\. Values are mean±\\mathbin\{\\pm\}sample standard deviation across the 30 paired splits\.ConditionPFN v2PFN v2\.5PFN v2\.6PFN v3ICL v2Identity0\.8479±0\.01820\.8479\\mathbin\{\\pm\}0\.01820\.8598±0\.01960\.8598\\mathbin\{\\pm\}0\.01960\.8650±0\.01920\.8650\\mathbin\{\\pm\}0\.01920\.8634±0\.02010\.8634\\mathbin\{\\pm\}0\.02010\.8636±0\.01800\.8636\\mathbin\{\\pm\}0\.0180Standard scaling0\.8475±0\.01830\.8475\\mathbin\{\\pm\}0\.01830\.8600±0\.01960\.8600\\mathbin\{\\pm\}0\.01960\.8626±0\.01920\.8626\\mathbin\{\\pm\}0\.01920\.8633±0\.02010\.8633\\mathbin\{\\pm\}0\.02010\.8636±0\.01800\.8636\\mathbin\{\\pm\}0\.0180Log transform0\.8478±0\.01860\.8478\\mathbin\{\\pm\}0\.01860\.8599±0\.01950\.8599\\mathbin\{\\pm\}0\.01950\.8651±0\.01910\.8651\\mathbin\{\\pm\}0\.01910\.8629±0\.01990\.8629\\mathbin\{\\pm\}0\.01990\.8637±0\.01810\.8637\\mathbin\{\\pm\}0\.0181Square\-root transform0\.8472±0\.01880\.8472\\mathbin\{\\pm\}0\.01880\.8598±0\.01960\.8598\\mathbin\{\\pm\}0\.01960\.8650±0\.01910\.8650\\mathbin\{\\pm\}0\.01910\.8632±0\.02000\.8632\\mathbin\{\\pm\}0\.02000\.8636±0\.01800\.8636\\mathbin\{\\pm\}0\.0180Box–Cox0\.8479±0\.01850\.8479\\mathbin\{\\pm\}0\.01850\.8598±0\.01980\.8598\\mathbin\{\\pm\}0\.01980\.8653±0\.01940\.8653\\mathbin\{\\pm\}0\.01940\.8634±0\.02000\.8634\\mathbin\{\\pm\}0\.02000\.8635±0\.01810\.8635\\mathbin\{\\pm\}0\.0181Min–max scaling0\.8479±0\.01830\.8479\\mathbin\{\\pm\}0\.01830\.8600±0\.01960\.8600\\mathbin\{\\pm\}0\.01960\.8648±0\.01900\.8648\\mathbin\{\\pm\}0\.01900\.8633±0\.02000\.8633\\mathbin\{\\pm\}0\.02000\.8636±0\.01800\.8636\\mathbin\{\\pm\}0\.0180One\-hot encoding0\.8441±0\.01780\.8441\\mathbin\{\\pm\}0\.01780\.8612±0\.02010\.8612\\mathbin\{\\pm\}0\.02010\.8648±0\.01930\.8648\\mathbin\{\\pm\}0\.01930\.8627±0\.02000\.8627\\mathbin\{\\pm\}0\.02000\.8635±0\.01820\.8635\\mathbin\{\\pm\}0\.0182Ordinal encoding0\.8478±0\.01850\.8478\\mathbin\{\\pm\}0\.01850\.8596±0\.02010\.8596\\mathbin\{\\pm\}0\.02010\.8649±0\.01910\.8649\\mathbin\{\\pm\}0\.01910\.8633±0\.02000\.8633\\mathbin\{\\pm\}0\.02000\.8634±0\.01800\.8634\\mathbin\{\\pm\}0\.0180Frequency encoding0\.8507±0\.01860\.8507\\mathbin\{\\pm\}0\.01860\.8605±0\.01980\.8605\\mathbin\{\\pm\}0\.01980\.8647±0\.01940\.8647\\mathbin\{\\pm\}0\.01940\.8638±0\.02000\.8638\\mathbin\{\\pm\}0\.02000\.8635±0\.01810\.8635\\mathbin\{\\pm\}0\.0181Target encoding0\.8543±0\.01900\.8543\\mathbin\{\\pm\}0\.01900\.8616±0\.01920\.8616\\mathbin\{\\pm\}0\.01920\.8643±0\.01900\.8643\\mathbin\{\\pm\}0\.01900\.8624±0\.01920\.8624\\mathbin\{\\pm\}0\.01920\.8616±0\.01850\.8616\\mathbin\{\\pm\}0\.0185Categorical crosses0\.8429±0\.01880\.8429\\mathbin\{\\pm\}0\.01880\.8604±0\.02000\.8604\\mathbin\{\\pm\}0\.02000\.8647±0\.01890\.8647\\mathbin\{\\pm\}0\.01890\.8614±0\.02020\.8614\\mathbin\{\\pm\}0\.02020\.8633±0\.01800\.8633\\mathbin\{\\pm\}0\.0180Equal\-width binning0\.8460±0\.01930\.8460\\mathbin\{\\pm\}0\.01930\.8484±0\.01970\.8484\\mathbin\{\\pm\}0\.01970\.8488±0\.02050\.8488\\mathbin\{\\pm\}0\.02050\.8497±0\.02070\.8497\\mathbin\{\\pm\}0\.02070\.8501±0\.01910\.8501\\mathbin\{\\pm\}0\.0191Equal\-frequency binning0\.8553±0\.02000\.8553\\mathbin\{\\pm\}0\.02000\.8576±0\.02000\.8576\\mathbin\{\\pm\}0\.02000\.8580±0\.02120\.8580\\mathbin\{\\pm\}0\.02120\.8587±0\.02140\.8587\\mathbin\{\\pm\}0\.02140\.8583±0\.02020\.8583\\mathbin\{\\pm\}0\.0202Numeric interactions0\.8479±0\.01820\.8479\\mathbin\{\\pm\}0\.01820\.8598±0\.01960\.8598\\mathbin\{\\pm\}0\.01960\.8650±0\.01920\.8650\\mathbin\{\\pm\}0\.01920\.8634±0\.02010\.8634\\mathbin\{\\pm\}0\.02010\.8636±0\.01800\.8636\\mathbin\{\\pm\}0\.0180Group aggregation0\.8423±0\.01810\.8423\\mathbin\{\\pm\}0\.01810\.8617±0\.02010\.8617\\mathbin\{\\pm\}0\.02010\.8651±0\.01920\.8651\\mathbin\{\\pm\}0\.01920\.8600±0\.02050\.8600\\mathbin\{\\pm\}0\.02050\.8634±0\.01820\.8634\\mathbin\{\\pm\}0\.0182Variance filter0\.8479±0\.01820\.8479\\mathbin\{\\pm\}0\.01820\.8598±0\.01960\.8598\\mathbin\{\\pm\}0\.01960\.8650±0\.01920\.8650\\mathbin\{\\pm\}0\.01920\.8634±0\.02010\.8634\\mathbin\{\\pm\}0\.02010\.8636±0\.01800\.8636\\mathbin\{\\pm\}0\.0180Collinearity filter0\.8479±0\.01820\.8479\\mathbin\{\\pm\}0\.01820\.8598±0\.01960\.8598\\mathbin\{\\pm\}0\.01960\.8650±0\.01920\.8650\\mathbin\{\\pm\}0\.01920\.8634±0\.02010\.8634\\mathbin\{\\pm\}0\.02010\.8636±0\.01800\.8636\\mathbin\{\\pm\}0\.0180PCA0\.8556±0\.01970\.8556\\mathbin\{\\pm\}0\.01970\.8583±0\.01920\.8583\\mathbin\{\\pm\}0\.01920\.8572±0\.01960\.8572\\mathbin\{\\pm\}0\.01960\.8575±0\.02010\.8575\\mathbin\{\\pm\}0\.02010\.8572±0\.01870\.8572\\mathbin\{\\pm\}0\.0187Supervised selection0\.7140±0\.02290\.7140\\mathbin\{\\pm\}0\.02290\.7146±0\.02390\.7146\\mathbin\{\\pm\}0\.02390\.7187±0\.02250\.7187\\mathbin\{\\pm\}0\.02250\.7206±0\.02210\.7206\\mathbin\{\\pm\}0\.02210\.7180±0\.02210\.7180\\mathbin\{\\pm\}0\.0221TabPrep full0\.7446±0\.22170\.7446\\mathbin\{\\pm\}0\.22170\.7550±0\.21320\.7550\\mathbin\{\\pm\}0\.21320\.7539±0\.21340\.7539\\mathbin\{\\pm\}0\.21340\.7519±0\.20960\.7519\\mathbin\{\\pm\}0\.20960\.7407±0\.23130\.7407\\mathbin\{\\pm\}0\.2313TabPrep w/o groupby0\.7748±0\.18130\.7748\\mathbin\{\\pm\}0\.18130\.7825±0\.18140\.7825\\mathbin\{\\pm\}0\.18140\.7833±0\.17500\.7833\\mathbin\{\\pm\}0\.17500\.7824±0\.17180\.7824\\mathbin\{\\pm\}0\.17180\.7793±0\.17730\.7793\\mathbin\{\\pm\}0\.1773TabPrep w/o RSFC0\.0862±0\.02960\.0862\\mathbin\{\\pm\}0\.02960\.0923±0\.03050\.0923\\mathbin\{\\pm\}0\.03050\.1046±0\.02560\.1046\\mathbin\{\\pm\}0\.02560\.1059±0\.02710\.1059\\mathbin\{\\pm\}0\.02710\.1112±0\.02230\.1112\\mathbin\{\\pm\}0\.0223TabPrep w/o arithmetic0\.7194±0\.02600\.7194\\mathbin\{\\pm\}0\.02600\.7242±0\.02860\.7242\\mathbin\{\\pm\}0\.02860\.7228±0\.02460\.7228\\mathbin\{\\pm\}0\.02460\.7203±0\.02540\.7203\\mathbin\{\\pm\}0\.02540\.7172±0\.02500\.7172\\mathbin\{\\pm\}0\.0250TabPrep w/o cat\. interact\.0\.6575±0\.27970\.6575\\mathbin\{\\pm\}0\.27970\.6677±0\.27620\.6677\\mathbin\{\\pm\}0\.27620\.6613±0\.27730\.6613\\mathbin\{\\pm\}0\.27730\.6727±0\.26420\.6727\\mathbin\{\\pm\}0\.26420\.6679±0\.26790\.6679\\mathbin\{\\pm\}0\.2679TabPrep w/o OOF\-TE0\.6930±0\.26840\.6930\\mathbin\{\\pm\}0\.26840\.6971±0\.27510\.6971\\mathbin\{\\pm\}0\.27510\.6839±0\.30420\.6839\\mathbin\{\\pm\}0\.30420\.7024±0\.25750\.7024\\mathbin\{\\pm\}0\.25750\.6980±0\.26110\.6980\\mathbin\{\\pm\}0\.2611Shared\-context kNN0\.8478±0\.01800\.8478\\mathbin\{\\pm\}0\.01800\.8598±0\.01960\.8598\\mathbin\{\\pm\}0\.01960\.8650±0\.01920\.8650\\mathbin\{\\pm\}0\.01920\.8634±0\.02010\.8634\\mathbin\{\\pm\}0\.02010\.8636±0\.01800\.8636\\mathbin\{\\pm\}0\.0180OOF prediction feature0\.8491±0\.01800\.8491\\mathbin\{\\pm\}0\.01800\.8597±0\.01950\.8597\\mathbin\{\\pm\}0\.01950\.8642±0\.01930\.8642\\mathbin\{\\pm\}0\.01930\.8632±0\.01960\.8632\\mathbin\{\\pm\}0\.01960\.8654±0\.01860\.8654\\mathbin\{\\pm\}0\.0186Table 23:Complete raw metric results for Healthcare insurance, metric rmse\. Values are mean±\\mathbin\{\\pm\}sample standard deviation across the 30 paired splits\.ConditionPFN v2PFN v2\.5PFN v2\.6PFN v3ICL v2Identity4704\.2±301\.94704\.2\\mathbin\{\\pm\}301\.94513\.1±334\.54513\.1\\mathbin\{\\pm\}334\.54428\.3±334\.24428\.3\\mathbin\{\\pm\}334\.24453\.9±346\.14453\.9\\mathbin\{\\pm\}346\.14452\.3±310\.64452\.3\\mathbin\{\\pm\}310\.6Standard scaling4710\.4±304\.84710\.4\\mathbin\{\\pm\}304\.84509\.6±335\.44509\.6\\mathbin\{\\pm\}335\.44468\.2±338\.84468\.2\\mathbin\{\\pm\}338\.84455\.7±345\.74455\.7\\mathbin\{\\pm\}345\.74452\.3±310\.64452\.3\\mathbin\{\\pm\}310\.6Log transform4705\.2±305\.54705\.2\\mathbin\{\\pm\}305\.54511\.7±333\.64511\.7\\mathbin\{\\pm\}333\.64427\.5±331\.74427\.5\\mathbin\{\\pm\}331\.74461\.3±343\.84461\.3\\mathbin\{\\pm\}343\.84450\.5±310\.54450\.5\\mathbin\{\\pm\}310\.5Square\-root transform4714\.0±306\.94714\.0\\mathbin\{\\pm\}306\.94512\.9±334\.54512\.9\\mathbin\{\\pm\}334\.54428\.6±331\.24428\.6\\mathbin\{\\pm\}331\.24457\.2±344\.04457\.2\\mathbin\{\\pm\}344\.04452\.3±310\.64452\.3\\mathbin\{\\pm\}310\.6Box–Cox4703\.0±303\.44703\.0\\mathbin\{\\pm\}303\.44512\.5±340\.74512\.5\\mathbin\{\\pm\}340\.74422\.8±335\.74422\.8\\mathbin\{\\pm\}335\.74453\.5±343\.34453\.5\\mathbin\{\\pm\}343\.34453\.7±309\.04453\.7\\mathbin\{\\pm\}309\.0Min–max scaling4703\.5±302\.34703\.5\\mathbin\{\\pm\}302\.34510\.4±334\.54510\.4\\mathbin\{\\pm\}334\.54431\.8±330\.34431\.8\\mathbin\{\\pm\}330\.34454\.6±345\.04454\.6\\mathbin\{\\pm\}345\.04452\.3±310\.64452\.3\\mathbin\{\\pm\}310\.6One\-hot encoding4762\.3±292\.54762\.3\\mathbin\{\\pm\}292\.54489\.8±345\.54489\.8\\mathbin\{\\pm\}345\.54430\.6±333\.04430\.6\\mathbin\{\\pm\}333\.04464\.4±342\.74464\.4\\mathbin\{\\pm\}342\.74453\.7±313\.04453\.7\\mathbin\{\\pm\}313\.0Ordinal encoding4705\.3±307\.14705\.3\\mathbin\{\\pm\}307\.14516\.7±344\.04516\.7\\mathbin\{\\pm\}344\.04430\.5±331\.94430\.5\\mathbin\{\\pm\}331\.94455\.9±346\.24455\.9\\mathbin\{\\pm\}346\.24455\.9±311\.64455\.9\\mathbin\{\\pm\}311\.6Frequency encoding4659\.0±306\.94659\.0\\mathbin\{\\pm\}306\.94501\.9±342\.54501\.9\\mathbin\{\\pm\}342\.54432\.4±338\.74432\.4\\mathbin\{\\pm\}338\.74447\.6±346\.44447\.6\\mathbin\{\\pm\}346\.44454\.6±317\.24454\.6\\mathbin\{\\pm\}317\.2Target encoding4602\.1±323\.64602\.1\\mathbin\{\\pm\}323\.64485\.5±335\.84485\.5\\mathbin\{\\pm\}335\.84440\.2±330\.54440\.2\\mathbin\{\\pm\}330\.54470\.7±335\.14470\.7\\mathbin\{\\pm\}335\.14485\.4±312\.04485\.4\\mathbin\{\\pm\}312\.0Categorical crosses4779\.2±294\.24779\.2\\mathbin\{\\pm\}294\.24502\.2±340\.84502\.2\\mathbin\{\\pm\}340\.84433\.5±328\.64433\.5\\mathbin\{\\pm\}328\.64486\.4±345\.24486\.4\\mathbin\{\\pm\}345\.24457\.6±309\.84457\.6\\mathbin\{\\pm\}309\.8Equal\-width binning4731\.8±312\.14731\.8\\mathbin\{\\pm\}312\.14694\.2±321\.24694\.2\\mathbin\{\\pm\}321\.24687\.2±329\.94687\.2\\mathbin\{\\pm\}329\.94672\.9±331\.54672\.9\\mathbin\{\\pm\}331\.54668\.9±307\.74668\.9\\mathbin\{\\pm\}307\.7Equal\-frequency binning4585\.8±331\.94585\.8\\mathbin\{\\pm\}331\.94548\.9±336\.74548\.9\\mathbin\{\\pm\}336\.74540\.6±352\.54540\.6\\mathbin\{\\pm\}352\.54528\.6±358\.34528\.6\\mathbin\{\\pm\}358\.34536\.0±332\.44536\.0\\mathbin\{\\pm\}332\.4Numeric interactions4704\.2±301\.94704\.2\\mathbin\{\\pm\}301\.94513\.1±334\.54513\.1\\mathbin\{\\pm\}334\.54428\.3±334\.24428\.3\\mathbin\{\\pm\}334\.24453\.9±346\.14453\.9\\mathbin\{\\pm\}346\.14452\.3±310\.64452\.3\\mathbin\{\\pm\}310\.6Group aggregation4789\.1±274\.64789\.1\\mathbin\{\\pm\}274\.64482\.5±346\.54482\.5\\mathbin\{\\pm\}346\.54426\.9±332\.54426\.9\\mathbin\{\\pm\}332\.54509\.0±350\.14509\.0\\mathbin\{\\pm\}350\.14456\.0±311\.84456\.0\\mathbin\{\\pm\}311\.8Variance filter4704\.2±301\.94704\.2\\mathbin\{\\pm\}301\.94513\.1±334\.54513\.1\\mathbin\{\\pm\}334\.54428\.3±334\.24428\.3\\mathbin\{\\pm\}334\.24453\.9±346\.14453\.9\\mathbin\{\\pm\}346\.14452\.3±310\.64452\.3\\mathbin\{\\pm\}310\.6Collinearity filter4704\.2±301\.94704\.2\\mathbin\{\\pm\}301\.94513\.1±334\.54513\.1\\mathbin\{\\pm\}334\.54428\.3±334\.24428\.3\\mathbin\{\\pm\}334\.24453\.9±346\.14453\.9\\mathbin\{\\pm\}346\.14452\.3±310\.64452\.3\\mathbin\{\\pm\}310\.6PCA4581\.6±339\.94581\.6\\mathbin\{\\pm\}339\.94538\.9±334\.44538\.9\\mathbin\{\\pm\}334\.44556\.4±343\.94556\.4\\mathbin\{\\pm\}343\.94549\.7±346\.94549\.7\\mathbin\{\\pm\}346\.94556\.6±320\.34556\.6\\mathbin\{\\pm\}320\.3Supervised selection6458\.4±342\.56458\.4\\mathbin\{\\pm\}342\.56450\.5±343\.46450\.5\\mathbin\{\\pm\}343\.46404\.6±318\.16404\.6\\mathbin\{\\pm\}318\.16383\.2±318\.66383\.2\\mathbin\{\\pm\}318\.66412\.7±311\.16412\.7\\mathbin\{\\pm\}311\.1TabPrep full5722\.7±2234\.95722\.7\\mathbin\{\\pm\}2234\.95600\.7±2198\.75600\.7\\mathbin\{\\pm\}2198\.75614\.3±2199\.85614\.3\\mathbin\{\\pm\}2199\.85656\.2±2158\.75656\.2\\mathbin\{\\pm\}2158\.75738\.7±2321\.95738\.7\\mathbin\{\\pm\}2321\.9TabPrep w/o groupby5473\.5±1960\.15473\.5\\mathbin\{\\pm\}1960\.15361\.5±1979\.65361\.5\\mathbin\{\\pm\}1979\.65367\.9±1924\.95367\.9\\mathbin\{\\pm\}1924\.95392\.3±1887\.35392\.3\\mathbin\{\\pm\}1887\.35421\.6±1930\.05421\.6\\mathbin\{\\pm\}1930\.0TabPrep w/o RSFC11556\.9±541\.911556\.9\\mathbin\{\\pm\}541\.911518\.2±551\.411518\.2\\mathbin\{\\pm\}551\.411438\.0±480\.411438\.0\\mathbin\{\\pm\}480\.411431\.6±532\.211431\.6\\mathbin\{\\pm\}532\.211395\.2±454\.211395\.2\\mathbin\{\\pm\}454\.2TabPrep w/o arithmetic6392\.3±311\.16392\.3\\mathbin\{\\pm\}311\.16334\.3±320\.66334\.3\\mathbin\{\\pm\}320\.66354\.6±306\.06354\.6\\mathbin\{\\pm\}306\.06383\.7±324\.36383\.7\\mathbin\{\\pm\}324\.36418\.3±309\.06418\.3\\mathbin\{\\pm\}309\.0TabPrep w/o cat\. interact\.6586\.3±2792\.96586\.3\\mathbin\{\\pm\}2792\.96471\.6±2790\.66471\.6\\mathbin\{\\pm\}2790\.66534\.6±2807\.46534\.6\\mathbin\{\\pm\}2807\.46451\.8±2695\.46451\.8\\mathbin\{\\pm\}2695\.46499\.5±2713\.36499\.5\\mathbin\{\\pm\}2713\.3TabPrep w/o OOF\-TE6217\.7±2625\.76217\.7\\mathbin\{\\pm\}2625\.76137\.8±2704\.26137\.8\\mathbin\{\\pm\}2704\.26227\.8±2829\.36227\.8\\mathbin\{\\pm\}2829\.36128\.9±2570\.16128\.9\\mathbin\{\\pm\}2570\.16172\.2±2592\.36172\.2\\mathbin\{\\pm\}2592\.3Shared\-context kNN4705\.7±298\.84705\.7\\mathbin\{\\pm\}298\.84512\.6±334\.24512\.6\\mathbin\{\\pm\}334\.24428\.4±333\.94428\.4\\mathbin\{\\pm\}333\.94453\.7±346\.54453\.7\\mathbin\{\\pm\}346\.54452\.4±310\.64452\.4\\mathbin\{\\pm\}310\.6OOF prediction feature4684\.3±294\.54684\.3\\mathbin\{\\pm\}294\.54514\.6±331\.74514\.6\\mathbin\{\\pm\}331\.74441\.9±332\.74441\.9\\mathbin\{\\pm\}332\.74457\.1±334\.34457\.1\\mathbin\{\\pm\}334\.34422\.6±315\.14422\.6\\mathbin\{\\pm\}315\.1Table 24:Complete TabPFN and TabICL raw metric results for Maternal health, metric accuracy\. Values are mean±\\mathbin\{\\pm\}sample standard deviation across the 30 paired splits\.ConditionPFN v1PFN v2PFN v2\.5PFN v2\.6PFN v3ICL v1ICL v2Identity0\.7739±0\.02570\.7739\\mathbin\{\\pm\}0\.02570\.8370±0\.02340\.8370\\mathbin\{\\pm\}0\.02340\.8321±0\.02230\.8321\\mathbin\{\\pm\}0\.02230\.8391±0\.02480\.8391\\mathbin\{\\pm\}0\.02480\.8411±0\.02380\.8411\\mathbin\{\\pm\}0\.02380\.8290±0\.02180\.8290\\mathbin\{\\pm\}0\.02180\.8451±0\.02660\.8451\\mathbin\{\\pm\}0\.0266Standard scaling0\.7739±0\.02570\.7739\\mathbin\{\\pm\}0\.02570\.8362±0\.02250\.8362\\mathbin\{\\pm\}0\.02250\.8319±0\.02120\.8319\\mathbin\{\\pm\}0\.02120\.8390±0\.02480\.8390\\mathbin\{\\pm\}0\.02480\.8410±0\.02330\.8410\\mathbin\{\\pm\}0\.02330\.8290±0\.02180\.8290\\mathbin\{\\pm\}0\.02180\.8451±0\.02660\.8451\\mathbin\{\\pm\}0\.0266Log transform0\.7741±0\.02760\.7741\\mathbin\{\\pm\}0\.02760\.8374±0\.02500\.8374\\mathbin\{\\pm\}0\.02500\.8329±0\.02240\.8329\\mathbin\{\\pm\}0\.02240\.8395±0\.02230\.8395\\mathbin\{\\pm\}0\.02230\.8427±0\.02370\.8427\\mathbin\{\\pm\}0\.02370\.8299±0\.02270\.8299\\mathbin\{\\pm\}0\.02270\.8437±0\.02610\.8437\\mathbin\{\\pm\}0\.0261Square\-root transform0\.7739±0\.02630\.7739\\mathbin\{\\pm\}0\.02630\.8372±0\.02210\.8372\\mathbin\{\\pm\}0\.02210\.8323±0\.02250\.8323\\mathbin\{\\pm\}0\.02250\.8388±0\.02390\.8388\\mathbin\{\\pm\}0\.02390\.8421±0\.02320\.8421\\mathbin\{\\pm\}0\.02320\.8297±0\.02230\.8297\\mathbin\{\\pm\}0\.02230\.8444±0\.02570\.8444\\mathbin\{\\pm\}0\.0257Box–Cox0\.7735±0\.02580\.7735\\mathbin\{\\pm\}0\.02580\.8386±0\.02470\.8386\\mathbin\{\\pm\}0\.02470\.8368±0\.02310\.8368\\mathbin\{\\pm\}0\.02310\.8380±0\.02270\.8380\\mathbin\{\\pm\}0\.02270\.8402±0\.02280\.8402\\mathbin\{\\pm\}0\.02280\.8293±0\.02330\.8293\\mathbin\{\\pm\}0\.02330\.8433±0\.02500\.8433\\mathbin\{\\pm\}0\.0250Min–max scaling0\.7739±0\.02570\.7739\\mathbin\{\\pm\}0\.02570\.8375±0\.02290\.8375\\mathbin\{\\pm\}0\.02290\.8331±0\.02250\.8331\\mathbin\{\\pm\}0\.02250\.8391±0\.02480\.8391\\mathbin\{\\pm\}0\.02480\.8412±0\.02210\.8412\\mathbin\{\\pm\}0\.02210\.8290±0\.02180\.8290\\mathbin\{\\pm\}0\.02180\.8451±0\.02660\.8451\\mathbin\{\\pm\}0\.0266One\-hot encoding———————Ordinal encoding———————Frequency encoding———————Target encoding———————Categorical crosses———————Equal\-width binning0\.7539±0\.02560\.7539\\mathbin\{\\pm\}0\.02560\.7725±0\.02370\.7725\\mathbin\{\\pm\}0\.02370\.7727±0\.02360\.7727\\mathbin\{\\pm\}0\.02360\.7705±0\.02290\.7705\\mathbin\{\\pm\}0\.02290\.7775±0\.02340\.7775\\mathbin\{\\pm\}0\.02340\.7669±0\.02440\.7669\\mathbin\{\\pm\}0\.02440\.7785±0\.02370\.7785\\mathbin\{\\pm\}0\.0237Equal\-frequency binning0\.7748±0\.02600\.7748\\mathbin\{\\pm\}0\.02600\.8167±0\.02240\.8167\\mathbin\{\\pm\}0\.02240\.8136±0\.02270\.8136\\mathbin\{\\pm\}0\.02270\.8168±0\.02070\.8168\\mathbin\{\\pm\}0\.02070\.8209±0\.02260\.8209\\mathbin\{\\pm\}0\.02260\.8092±0\.02050\.8092\\mathbin\{\\pm\}0\.02050\.8224±0\.02040\.8224\\mathbin\{\\pm\}0\.0204Numeric interactions0\.7640±0\.02810\.7640\\mathbin\{\\pm\}0\.02810\.8352±0\.02310\.8352\\mathbin\{\\pm\}0\.02310\.8278±0\.02100\.8278\\mathbin\{\\pm\}0\.02100\.8379±0\.02460\.8379\\mathbin\{\\pm\}0\.02460\.8393±0\.02470\.8393\\mathbin\{\\pm\}0\.02470\.8338±0\.02380\.8338\\mathbin\{\\pm\}0\.02380\.8436±0\.02550\.8436\\mathbin\{\\pm\}0\.0255Group aggregation———————Variance filter0\.7739±0\.02570\.7739\\mathbin\{\\pm\}0\.02570\.8370±0\.02340\.8370\\mathbin\{\\pm\}0\.02340\.8321±0\.02230\.8321\\mathbin\{\\pm\}0\.02230\.8391±0\.02480\.8391\\mathbin\{\\pm\}0\.02480\.8411±0\.02380\.8411\\mathbin\{\\pm\}0\.02380\.8290±0\.02180\.8290\\mathbin\{\\pm\}0\.02180\.8451±0\.02660\.8451\\mathbin\{\\pm\}0\.0266Collinearity filter0\.7739±0\.02570\.7739\\mathbin\{\\pm\}0\.02570\.8370±0\.02340\.8370\\mathbin\{\\pm\}0\.02340\.8321±0\.02230\.8321\\mathbin\{\\pm\}0\.02230\.8391±0\.02480\.8391\\mathbin\{\\pm\}0\.02480\.8411±0\.02380\.8411\\mathbin\{\\pm\}0\.02380\.8290±0\.02180\.8290\\mathbin\{\\pm\}0\.02180\.8451±0\.02660\.8451\\mathbin\{\\pm\}0\.0266PCA0\.7788±0\.02510\.7788\\mathbin\{\\pm\}0\.02510\.8244±0\.02170\.8244\\mathbin\{\\pm\}0\.02170\.8000±0\.02270\.8000\\mathbin\{\\pm\}0\.02270\.8176±0\.02270\.8176\\mathbin\{\\pm\}0\.02270\.8295±0\.02470\.8295\\mathbin\{\\pm\}0\.02470\.8070±0\.02070\.8070\\mathbin\{\\pm\}0\.02070\.8361±0\.02490\.8361\\mathbin\{\\pm\}0\.0249Supervised selection0\.7442±0\.02120\.7442\\mathbin\{\\pm\}0\.02120\.8023±0\.01740\.8023\\mathbin\{\\pm\}0\.01740\.7805±0\.02420\.7805\\mathbin\{\\pm\}0\.02420\.8046±0\.01970\.8046\\mathbin\{\\pm\}0\.01970\.8137±0\.02090\.8137\\mathbin\{\\pm\}0\.02090\.8052±0\.02390\.8052\\mathbin\{\\pm\}0\.02390\.8184±0\.02060\.8184\\mathbin\{\\pm\}0\.0206TabPrep full0\.7375±0\.02640\.7375\\mathbin\{\\pm\}0\.02640\.8200±0\.02480\.8200\\mathbin\{\\pm\}0\.02480\.8155±0\.02140\.8155\\mathbin\{\\pm\}0\.02140\.8245±0\.02390\.8245\\mathbin\{\\pm\}0\.02390\.8262±0\.02490\.8262\\mathbin\{\\pm\}0\.02490\.7984±0\.02210\.7984\\mathbin\{\\pm\}0\.02210\.8292±0\.02430\.8292\\mathbin\{\\pm\}0\.0243TabPrep w/o groupby0\.7397±0\.02740\.7397\\mathbin\{\\pm\}0\.02740\.8235±0\.02190\.8235\\mathbin\{\\pm\}0\.02190\.8179±0\.02160\.8179\\mathbin\{\\pm\}0\.02160\.8256±0\.02200\.8256\\mathbin\{\\pm\}0\.02200\.8258±0\.02460\.8258\\mathbin\{\\pm\}0\.02460\.7993±0\.02290\.7993\\mathbin\{\\pm\}0\.02290\.8286±0\.02450\.8286\\mathbin\{\\pm\}0\.0245TabPrep w/o RSFC0\.7355±0\.02340\.7355\\mathbin\{\\pm\}0\.02340\.8214±0\.02290\.8214\\mathbin\{\\pm\}0\.02290\.8166±0\.02140\.8166\\mathbin\{\\pm\}0\.02140\.8262±0\.02190\.8262\\mathbin\{\\pm\}0\.02190\.8246±0\.02260\.8246\\mathbin\{\\pm\}0\.02260\.7982±0\.02210\.7982\\mathbin\{\\pm\}0\.02210\.8279±0\.02610\.8279\\mathbin\{\\pm\}0\.0261TabPrep w/o arithmetic0\.8404±0\.02310\.8404\\mathbin\{\\pm\}0\.02310\.8464±0\.02580\.8464\\mathbin\{\\pm\}0\.02580\.8446±0\.02470\.8446\\mathbin\{\\pm\}0\.02470\.8494±0\.02540\.8494\\mathbin\{\\pm\}0\.02540\.8455±0\.02380\.8455\\mathbin\{\\pm\}0\.02380\.8396±0\.02330\.8396\\mathbin\{\\pm\}0\.02330\.8432±0\.02420\.8432\\mathbin\{\\pm\}0\.0242TabPrep w/o cat\. interact\.0\.7352±0\.02310\.7352\\mathbin\{\\pm\}0\.02310\.8213±0\.02360\.8213\\mathbin\{\\pm\}0\.02360\.8171±0\.02190\.8171\\mathbin\{\\pm\}0\.02190\.8241±0\.02180\.8241\\mathbin\{\\pm\}0\.02180\.8276±0\.02540\.8276\\mathbin\{\\pm\}0\.02540\.7999±0\.02320\.7999\\mathbin\{\\pm\}0\.02320\.8281±0\.02380\.8281\\mathbin\{\\pm\}0\.0238TabPrep w/o OOF\-TE0\.7376±0\.02700\.7376\\mathbin\{\\pm\}0\.02700\.8194±0\.02010\.8194\\mathbin\{\\pm\}0\.02010\.8164±0\.02140\.8164\\mathbin\{\\pm\}0\.02140\.8274±0\.02260\.8274\\mathbin\{\\pm\}0\.02260\.8278±0\.02370\.8278\\mathbin\{\\pm\}0\.02370\.7990±0\.02340\.7990\\mathbin\{\\pm\}0\.02340\.8279±0\.02440\.8279\\mathbin\{\\pm\}0\.0244Shared\-context kNN0\.7752±0\.02530\.7752\\mathbin\{\\pm\}0\.02530\.8364±0\.02400\.8364\\mathbin\{\\pm\}0\.02400\.8318±0\.02030\.8318\\mathbin\{\\pm\}0\.02030\.8393±0\.02330\.8393\\mathbin\{\\pm\}0\.02330\.8402±0\.02390\.8402\\mathbin\{\\pm\}0\.02390\.8295±0\.02200\.8295\\mathbin\{\\pm\}0\.02200\.8447±0\.02620\.8447\\mathbin\{\\pm\}0\.0262OOF prediction feature0\.7653±0\.02650\.7653\\mathbin\{\\pm\}0\.02650\.8368±0\.02370\.8368\\mathbin\{\\pm\}0\.02370\.8179±0\.02410\.8179\\mathbin\{\\pm\}0\.02410\.8374±0\.02210\.8374\\mathbin\{\\pm\}0\.02210\.8457±0\.01970\.8457\\mathbin\{\\pm\}0\.01970\.8187±0\.02250\.8187\\mathbin\{\\pm\}0\.02250\.8432±0\.02630\.8432\\mathbin\{\\pm\}0\.0263Table 25:Complete TabPFN and TabICL raw metric results for Maternal health, metric macro f1\. Values are mean±\\mathbin\{\\pm\}sample standard deviation across the 30 paired splits\.ConditionPFN v1PFN v2PFN v2\.5PFN v2\.6PFN v3ICL v1ICL v2Identity0\.7760±0\.02620\.7760\\mathbin\{\\pm\}0\.02620\.8390±0\.02350\.8390\\mathbin\{\\pm\}0\.02350\.8344±0\.02230\.8344\\mathbin\{\\pm\}0\.02230\.8412±0\.02490\.8412\\mathbin\{\\pm\}0\.02490\.8433±0\.02370\.8433\\mathbin\{\\pm\}0\.02370\.8314±0\.02240\.8314\\mathbin\{\\pm\}0\.02240\.8471±0\.02650\.8471\\mathbin\{\\pm\}0\.0265Standard scaling0\.7760±0\.02620\.7760\\mathbin\{\\pm\}0\.02620\.8382±0\.02240\.8382\\mathbin\{\\pm\}0\.02240\.8341±0\.02140\.8341\\mathbin\{\\pm\}0\.02140\.8411±0\.02490\.8411\\mathbin\{\\pm\}0\.02490\.8434±0\.02320\.8434\\mathbin\{\\pm\}0\.02320\.8314±0\.02240\.8314\\mathbin\{\\pm\}0\.02240\.8471±0\.02650\.8471\\mathbin\{\\pm\}0\.0265Log transform0\.7759±0\.02770\.7759\\mathbin\{\\pm\}0\.02770\.8396±0\.02480\.8396\\mathbin\{\\pm\}0\.02480\.8351±0\.02240\.8351\\mathbin\{\\pm\}0\.02240\.8419±0\.02240\.8419\\mathbin\{\\pm\}0\.02240\.8449±0\.02370\.8449\\mathbin\{\\pm\}0\.02370\.8323±0\.02320\.8323\\mathbin\{\\pm\}0\.02320\.8457±0\.02620\.8457\\mathbin\{\\pm\}0\.0262Square\-root transform0\.7758±0\.02670\.7758\\mathbin\{\\pm\}0\.02670\.8392±0\.02210\.8392\\mathbin\{\\pm\}0\.02210\.8347±0\.02230\.8347\\mathbin\{\\pm\}0\.02230\.8411±0\.02400\.8411\\mathbin\{\\pm\}0\.02400\.8445±0\.02300\.8445\\mathbin\{\\pm\}0\.02300\.8321±0\.02300\.8321\\mathbin\{\\pm\}0\.02300\.8464±0\.02580\.8464\\mathbin\{\\pm\}0\.0258Box–Cox0\.7755±0\.02550\.7755\\mathbin\{\\pm\}0\.02550\.8405±0\.02440\.8405\\mathbin\{\\pm\}0\.02440\.8385±0\.02330\.8385\\mathbin\{\\pm\}0\.02330\.8402±0\.02280\.8402\\mathbin\{\\pm\}0\.02280\.8428±0\.02260\.8428\\mathbin\{\\pm\}0\.02260\.8318±0\.02370\.8318\\mathbin\{\\pm\}0\.02370\.8454±0\.02500\.8454\\mathbin\{\\pm\}0\.0250Min–max scaling0\.7760±0\.02620\.7760\\mathbin\{\\pm\}0\.02620\.8395±0\.02250\.8395\\mathbin\{\\pm\}0\.02250\.8355±0\.02240\.8355\\mathbin\{\\pm\}0\.02240\.8412±0\.02490\.8412\\mathbin\{\\pm\}0\.02490\.8436±0\.02230\.8436\\mathbin\{\\pm\}0\.02230\.8314±0\.02240\.8314\\mathbin\{\\pm\}0\.02240\.8471±0\.02650\.8471\\mathbin\{\\pm\}0\.0265One\-hot encoding———————Ordinal encoding———————Frequency encoding———————Target encoding———————Categorical crosses———————Equal\-width binning0\.7562±0\.02630\.7562\\mathbin\{\\pm\}0\.02630\.7744±0\.02440\.7744\\mathbin\{\\pm\}0\.02440\.7748±0\.02400\.7748\\mathbin\{\\pm\}0\.02400\.7734±0\.02250\.7734\\mathbin\{\\pm\}0\.02250\.7807±0\.02320\.7807\\mathbin\{\\pm\}0\.02320\.7681±0\.02460\.7681\\mathbin\{\\pm\}0\.02460\.7811±0\.02400\.7811\\mathbin\{\\pm\}0\.0240Equal\-frequency binning0\.7770±0\.02590\.7770\\mathbin\{\\pm\}0\.02590\.8175±0\.02290\.8175\\mathbin\{\\pm\}0\.02290\.8146±0\.02340\.8146\\mathbin\{\\pm\}0\.02340\.8187±0\.02050\.8187\\mathbin\{\\pm\}0\.02050\.8229±0\.02230\.8229\\mathbin\{\\pm\}0\.02230\.8111±0\.02100\.8111\\mathbin\{\\pm\}0\.02100\.8235±0\.02070\.8235\\mathbin\{\\pm\}0\.0207Numeric interactions0\.7637±0\.02850\.7637\\mathbin\{\\pm\}0\.02850\.8374±0\.02290\.8374\\mathbin\{\\pm\}0\.02290\.8301±0\.02160\.8301\\mathbin\{\\pm\}0\.02160\.8401±0\.02470\.8401\\mathbin\{\\pm\}0\.02470\.8419±0\.02490\.8419\\mathbin\{\\pm\}0\.02490\.8354±0\.02420\.8354\\mathbin\{\\pm\}0\.02420\.8453±0\.02550\.8453\\mathbin\{\\pm\}0\.0255Group aggregation———————Variance filter0\.7760±0\.02620\.7760\\mathbin\{\\pm\}0\.02620\.8390±0\.02350\.8390\\mathbin\{\\pm\}0\.02350\.8344±0\.02230\.8344\\mathbin\{\\pm\}0\.02230\.8412±0\.02490\.8412\\mathbin\{\\pm\}0\.02490\.8433±0\.02370\.8433\\mathbin\{\\pm\}0\.02370\.8314±0\.02240\.8314\\mathbin\{\\pm\}0\.02240\.8471±0\.02650\.8471\\mathbin\{\\pm\}0\.0265Collinearity filter0\.7760±0\.02620\.7760\\mathbin\{\\pm\}0\.02620\.8390±0\.02350\.8390\\mathbin\{\\pm\}0\.02350\.8344±0\.02230\.8344\\mathbin\{\\pm\}0\.02230\.8412±0\.02490\.8412\\mathbin\{\\pm\}0\.02490\.8433±0\.02370\.8433\\mathbin\{\\pm\}0\.02370\.8314±0\.02240\.8314\\mathbin\{\\pm\}0\.02240\.8471±0\.02650\.8471\\mathbin\{\\pm\}0\.0265PCA0\.7815±0\.02630\.7815\\mathbin\{\\pm\}0\.02630\.8282±0\.02210\.8282\\mathbin\{\\pm\}0\.02210\.8036±0\.02300\.8036\\mathbin\{\\pm\}0\.02300\.8212±0\.02340\.8212\\mathbin\{\\pm\}0\.02340\.8320±0\.02480\.8320\\mathbin\{\\pm\}0\.02480\.8113±0\.02100\.8113\\mathbin\{\\pm\}0\.02100\.8388±0\.02530\.8388\\mathbin\{\\pm\}0\.0253Supervised selection0\.7460±0\.02160\.7460\\mathbin\{\\pm\}0\.02160\.8061±0\.01820\.8061\\mathbin\{\\pm\}0\.01820\.7841±0\.02440\.7841\\mathbin\{\\pm\}0\.02440\.8079±0\.02050\.8079\\mathbin\{\\pm\}0\.02050\.8170±0\.02070\.8170\\mathbin\{\\pm\}0\.02070\.8082±0\.02410\.8082\\mathbin\{\\pm\}0\.02410\.8215±0\.02070\.8215\\mathbin\{\\pm\}0\.0207TabPrep full0\.7366±0\.02730\.7366\\mathbin\{\\pm\}0\.02730\.8234±0\.02490\.8234\\mathbin\{\\pm\}0\.02490\.8191±0\.02210\.8191\\mathbin\{\\pm\}0\.02210\.8275±0\.02390\.8275\\mathbin\{\\pm\}0\.02390\.8293±0\.02470\.8293\\mathbin\{\\pm\}0\.02470\.8030±0\.02330\.8030\\mathbin\{\\pm\}0\.02330\.8321±0\.02450\.8321\\mathbin\{\\pm\}0\.0245TabPrep w/o groupby0\.7389±0\.02840\.7389\\mathbin\{\\pm\}0\.02840\.8269±0\.02220\.8269\\mathbin\{\\pm\}0\.02220\.8212±0\.02240\.8212\\mathbin\{\\pm\}0\.02240\.8289±0\.02210\.8289\\mathbin\{\\pm\}0\.02210\.8288±0\.02470\.8288\\mathbin\{\\pm\}0\.02470\.8037±0\.02390\.8037\\mathbin\{\\pm\}0\.02390\.8315±0\.02470\.8315\\mathbin\{\\pm\}0\.0247TabPrep w/o RSFC0\.7348±0\.02410\.7348\\mathbin\{\\pm\}0\.02410\.8248±0\.02310\.8248\\mathbin\{\\pm\}0\.02310\.8200±0\.02220\.8200\\mathbin\{\\pm\}0\.02220\.8294±0\.02220\.8294\\mathbin\{\\pm\}0\.02220\.8275±0\.02270\.8275\\mathbin\{\\pm\}0\.02270\.8027±0\.02290\.8027\\mathbin\{\\pm\}0\.02290\.8308±0\.02620\.8308\\mathbin\{\\pm\}0\.0262TabPrep w/o arithmetic0\.8419±0\.02370\.8419\\mathbin\{\\pm\}0\.02370\.8469±0\.02620\.8469\\mathbin\{\\pm\}0\.02620\.8453±0\.02460\.8453\\mathbin\{\\pm\}0\.02460\.8499±0\.02590\.8499\\mathbin\{\\pm\}0\.02590\.8465±0\.02410\.8465\\mathbin\{\\pm\}0\.02410\.8408±0\.02390\.8408\\mathbin\{\\pm\}0\.02390\.8443±0\.02460\.8443\\mathbin\{\\pm\}0\.0246TabPrep w/o cat\. interact\.0\.7338±0\.02400\.7338\\mathbin\{\\pm\}0\.02400\.8247±0\.02360\.8247\\mathbin\{\\pm\}0\.02360\.8203±0\.02260\.8203\\mathbin\{\\pm\}0\.02260\.8271±0\.02190\.8271\\mathbin\{\\pm\}0\.02190\.8307±0\.02520\.8307\\mathbin\{\\pm\}0\.02520\.8043±0\.02440\.8043\\mathbin\{\\pm\}0\.02440\.8311±0\.02390\.8311\\mathbin\{\\pm\}0\.0239TabPrep w/o OOF\-TE0\.7367±0\.02800\.7367\\mathbin\{\\pm\}0\.02800\.8230±0\.02030\.8230\\mathbin\{\\pm\}0\.02030\.8198±0\.02220\.8198\\mathbin\{\\pm\}0\.02220\.8304±0\.02260\.8304\\mathbin\{\\pm\}0\.02260\.8308±0\.02400\.8308\\mathbin\{\\pm\}0\.02400\.8035±0\.02420\.8035\\mathbin\{\\pm\}0\.02420\.8308±0\.02440\.8308\\mathbin\{\\pm\}0\.0244Shared\-context kNN0\.7774±0\.02580\.7774\\mathbin\{\\pm\}0\.02580\.8384±0\.02370\.8384\\mathbin\{\\pm\}0\.02370\.8341±0\.02010\.8341\\mathbin\{\\pm\}0\.02010\.8417±0\.02360\.8417\\mathbin\{\\pm\}0\.02360\.8426±0\.02370\.8426\\mathbin\{\\pm\}0\.02370\.8318±0\.02260\.8318\\mathbin\{\\pm\}0\.02260\.8467±0\.02610\.8467\\mathbin\{\\pm\}0\.0261OOF prediction feature0\.7661±0\.02770\.7661\\mathbin\{\\pm\}0\.02770\.8379±0\.02410\.8379\\mathbin\{\\pm\}0\.02410\.8199±0\.02540\.8199\\mathbin\{\\pm\}0\.02540\.8386±0\.02320\.8386\\mathbin\{\\pm\}0\.02320\.8473±0\.01950\.8473\\mathbin\{\\pm\}0\.01950\.8208±0\.02360\.8208\\mathbin\{\\pm\}0\.02360\.8448±0\.02670\.8448\\mathbin\{\\pm\}0\.0267Table 26:Complete TabPFN and TabICL raw metric results for QSAR biodeg, metric accuracy\. Values are mean±\\mathbin\{\\pm\}sample standard deviation across the 30 paired splits\.ConditionPFN v1PFN v2PFN v2\.5PFN v2\.6PFN v3ICL v1ICL v2Identity0\.8839±0\.01620\.8839\\mathbin\{\\pm\}0\.01620\.8766±0\.01470\.8766\\mathbin\{\\pm\}0\.01470\.8782±0\.01660\.8782\\mathbin\{\\pm\}0\.01660\.8749±0\.01660\.8749\\mathbin\{\\pm\}0\.01660\.8822±0\.01480\.8822\\mathbin\{\\pm\}0\.01480\.8780±0\.01710\.8780\\mathbin\{\\pm\}0\.01710\.8845±0\.01340\.8845\\mathbin\{\\pm\}0\.0134Standard scaling0\.8833±0\.01610\.8833\\mathbin\{\\pm\}0\.01610\.8770±0\.01510\.8770\\mathbin\{\\pm\}0\.01510\.8782±0\.01580\.8782\\mathbin\{\\pm\}0\.01580\.8759±0\.01630\.8759\\mathbin\{\\pm\}0\.01630\.8807±0\.01290\.8807\\mathbin\{\\pm\}0\.01290\.8784±0\.01750\.8784\\mathbin\{\\pm\}0\.01750\.8845±0\.01340\.8845\\mathbin\{\\pm\}0\.0134Log transform0\.8809±0\.01470\.8809\\mathbin\{\\pm\}0\.01470\.8756±0\.01470\.8756\\mathbin\{\\pm\}0\.01470\.8787±0\.01520\.8787\\mathbin\{\\pm\}0\.01520\.8760±0\.01630\.8760\\mathbin\{\\pm\}0\.01630\.8813±0\.01420\.8813\\mathbin\{\\pm\}0\.01420\.8744±0\.01710\.8744\\mathbin\{\\pm\}0\.01710\.8839±0\.01420\.8839\\mathbin\{\\pm\}0\.0142Square\-root transform0\.8767±0\.01650\.8767\\mathbin\{\\pm\}0\.01650\.8767±0\.01520\.8767\\mathbin\{\\pm\}0\.01520\.8785±0\.01570\.8785\\mathbin\{\\pm\}0\.01570\.8747±0\.01660\.8747\\mathbin\{\\pm\}0\.01660\.8808±0\.01350\.8808\\mathbin\{\\pm\}0\.01350\.8726±0\.01760\.8726\\mathbin\{\\pm\}0\.01760\.8842±0\.01370\.8842\\mathbin\{\\pm\}0\.0137Box–Cox0\.8817±0\.01610\.8817\\mathbin\{\\pm\}0\.01610\.8768±0\.01600\.8768\\mathbin\{\\pm\}0\.01600\.8783±0\.01580\.8783\\mathbin\{\\pm\}0\.01580\.8745±0\.01700\.8745\\mathbin\{\\pm\}0\.01700\.8825±0\.01490\.8825\\mathbin\{\\pm\}0\.01490\.8784±0\.01660\.8784\\mathbin\{\\pm\}0\.01660\.8834±0\.01290\.8834\\mathbin\{\\pm\}0\.0129Min–max scaling0\.8833±0\.01610\.8833\\mathbin\{\\pm\}0\.01610\.8760±0\.01560\.8760\\mathbin\{\\pm\}0\.01560\.8780±0\.01540\.8780\\mathbin\{\\pm\}0\.01540\.8752±0\.01650\.8752\\mathbin\{\\pm\}0\.01650\.8808±0\.01260\.8808\\mathbin\{\\pm\}0\.01260\.8782±0\.01750\.8782\\mathbin\{\\pm\}0\.01750\.8845±0\.01340\.8845\\mathbin\{\\pm\}0\.0134One\-hot encoding0\.8789±0\.01640\.8789\\mathbin\{\\pm\}0\.01640\.8756±0\.01510\.8756\\mathbin\{\\pm\}0\.01510\.8787±0\.01570\.8787\\mathbin\{\\pm\}0\.01570\.8768±0\.01400\.8768\\mathbin\{\\pm\}0\.01400\.8806±0\.01500\.8806\\mathbin\{\\pm\}0\.01500\.8781±0\.01810\.8781\\mathbin\{\\pm\}0\.01810\.8847±0\.01260\.8847\\mathbin\{\\pm\}0\.0126Ordinal encoding0\.8847±0\.01600\.8847\\mathbin\{\\pm\}0\.01600\.8753±0\.01560\.8753\\mathbin\{\\pm\}0\.01560\.8775±0\.01640\.8775\\mathbin\{\\pm\}0\.01640\.8734±0\.01580\.8734\\mathbin\{\\pm\}0\.01580\.8818±0\.01580\.8818\\mathbin\{\\pm\}0\.01580\.8771±0\.01810\.8771\\mathbin\{\\pm\}0\.01810\.8846±0\.01530\.8846\\mathbin\{\\pm\}0\.0153Frequency encoding0\.8829±0\.01700\.8829\\mathbin\{\\pm\}0\.01700\.8759±0\.01470\.8759\\mathbin\{\\pm\}0\.01470\.8796±0\.01550\.8796\\mathbin\{\\pm\}0\.01550\.8751±0\.01490\.8751\\mathbin\{\\pm\}0\.01490\.8824±0\.01500\.8824\\mathbin\{\\pm\}0\.01500\.8775±0\.01730\.8775\\mathbin\{\\pm\}0\.01730\.8843±0\.01360\.8843\\mathbin\{\\pm\}0\.0136Target encoding0\.8817±0\.01770\.8817\\mathbin\{\\pm\}0\.01770\.8760±0\.01500\.8760\\mathbin\{\\pm\}0\.01500\.8786±0\.01540\.8786\\mathbin\{\\pm\}0\.01540\.8763±0\.01590\.8763\\mathbin\{\\pm\}0\.01590\.8816±0\.01510\.8816\\mathbin\{\\pm\}0\.01510\.8774±0\.01730\.8774\\mathbin\{\\pm\}0\.01730\.8822±0\.01470\.8822\\mathbin\{\\pm\}0\.0147Categorical crosses0\.8809±0\.01660\.8809\\mathbin\{\\pm\}0\.01660\.8753±0\.01450\.8753\\mathbin\{\\pm\}0\.01450\.8784±0\.01510\.8784\\mathbin\{\\pm\}0\.01510\.8727±0\.01600\.8727\\mathbin\{\\pm\}0\.01600\.8790±0\.01540\.8790\\mathbin\{\\pm\}0\.01540\.8768±0\.01690\.8768\\mathbin\{\\pm\}0\.01690\.8836±0\.01430\.8836\\mathbin\{\\pm\}0\.0143Equal\-width binning0\.8687±0\.01490\.8687\\mathbin\{\\pm\}0\.01490\.8676±0\.01550\.8676\\mathbin\{\\pm\}0\.01550\.8694±0\.01440\.8694\\mathbin\{\\pm\}0\.01440\.8668±0\.01710\.8668\\mathbin\{\\pm\}0\.01710\.8707±0\.01570\.8707\\mathbin\{\\pm\}0\.01570\.8674±0\.01610\.8674\\mathbin\{\\pm\}0\.01610\.8702±0\.01420\.8702\\mathbin\{\\pm\}0\.0142Equal\-frequency binning0\.8717±0\.01510\.8717\\mathbin\{\\pm\}0\.01510\.8719±0\.01530\.8719\\mathbin\{\\pm\}0\.01530\.8732±0\.01470\.8732\\mathbin\{\\pm\}0\.01470\.8700±0\.01570\.8700\\mathbin\{\\pm\}0\.01570\.8739±0\.01440\.8739\\mathbin\{\\pm\}0\.01440\.8744±0\.01940\.8744\\mathbin\{\\pm\}0\.01940\.8748±0\.01410\.8748\\mathbin\{\\pm\}0\.0141Numeric interactions0\.8772±0\.01640\.8772\\mathbin\{\\pm\}0\.01640\.8736±0\.01500\.8736\\mathbin\{\\pm\}0\.01500\.8747±0\.01640\.8747\\mathbin\{\\pm\}0\.01640\.8729±0\.01460\.8729\\mathbin\{\\pm\}0\.01460\.8788±0\.01500\.8788\\mathbin\{\\pm\}0\.01500\.8713±0\.01690\.8713\\mathbin\{\\pm\}0\.01690\.8769±0\.01450\.8769\\mathbin\{\\pm\}0\.0145Group aggregation0\.8757±0\.01910\.8757\\mathbin\{\\pm\}0\.01910\.8750±0\.01780\.8750\\mathbin\{\\pm\}0\.01780\.8743±0\.01550\.8743\\mathbin\{\\pm\}0\.01550\.8736±0\.01540\.8736\\mathbin\{\\pm\}0\.01540\.8796±0\.01460\.8796\\mathbin\{\\pm\}0\.01460\.8694±0\.01710\.8694\\mathbin\{\\pm\}0\.01710\.8821±0\.01480\.8821\\mathbin\{\\pm\}0\.0148Variance filter0\.8816±0\.01550\.8816\\mathbin\{\\pm\}0\.01550\.8736±0\.01590\.8736\\mathbin\{\\pm\}0\.01590\.8753±0\.01730\.8753\\mathbin\{\\pm\}0\.01730\.8736±0\.01660\.8736\\mathbin\{\\pm\}0\.01660\.8803±0\.01550\.8803\\mathbin\{\\pm\}0\.01550\.8779±0\.01770\.8779\\mathbin\{\\pm\}0\.01770\.8837±0\.01500\.8837\\mathbin\{\\pm\}0\.0150Collinearity filter0\.8839±0\.01620\.8839\\mathbin\{\\pm\}0\.01620\.8766±0\.01470\.8766\\mathbin\{\\pm\}0\.01470\.8782±0\.01660\.8782\\mathbin\{\\pm\}0\.01660\.8749±0\.01660\.8749\\mathbin\{\\pm\}0\.01660\.8822±0\.01480\.8822\\mathbin\{\\pm\}0\.01480\.8780±0\.01710\.8780\\mathbin\{\\pm\}0\.01710\.8845±0\.01340\.8845\\mathbin\{\\pm\}0\.0134PCA0\.8812±0\.01500\.8812\\mathbin\{\\pm\}0\.01500\.8800±0\.01540\.8800\\mathbin\{\\pm\}0\.01540\.8814±0\.01440\.8814\\mathbin\{\\pm\}0\.01440\.8787±0\.01510\.8787\\mathbin\{\\pm\}0\.01510\.8808±0\.01430\.8808\\mathbin\{\\pm\}0\.01430\.8816±0\.01420\.8816\\mathbin\{\\pm\}0\.01420\.8824±0\.01290\.8824\\mathbin\{\\pm\}0\.0129Supervised selection0\.8665±0\.01530\.8665\\mathbin\{\\pm\}0\.01530\.8657±0\.01530\.8657\\mathbin\{\\pm\}0\.01530\.8663±0\.01840\.8663\\mathbin\{\\pm\}0\.01840\.8625±0\.01610\.8625\\mathbin\{\\pm\}0\.01610\.8657±0\.01770\.8657\\mathbin\{\\pm\}0\.01770\.8655±0\.01450\.8655\\mathbin\{\\pm\}0\.01450\.8714±0\.01630\.8714\\mathbin\{\\pm\}0\.0163TabPrep full0\.8583±0\.02080\.8583\\mathbin\{\\pm\}0\.02080\.8653±0\.01570\.8653\\mathbin\{\\pm\}0\.01570\.8683±0\.01690\.8683\\mathbin\{\\pm\}0\.01690\.8629±0\.01390\.8629\\mathbin\{\\pm\}0\.01390\.8677±0\.01590\.8677\\mathbin\{\\pm\}0\.01590\.8660±0\.01750\.8660\\mathbin\{\\pm\}0\.01750\.8687±0\.01670\.8687\\mathbin\{\\pm\}0\.0167TabPrep w/o groupby0\.8612±0\.01550\.8612\\mathbin\{\\pm\}0\.01550\.8629±0\.01170\.8629\\mathbin\{\\pm\}0\.01170\.8683±0\.01270\.8683\\mathbin\{\\pm\}0\.01270\.8629±0\.01470\.8629\\mathbin\{\\pm\}0\.01470\.8677±0\.01290\.8677\\mathbin\{\\pm\}0\.01290\.8644±0\.01760\.8644\\mathbin\{\\pm\}0\.01760\.8683±0\.01330\.8683\\mathbin\{\\pm\}0\.0133TabPrep w/o RSFC0\.8597±0\.01780\.8597\\mathbin\{\\pm\}0\.01780\.8643±0\.01410\.8643\\mathbin\{\\pm\}0\.01410\.8677±0\.01480\.8677\\mathbin\{\\pm\}0\.01480\.8640±0\.01490\.8640\\mathbin\{\\pm\}0\.01490\.8689±0\.01410\.8689\\mathbin\{\\pm\}0\.01410\.8662±0\.01610\.8662\\mathbin\{\\pm\}0\.01610\.8704±0\.01680\.8704\\mathbin\{\\pm\}0\.0168TabPrep w/o arithmetic0\.7760±0\.01970\.7760\\mathbin\{\\pm\}0\.01970\.7738±0\.01740\.7738\\mathbin\{\\pm\}0\.01740\.7751±0\.01820\.7751\\mathbin\{\\pm\}0\.01820\.7793±0\.01940\.7793\\mathbin\{\\pm\}0\.01940\.7775±0\.01900\.7775\\mathbin\{\\pm\}0\.01900\.7743±0\.01820\.7743\\mathbin\{\\pm\}0\.01820\.7773±0\.01860\.7773\\mathbin\{\\pm\}0\.0186TabPrep w/o cat\. interact\.0\.8620±0\.01800\.8620\\mathbin\{\\pm\}0\.01800\.8628±0\.01610\.8628\\mathbin\{\\pm\}0\.01610\.8665±0\.01630\.8665\\mathbin\{\\pm\}0\.01630\.8618±0\.01530\.8618\\mathbin\{\\pm\}0\.01530\.8663±0\.01520\.8663\\mathbin\{\\pm\}0\.01520\.8651±0\.01890\.8651\\mathbin\{\\pm\}0\.01890\.8680±0\.01660\.8680\\mathbin\{\\pm\}0\.0166TabPrep w/o OOF\-TE0\.8602±0\.02030\.8602\\mathbin\{\\pm\}0\.02030\.8635±0\.01660\.8635\\mathbin\{\\pm\}0\.01660\.8688±0\.01380\.8688\\mathbin\{\\pm\}0\.01380\.8616±0\.01620\.8616\\mathbin\{\\pm\}0\.01620\.8687±0\.01650\.8687\\mathbin\{\\pm\}0\.01650\.8655±0\.01780\.8655\\mathbin\{\\pm\}0\.01780\.8681±0\.01480\.8681\\mathbin\{\\pm\}0\.0148Shared\-context kNN0\.8839±0\.01580\.8839\\mathbin\{\\pm\}0\.01580\.8780±0\.01360\.8780\\mathbin\{\\pm\}0\.01360\.8788±0\.01590\.8788\\mathbin\{\\pm\}0\.01590\.8751±0\.01580\.8751\\mathbin\{\\pm\}0\.01580\.8806±0\.01460\.8806\\mathbin\{\\pm\}0\.01460\.8779±0\.01760\.8779\\mathbin\{\\pm\}0\.01760\.8837±0\.01390\.8837\\mathbin\{\\pm\}0\.0139OOF prediction feature0\.8823±0\.01510\.8823\\mathbin\{\\pm\}0\.01510\.8771±0\.01590\.8771\\mathbin\{\\pm\}0\.01590\.8778±0\.01640\.8778\\mathbin\{\\pm\}0\.01640\.8710±0\.01660\.8710\\mathbin\{\\pm\}0\.01660\.8736±0\.01740\.8736\\mathbin\{\\pm\}0\.01740\.8771±0\.01700\.8771\\mathbin\{\\pm\}0\.01700\.8775±0\.01670\.8775\\mathbin\{\\pm\}0\.0167Table 27:Complete TabPFN and TabICL raw metric results for QSAR biodeg, metric macro f1\. Values are mean±\\mathbin\{\\pm\}sample standard deviation across the 30 paired splits\.ConditionPFN v1PFN v2PFN v2\.5PFN v2\.6PFN v3ICL v1ICL v2Identity0\.8685±0\.01770\.8685\\mathbin\{\\pm\}0\.01770\.8588±0\.01710\.8588\\mathbin\{\\pm\}0\.01710\.8610±0\.01890\.8610\\mathbin\{\\pm\}0\.01890\.8574±0\.01870\.8574\\mathbin\{\\pm\}0\.01870\.8659±0\.01710\.8659\\mathbin\{\\pm\}0\.01710\.8613±0\.01920\.8613\\mathbin\{\\pm\}0\.01920\.8685±0\.01550\.8685\\mathbin\{\\pm\}0\.0155Standard scaling0\.8677±0\.01790\.8677\\mathbin\{\\pm\}0\.01790\.8595±0\.01730\.8595\\mathbin\{\\pm\}0\.01730\.8608±0\.01800\.8608\\mathbin\{\\pm\}0\.01800\.8584±0\.01850\.8584\\mathbin\{\\pm\}0\.01850\.8643±0\.01480\.8643\\mathbin\{\\pm\}0\.01480\.8617±0\.01980\.8617\\mathbin\{\\pm\}0\.01980\.8685±0\.01550\.8685\\mathbin\{\\pm\}0\.0155Log transform0\.8648±0\.01630\.8648\\mathbin\{\\pm\}0\.01630\.8577±0\.01680\.8577\\mathbin\{\\pm\}0\.01680\.8610±0\.01740\.8610\\mathbin\{\\pm\}0\.01740\.8585±0\.01850\.8585\\mathbin\{\\pm\}0\.01850\.8647±0\.01630\.8647\\mathbin\{\\pm\}0\.01630\.8573±0\.01890\.8573\\mathbin\{\\pm\}0\.01890\.8677±0\.01650\.8677\\mathbin\{\\pm\}0\.0165Square\-root transform0\.8598±0\.01860\.8598\\mathbin\{\\pm\}0\.01860\.8587±0\.01750\.8587\\mathbin\{\\pm\}0\.01750\.8608±0\.01800\.8608\\mathbin\{\\pm\}0\.01800\.8570±0\.01880\.8570\\mathbin\{\\pm\}0\.01880\.8643±0\.01550\.8643\\mathbin\{\\pm\}0\.01550\.8552±0\.01940\.8552\\mathbin\{\\pm\}0\.01940\.8681±0\.01600\.8681\\mathbin\{\\pm\}0\.0160Box–Cox0\.8660±0\.01780\.8660\\mathbin\{\\pm\}0\.01780\.8593±0\.01860\.8593\\mathbin\{\\pm\}0\.01860\.8610±0\.01800\.8610\\mathbin\{\\pm\}0\.01800\.8568±0\.01940\.8568\\mathbin\{\\pm\}0\.01940\.8662±0\.01700\.8662\\mathbin\{\\pm\}0\.01700\.8617±0\.01880\.8617\\mathbin\{\\pm\}0\.01880\.8672±0\.01510\.8672\\mathbin\{\\pm\}0\.0151Min–max scaling0\.8677±0\.01790\.8677\\mathbin\{\\pm\}0\.01790\.8582±0\.01790\.8582\\mathbin\{\\pm\}0\.01790\.8606±0\.01760\.8606\\mathbin\{\\pm\}0\.01760\.8577±0\.01880\.8577\\mathbin\{\\pm\}0\.01880\.8644±0\.01440\.8644\\mathbin\{\\pm\}0\.01440\.8615±0\.01980\.8615\\mathbin\{\\pm\}0\.01980\.8685±0\.01550\.8685\\mathbin\{\\pm\}0\.0155One\-hot encoding0\.8631±0\.01790\.8631\\mathbin\{\\pm\}0\.01790\.8576±0\.01780\.8576\\mathbin\{\\pm\}0\.01780\.8616±0\.01810\.8616\\mathbin\{\\pm\}0\.01810\.8595±0\.01580\.8595\\mathbin\{\\pm\}0\.01580\.8643±0\.01730\.8643\\mathbin\{\\pm\}0\.01730\.8616±0\.02010\.8616\\mathbin\{\\pm\}0\.02010\.8686±0\.01480\.8686\\mathbin\{\\pm\}0\.0148Ordinal encoding0\.8695±0\.01750\.8695\\mathbin\{\\pm\}0\.01750\.8574±0\.01840\.8574\\mathbin\{\\pm\}0\.01840\.8602±0\.01900\.8602\\mathbin\{\\pm\}0\.01900\.8557±0\.01800\.8557\\mathbin\{\\pm\}0\.01800\.8656±0\.01810\.8656\\mathbin\{\\pm\}0\.01810\.8604±0\.02020\.8604\\mathbin\{\\pm\}0\.02020\.8686±0\.01750\.8686\\mathbin\{\\pm\}0\.0175Frequency encoding0\.8674±0\.01890\.8674\\mathbin\{\\pm\}0\.01890\.8581±0\.01700\.8581\\mathbin\{\\pm\}0\.01700\.8623±0\.01790\.8623\\mathbin\{\\pm\}0\.01790\.8574±0\.01710\.8574\\mathbin\{\\pm\}0\.01710\.8662±0\.01700\.8662\\mathbin\{\\pm\}0\.01700\.8607±0\.01940\.8607\\mathbin\{\\pm\}0\.01940\.8682±0\.01580\.8682\\mathbin\{\\pm\}0\.0158Target encoding0\.8660±0\.01940\.8660\\mathbin\{\\pm\}0\.01940\.8583±0\.01730\.8583\\mathbin\{\\pm\}0\.01730\.8612±0\.01770\.8612\\mathbin\{\\pm\}0\.01770\.8589±0\.01810\.8589\\mathbin\{\\pm\}0\.01810\.8650±0\.01730\.8650\\mathbin\{\\pm\}0\.01730\.8603±0\.01960\.8603\\mathbin\{\\pm\}0\.01960\.8644±0\.01740\.8644\\mathbin\{\\pm\}0\.0174Categorical crosses0\.8653±0\.01820\.8653\\mathbin\{\\pm\}0\.01820\.8574±0\.01620\.8574\\mathbin\{\\pm\}0\.01620\.8612±0\.01720\.8612\\mathbin\{\\pm\}0\.01720\.8547±0\.01820\.8547\\mathbin\{\\pm\}0\.01820\.8623±0\.01760\.8623\\mathbin\{\\pm\}0\.01760\.8600±0\.01900\.8600\\mathbin\{\\pm\}0\.01900\.8674±0\.01660\.8674\\mathbin\{\\pm\}0\.0166Equal\-width binning0\.8511±0\.01720\.8511\\mathbin\{\\pm\}0\.01720\.8486±0\.01810\.8486\\mathbin\{\\pm\}0\.01810\.8510±0\.01660\.8510\\mathbin\{\\pm\}0\.01660\.8481±0\.01980\.8481\\mathbin\{\\pm\}0\.01980\.8528±0\.01810\.8528\\mathbin\{\\pm\}0\.01810\.8494±0\.01860\.8494\\mathbin\{\\pm\}0\.01860\.8524±0\.01590\.8524\\mathbin\{\\pm\}0\.0159Equal\-frequency binning0\.8538±0\.01700\.8538\\mathbin\{\\pm\}0\.01700\.8532±0\.01780\.8532\\mathbin\{\\pm\}0\.01780\.8550±0\.01700\.8550\\mathbin\{\\pm\}0\.01700\.8515±0\.01840\.8515\\mathbin\{\\pm\}0\.01840\.8563±0\.01650\.8563\\mathbin\{\\pm\}0\.01650\.8569±0\.02170\.8569\\mathbin\{\\pm\}0\.02170\.8570±0\.01620\.8570\\mathbin\{\\pm\}0\.0162Numeric interactions0\.8609±0\.01800\.8609\\mathbin\{\\pm\}0\.01800\.8558±0\.01720\.8558\\mathbin\{\\pm\}0\.01720\.8571±0\.01840\.8571\\mathbin\{\\pm\}0\.01840\.8548±0\.01650\.8548\\mathbin\{\\pm\}0\.01650\.8620±0\.01720\.8620\\mathbin\{\\pm\}0\.01720\.8537±0\.01900\.8537\\mathbin\{\\pm\}0\.01900\.8596±0\.01650\.8596\\mathbin\{\\pm\}0\.0165Group aggregation0\.8596±0\.02060\.8596\\mathbin\{\\pm\}0\.02060\.8573±0\.02010\.8573\\mathbin\{\\pm\}0\.02010\.8564±0\.01790\.8564\\mathbin\{\\pm\}0\.01790\.8560±0\.01720\.8560\\mathbin\{\\pm\}0\.01720\.8630±0\.01650\.8630\\mathbin\{\\pm\}0\.01650\.8514±0\.01880\.8514\\mathbin\{\\pm\}0\.01880\.8659±0\.01690\.8659\\mathbin\{\\pm\}0\.0169Variance filter0\.8659±0\.01730\.8659\\mathbin\{\\pm\}0\.01730\.8555±0\.01820\.8555\\mathbin\{\\pm\}0\.01820\.8578±0\.02000\.8578\\mathbin\{\\pm\}0\.02000\.8557±0\.01870\.8557\\mathbin\{\\pm\}0\.01870\.8638±0\.01760\.8638\\mathbin\{\\pm\}0\.01760\.8611±0\.02000\.8611\\mathbin\{\\pm\}0\.02000\.8676±0\.01710\.8676\\mathbin\{\\pm\}0\.0171Collinearity filter0\.8685±0\.01770\.8685\\mathbin\{\\pm\}0\.01770\.8588±0\.01710\.8588\\mathbin\{\\pm\}0\.01710\.8610±0\.01890\.8610\\mathbin\{\\pm\}0\.01890\.8574±0\.01870\.8574\\mathbin\{\\pm\}0\.01870\.8659±0\.01710\.8659\\mathbin\{\\pm\}0\.01710\.8613±0\.01920\.8613\\mathbin\{\\pm\}0\.01920\.8685±0\.01550\.8685\\mathbin\{\\pm\}0\.0155PCA0\.8655±0\.01680\.8655\\mathbin\{\\pm\}0\.01680\.8638±0\.01720\.8638\\mathbin\{\\pm\}0\.01720\.8651±0\.01640\.8651\\mathbin\{\\pm\}0\.01640\.8621±0\.01650\.8621\\mathbin\{\\pm\}0\.01650\.8649±0\.01640\.8649\\mathbin\{\\pm\}0\.01640\.8661±0\.01610\.8661\\mathbin\{\\pm\}0\.01610\.8665±0\.01500\.8665\\mathbin\{\\pm\}0\.0150Supervised selection0\.8482±0\.01730\.8482\\mathbin\{\\pm\}0\.01730\.8466±0\.01780\.8466\\mathbin\{\\pm\}0\.01780\.8473±0\.02100\.8473\\mathbin\{\\pm\}0\.02100\.8432±0\.01870\.8432\\mathbin\{\\pm\}0\.01870\.8469±0\.02060\.8469\\mathbin\{\\pm\}0\.02060\.8474±0\.01640\.8474\\mathbin\{\\pm\}0\.01640\.8537±0\.01860\.8537\\mathbin\{\\pm\}0\.0186TabPrep full0\.8383±0\.02350\.8383\\mathbin\{\\pm\}0\.02350\.8451±0\.01830\.8451\\mathbin\{\\pm\}0\.01830\.8491±0\.01930\.8491\\mathbin\{\\pm\}0\.01930\.8423±0\.01620\.8423\\mathbin\{\\pm\}0\.01620\.8490±0\.01820\.8490\\mathbin\{\\pm\}0\.01820\.8468±0\.01990\.8468\\mathbin\{\\pm\}0\.01990\.8498±0\.01880\.8498\\mathbin\{\\pm\}0\.0188TabPrep w/o groupby0\.8416±0\.01790\.8416\\mathbin\{\\pm\}0\.01790\.8422±0\.01380\.8422\\mathbin\{\\pm\}0\.01380\.8490±0\.01460\.8490\\mathbin\{\\pm\}0\.01460\.8426±0\.01670\.8426\\mathbin\{\\pm\}0\.01670\.8484±0\.01500\.8484\\mathbin\{\\pm\}0\.01500\.8448±0\.02000\.8448\\mathbin\{\\pm\}0\.02000\.8493±0\.01530\.8493\\mathbin\{\\pm\}0\.0153TabPrep w/o RSFC0\.8396±0\.02060\.8396\\mathbin\{\\pm\}0\.02060\.8442±0\.01580\.8442\\mathbin\{\\pm\}0\.01580\.8484±0\.01690\.8484\\mathbin\{\\pm\}0\.01690\.8439±0\.01690\.8439\\mathbin\{\\pm\}0\.01690\.8498±0\.01640\.8498\\mathbin\{\\pm\}0\.01640\.8470±0\.01840\.8470\\mathbin\{\\pm\}0\.01840\.8520±0\.01900\.8520\\mathbin\{\\pm\}0\.0190TabPrep w/o arithmetic0\.7450±0\.01950\.7450\\mathbin\{\\pm\}0\.01950\.7407±0\.01940\.7407\\mathbin\{\\pm\}0\.01940\.7438±0\.02000\.7438\\mathbin\{\\pm\}0\.02000\.7479±0\.02120\.7479\\mathbin\{\\pm\}0\.02120\.7482±0\.02040\.7482\\mathbin\{\\pm\}0\.02040\.7418±0\.02000\.7418\\mathbin\{\\pm\}0\.02000\.7457±0\.02070\.7457\\mathbin\{\\pm\}0\.0207TabPrep w/o cat\. interact\.0\.8424±0\.02070\.8424\\mathbin\{\\pm\}0\.02070\.8425±0\.01850\.8425\\mathbin\{\\pm\}0\.01850\.8469±0\.01870\.8469\\mathbin\{\\pm\}0\.01870\.8414±0\.01790\.8414\\mathbin\{\\pm\}0\.01790\.8474±0\.01770\.8474\\mathbin\{\\pm\}0\.01770\.8456±0\.02160\.8456\\mathbin\{\\pm\}0\.02160\.8495±0\.01900\.8495\\mathbin\{\\pm\}0\.0190TabPrep w/o OOF\-TE0\.8407±0\.02320\.8407\\mathbin\{\\pm\}0\.02320\.8431±0\.01910\.8431\\mathbin\{\\pm\}0\.01910\.8498±0\.01580\.8498\\mathbin\{\\pm\}0\.01580\.8412±0\.01860\.8412\\mathbin\{\\pm\}0\.01860\.8498±0\.01900\.8498\\mathbin\{\\pm\}0\.01900\.8462±0\.02030\.8462\\mathbin\{\\pm\}0\.02030\.8494±0\.01670\.8494\\mathbin\{\\pm\}0\.0167Shared\-context kNN0\.8685±0\.01730\.8685\\mathbin\{\\pm\}0\.01730\.8606±0\.01580\.8606\\mathbin\{\\pm\}0\.01580\.8616±0\.01830\.8616\\mathbin\{\\pm\}0\.01830\.8577±0\.01770\.8577\\mathbin\{\\pm\}0\.01770\.8641±0\.01670\.8641\\mathbin\{\\pm\}0\.01670\.8613±0\.01980\.8613\\mathbin\{\\pm\}0\.01980\.8675±0\.01610\.8675\\mathbin\{\\pm\}0\.0161OOF prediction feature0\.8664±0\.01690\.8664\\mathbin\{\\pm\}0\.01690\.8593±0\.01820\.8593\\mathbin\{\\pm\}0\.01820\.8604±0\.01880\.8604\\mathbin\{\\pm\}0\.01880\.8521±0\.01900\.8521\\mathbin\{\\pm\}0\.01900\.8558±0\.02010\.8558\\mathbin\{\\pm\}0\.02010\.8598±0\.01960\.8598\\mathbin\{\\pm\}0\.01960\.8606±0\.01960\.8606\\mathbin\{\\pm\}0\.0196Table 28:Complete raw metric results for QSAR fish toxicity, metric r2\. Values are mean±\\mathbin\{\\pm\}sample standard deviation across the 30 paired splits\.ConditionPFN v2PFN v2\.5PFN v2\.6PFN v3ICL v2Identity0\.6420±0\.03180\.6420\\mathbin\{\\pm\}0\.03180\.6450±0\.03200\.6450\\mathbin\{\\pm\}0\.03200\.6483±0\.03440\.6483\\mathbin\{\\pm\}0\.03440\.6473±0\.03370\.6473\\mathbin\{\\pm\}0\.03370\.6505±0\.03140\.6505\\mathbin\{\\pm\}0\.0314Standard scaling0\.6431±0\.03270\.6431\\mathbin\{\\pm\}0\.03270\.6449±0\.03220\.6449\\mathbin\{\\pm\}0\.03220\.6400±0\.03360\.6400\\mathbin\{\\pm\}0\.03360\.6469±0\.03370\.6469\\mathbin\{\\pm\}0\.03370\.6505±0\.03140\.6505\\mathbin\{\\pm\}0\.0314Log transform0\.6420±0\.03280\.6420\\mathbin\{\\pm\}0\.03280\.6447±0\.03220\.6447\\mathbin\{\\pm\}0\.03220\.6476±0\.03380\.6476\\mathbin\{\\pm\}0\.03380\.6480±0\.03360\.6480\\mathbin\{\\pm\}0\.03360\.6518±0\.03080\.6518\\mathbin\{\\pm\}0\.0308Square\-root transform0\.6433±0\.03200\.6433\\mathbin\{\\pm\}0\.03200\.6454±0\.03250\.6454\\mathbin\{\\pm\}0\.03250\.6485±0\.03360\.6485\\mathbin\{\\pm\}0\.03360\.6483±0\.03300\.6483\\mathbin\{\\pm\}0\.03300\.6526±0\.03010\.6526\\mathbin\{\\pm\}0\.0301Box–Cox0\.6444±0\.03370\.6444\\mathbin\{\\pm\}0\.03370\.6444±0\.03280\.6444\\mathbin\{\\pm\}0\.03280\.6482±0\.03330\.6482\\mathbin\{\\pm\}0\.03330\.6461±0\.03420\.6461\\mathbin\{\\pm\}0\.03420\.6504±0\.03120\.6504\\mathbin\{\\pm\}0\.0312Min–max scaling0\.6429±0\.03230\.6429\\mathbin\{\\pm\}0\.03230\.6450±0\.03220\.6450\\mathbin\{\\pm\}0\.03220\.6474±0\.03380\.6474\\mathbin\{\\pm\}0\.03380\.6472±0\.03370\.6472\\mathbin\{\\pm\}0\.03370\.6505±0\.03140\.6505\\mathbin\{\\pm\}0\.0314One\-hot encoding—————Ordinal encoding—————Frequency encoding—————Target encoding—————Categorical crosses—————Equal\-width binning0\.6203±0\.03830\.6203\\mathbin\{\\pm\}0\.03830\.6223±0\.03620\.6223\\mathbin\{\\pm\}0\.03620\.6215±0\.03680\.6215\\mathbin\{\\pm\}0\.03680\.6204±0\.03970\.6204\\mathbin\{\\pm\}0\.03970\.6206±0\.03760\.6206\\mathbin\{\\pm\}0\.0376Equal\-frequency binning0\.6375±0\.03410\.6375\\mathbin\{\\pm\}0\.03410\.6385±0\.03250\.6385\\mathbin\{\\pm\}0\.03250\.6378±0\.03470\.6378\\mathbin\{\\pm\}0\.03470\.6378±0\.03320\.6378\\mathbin\{\\pm\}0\.03320\.6355±0\.03400\.6355\\mathbin\{\\pm\}0\.0340Numeric interactions0\.6429±0\.03300\.6429\\mathbin\{\\pm\}0\.03300\.6411±0\.03170\.6411\\mathbin\{\\pm\}0\.03170\.6493±0\.03370\.6493\\mathbin\{\\pm\}0\.03370\.6419±0\.03270\.6419\\mathbin\{\\pm\}0\.03270\.6478±0\.03030\.6478\\mathbin\{\\pm\}0\.0303Group aggregation—————Variance filter0\.6420±0\.03180\.6420\\mathbin\{\\pm\}0\.03180\.6450±0\.03200\.6450\\mathbin\{\\pm\}0\.03200\.6483±0\.03440\.6483\\mathbin\{\\pm\}0\.03440\.6473±0\.03370\.6473\\mathbin\{\\pm\}0\.03370\.6505±0\.03140\.6505\\mathbin\{\\pm\}0\.0314Collinearity filter0\.6420±0\.03180\.6420\\mathbin\{\\pm\}0\.03180\.6450±0\.03200\.6450\\mathbin\{\\pm\}0\.03200\.6483±0\.03440\.6483\\mathbin\{\\pm\}0\.03440\.6473±0\.03370\.6473\\mathbin\{\\pm\}0\.03370\.6505±0\.03140\.6505\\mathbin\{\\pm\}0\.0314PCA0\.6146±0\.03820\.6146\\mathbin\{\\pm\}0\.03820\.6107±0\.03940\.6107\\mathbin\{\\pm\}0\.03940\.6016±0\.04300\.6016\\mathbin\{\\pm\}0\.04300\.6226±0\.03820\.6226\\mathbin\{\\pm\}0\.03820\.6215±0\.03730\.6215\\mathbin\{\\pm\}0\.0373Supervised selection0\.5554±0\.05330\.5554\\mathbin\{\\pm\}0\.05330\.5532±0\.05390\.5532\\mathbin\{\\pm\}0\.05390\.5540±0\.05510\.5540\\mathbin\{\\pm\}0\.05510\.5548±0\.05480\.5548\\mathbin\{\\pm\}0\.05480\.5579±0\.05080\.5579\\mathbin\{\\pm\}0\.0508TabPrep full0\.6437±0\.03410\.6437\\mathbin\{\\pm\}0\.03410\.6387±0\.03340\.6387\\mathbin\{\\pm\}0\.03340\.6423±0\.03500\.6423\\mathbin\{\\pm\}0\.03500\.6376±0\.03330\.6376\\mathbin\{\\pm\}0\.03330\.6426±0\.03220\.6426\\mathbin\{\\pm\}0\.0322TabPrep w/o groupby0\.6436±0\.03270\.6436\\mathbin\{\\pm\}0\.03270\.6392±0\.03370\.6392\\mathbin\{\\pm\}0\.03370\.6433±0\.03360\.6433\\mathbin\{\\pm\}0\.03360\.6378±0\.03380\.6378\\mathbin\{\\pm\}0\.03380\.6430±0\.03230\.6430\\mathbin\{\\pm\}0\.0323TabPrep w/o RSFC0\.6424±0\.03260\.6424\\mathbin\{\\pm\}0\.03260\.6393±0\.03240\.6393\\mathbin\{\\pm\}0\.03240\.6445±0\.03360\.6445\\mathbin\{\\pm\}0\.03360\.6375±0\.03350\.6375\\mathbin\{\\pm\}0\.03350\.6431±0\.03220\.6431\\mathbin\{\\pm\}0\.0322TabPrep w/o arithmetic0\.5850±0\.04600\.5850\\mathbin\{\\pm\}0\.04600\.5896±0\.04450\.5896\\mathbin\{\\pm\}0\.04450\.5913±0\.04730\.5913\\mathbin\{\\pm\}0\.04730\.5831±0\.04510\.5831\\mathbin\{\\pm\}0\.04510\.5733±0\.04320\.5733\\mathbin\{\\pm\}0\.0432TabPrep w/o cat\. interact\.0\.6422±0\.03270\.6422\\mathbin\{\\pm\}0\.03270\.6383±0\.03350\.6383\\mathbin\{\\pm\}0\.03350\.6424±0\.03550\.6424\\mathbin\{\\pm\}0\.03550\.6380±0\.03360\.6380\\mathbin\{\\pm\}0\.03360\.6425±0\.03210\.6425\\mathbin\{\\pm\}0\.0321TabPrep w/o OOF\-TE0\.6421±0\.03420\.6421\\mathbin\{\\pm\}0\.03420\.6383±0\.03350\.6383\\mathbin\{\\pm\}0\.03350\.6408±0\.03480\.6408\\mathbin\{\\pm\}0\.03480\.6379±0\.03380\.6379\\mathbin\{\\pm\}0\.03380\.6419±0\.03250\.6419\\mathbin\{\\pm\}0\.0325Shared\-context kNN0\.6423±0\.03270\.6423\\mathbin\{\\pm\}0\.03270\.6446±0\.03210\.6446\\mathbin\{\\pm\}0\.03210\.6481±0\.03450\.6481\\mathbin\{\\pm\}0\.03450\.6474±0\.03410\.6474\\mathbin\{\\pm\}0\.03410\.6504±0\.03150\.6504\\mathbin\{\\pm\}0\.0315OOF prediction feature0\.6296±0\.03480\.6296\\mathbin\{\\pm\}0\.03480\.6281±0\.03460\.6281\\mathbin\{\\pm\}0\.03460\.6366±0\.03610\.6366\\mathbin\{\\pm\}0\.03610\.6067±0\.03840\.6067\\mathbin\{\\pm\}0\.03840\.6341±0\.03190\.6341\\mathbin\{\\pm\}0\.0319Table 29:Complete raw metric results for QSAR fish toxicity, metric rmse\. Values are mean±\\mathbin\{\\pm\}sample standard deviation across the 30 paired splits\.ConditionPFN v2PFN v2\.5PFN v2\.6PFN v3ICL v2Identity0\.8683±0\.04640\.8683\\mathbin\{\\pm\}0\.04640\.8647±0\.04750\.8647\\mathbin\{\\pm\}0\.04750\.8605±0\.04910\.8605\\mathbin\{\\pm\}0\.04910\.8618±0\.04990\.8618\\mathbin\{\\pm\}0\.04990\.8581±0\.04930\.8581\\mathbin\{\\pm\}0\.0493Standard scaling0\.8668±0\.04720\.8668\\mathbin\{\\pm\}0\.04720\.8647±0\.04760\.8647\\mathbin\{\\pm\}0\.04760\.8708±0\.05050\.8708\\mathbin\{\\pm\}0\.05050\.8622±0\.04970\.8622\\mathbin\{\\pm\}0\.04970\.8581±0\.04930\.8581\\mathbin\{\\pm\}0\.0493Log transform0\.8683±0\.04750\.8683\\mathbin\{\\pm\}0\.04750\.8649±0\.04740\.8649\\mathbin\{\\pm\}0\.04740\.8614±0\.04830\.8614\\mathbin\{\\pm\}0\.04830\.8610±0\.05040\.8610\\mathbin\{\\pm\}0\.05040\.8565±0\.04860\.8565\\mathbin\{\\pm\}0\.0486Square\-root transform0\.8667±0\.04680\.8667\\mathbin\{\\pm\}0\.04680\.8641±0\.04760\.8641\\mathbin\{\\pm\}0\.04760\.8602±0\.04770\.8602\\mathbin\{\\pm\}0\.04770\.8606±0\.04930\.8606\\mathbin\{\\pm\}0\.04930\.8555±0\.04690\.8555\\mathbin\{\\pm\}0\.0469Box–Cox0\.8654±0\.04910\.8654\\mathbin\{\\pm\}0\.04910\.8653±0\.04820\.8653\\mathbin\{\\pm\}0\.04820\.8606±0\.04790\.8606\\mathbin\{\\pm\}0\.04790\.8632±0\.04990\.8632\\mathbin\{\\pm\}0\.04990\.8582±0\.04880\.8582\\mathbin\{\\pm\}0\.0488Min–max scaling0\.8672±0\.04710\.8672\\mathbin\{\\pm\}0\.04710\.8647±0\.04790\.8647\\mathbin\{\\pm\}0\.04790\.8616±0\.04770\.8616\\mathbin\{\\pm\}0\.04770\.8619±0\.04990\.8619\\mathbin\{\\pm\}0\.04990\.8581±0\.04930\.8581\\mathbin\{\\pm\}0\.0493One\-hot encoding—————Ordinal encoding—————Frequency encoding—————Target encoding—————Categorical crosses—————Equal\-width binning0\.8940±0\.05150\.8940\\mathbin\{\\pm\}0\.05150\.8917±0\.05150\.8917\\mathbin\{\\pm\}0\.05150\.8926±0\.05000\.8926\\mathbin\{\\pm\}0\.05000\.8937±0\.05390\.8937\\mathbin\{\\pm\}0\.05390\.8937±0\.05240\.8937\\mathbin\{\\pm\}0\.0524Equal\-frequency binning0\.8738±0\.05160\.8738\\mathbin\{\\pm\}0\.05160\.8727±0\.05060\.8727\\mathbin\{\\pm\}0\.05060\.8734±0\.05120\.8734\\mathbin\{\\pm\}0\.05120\.8735±0\.05070\.8735\\mathbin\{\\pm\}0\.05070\.8762±0\.05120\.8762\\mathbin\{\\pm\}0\.0512Numeric interactions0\.8671±0\.04610\.8671\\mathbin\{\\pm\}0\.04610\.8695±0\.04750\.8695\\mathbin\{\\pm\}0\.04750\.8593±0\.04910\.8593\\mathbin\{\\pm\}0\.04910\.8684±0\.04860\.8684\\mathbin\{\\pm\}0\.04860\.8613±0\.04700\.8613\\mathbin\{\\pm\}0\.0470Group aggregation—————Variance filter0\.8683±0\.04640\.8683\\mathbin\{\\pm\}0\.04640\.8647±0\.04750\.8647\\mathbin\{\\pm\}0\.04750\.8605±0\.04910\.8605\\mathbin\{\\pm\}0\.04910\.8618±0\.04990\.8618\\mathbin\{\\pm\}0\.04990\.8581±0\.04930\.8581\\mathbin\{\\pm\}0\.0493Collinearity filter0\.8683±0\.04640\.8683\\mathbin\{\\pm\}0\.04640\.8647±0\.04750\.8647\\mathbin\{\\pm\}0\.04750\.8605±0\.04910\.8605\\mathbin\{\\pm\}0\.04910\.8618±0\.04990\.8618\\mathbin\{\\pm\}0\.04990\.8581±0\.04930\.8581\\mathbin\{\\pm\}0\.0493PCA0\.9009±0\.05610\.9009\\mathbin\{\\pm\}0\.05610\.9054±0\.05650\.9054\\mathbin\{\\pm\}0\.05650\.9159±0\.06250\.9159\\mathbin\{\\pm\}0\.06250\.8915±0\.05680\.8915\\mathbin\{\\pm\}0\.05680\.8929±0\.05660\.8929\\mathbin\{\\pm\}0\.0566Supervised selection0\.9669±0\.06300\.9669\\mathbin\{\\pm\}0\.06300\.9693±0\.06390\.9693\\mathbin\{\\pm\}0\.06390\.9682±0\.06380\.9682\\mathbin\{\\pm\}0\.06380\.9675±0\.06510\.9675\\mathbin\{\\pm\}0\.06510\.9642±0\.06020\.9642\\mathbin\{\\pm\}0\.0602TabPrep full0\.8661±0\.04970\.8661\\mathbin\{\\pm\}0\.04970\.8723±0\.04910\.8723\\mathbin\{\\pm\}0\.04910\.8678±0\.05090\.8678\\mathbin\{\\pm\}0\.05090\.8736±0\.04990\.8736\\mathbin\{\\pm\}0\.04990\.8677±0\.04920\.8677\\mathbin\{\\pm\}0\.0492TabPrep w/o groupby0\.8664±0\.04850\.8664\\mathbin\{\\pm\}0\.04850\.8717±0\.04990\.8717\\mathbin\{\\pm\}0\.04990\.8667±0\.05010\.8667\\mathbin\{\\pm\}0\.05010\.8734±0\.05090\.8734\\mathbin\{\\pm\}0\.05090\.8672±0\.04980\.8672\\mathbin\{\\pm\}0\.0498TabPrep w/o RSFC0\.8678±0\.04770\.8678\\mathbin\{\\pm\}0\.04770\.8716±0\.04840\.8716\\mathbin\{\\pm\}0\.04840\.8652±0\.05030\.8652\\mathbin\{\\pm\}0\.05030\.8738±0\.05040\.8738\\mathbin\{\\pm\}0\.05040\.8671±0\.04960\.8671\\mathbin\{\\pm\}0\.0496TabPrep w/o arithmetic0\.9342±0\.05590\.9342\\mathbin\{\\pm\}0\.05590\.9292±0\.05570\.9292\\mathbin\{\\pm\}0\.05570\.9271±0\.05800\.9271\\mathbin\{\\pm\}0\.05800\.9365±0\.05400\.9365\\mathbin\{\\pm\}0\.05400\.9476±0\.05260\.9476\\mathbin\{\\pm\}0\.0526TabPrep w/o cat\. interact\.0\.8680±0\.04820\.8680\\mathbin\{\\pm\}0\.04820\.8728±0\.04930\.8728\\mathbin\{\\pm\}0\.04930\.8677±0\.05190\.8677\\mathbin\{\\pm\}0\.05190\.8732±0\.05000\.8732\\mathbin\{\\pm\}0\.05000\.8678±0\.04900\.8678\\mathbin\{\\pm\}0\.0490TabPrep w/o OOF\-TE0\.8681±0\.04900\.8681\\mathbin\{\\pm\}0\.04900\.8727±0\.04900\.8727\\mathbin\{\\pm\}0\.04900\.8696±0\.05080\.8696\\mathbin\{\\pm\}0\.05080\.8732±0\.05010\.8732\\mathbin\{\\pm\}0\.05010\.8685±0\.04950\.8685\\mathbin\{\\pm\}0\.0495Shared\-context kNN0\.8679±0\.04740\.8679\\mathbin\{\\pm\}0\.04740\.8652±0\.04770\.8652\\mathbin\{\\pm\}0\.04770\.8607±0\.04900\.8607\\mathbin\{\\pm\}0\.04900\.8616±0\.05040\.8616\\mathbin\{\\pm\}0\.05040\.8582±0\.04930\.8582\\mathbin\{\\pm\}0\.0493OOF prediction feature0\.8831±0\.05010\.8831\\mathbin\{\\pm\}0\.05010\.8851±0\.05330\.8851\\mathbin\{\\pm\}0\.05330\.8747±0\.05330\.8747\\mathbin\{\\pm\}0\.05330\.9099±0\.05370\.9099\\mathbin\{\\pm\}0\.05370\.8780±0\.04940\.8780\\mathbin\{\\pm\}0\.0494Table 30:Complete TabPFN and TabICL raw metric results for Website phishing, metric accuracy\. Values are mean±\\mathbin\{\\pm\}sample standard deviation across the 30 paired splits\.ConditionPFN v1PFN v2PFN v2\.5PFN v2\.6PFN v3ICL v1ICL v2Identity0\.8832±0\.01180\.8832\\mathbin\{\\pm\}0\.01180\.9120±0\.01170\.9120\\mathbin\{\\pm\}0\.01170\.9135±0\.01090\.9135\\mathbin\{\\pm\}0\.01090\.9159±0\.01250\.9159\\mathbin\{\\pm\}0\.01250\.9166±0\.01240\.9166\\mathbin\{\\pm\}0\.01240\.9081±0\.01250\.9081\\mathbin\{\\pm\}0\.01250\.9150±0\.01280\.9150\\mathbin\{\\pm\}0\.0128Standard scaling———————Log transform———————Square\-root transform———————Box–Cox———————Min–max scaling———————One\-hot encoding0\.9013±0\.01110\.9013\\mathbin\{\\pm\}0\.01110\.9122±0\.01150\.9122\\mathbin\{\\pm\}0\.01150\.9155±0\.01130\.9155\\mathbin\{\\pm\}0\.01130\.9132±0\.01200\.9132\\mathbin\{\\pm\}0\.01200\.9179±0\.01080\.9179\\mathbin\{\\pm\}0\.01080\.9030±0\.00980\.9030\\mathbin\{\\pm\}0\.00980\.9160±0\.01170\.9160\\mathbin\{\\pm\}0\.0117Ordinal encoding0\.8832±0\.01180\.8832\\mathbin\{\\pm\}0\.01180\.9120±0\.01170\.9120\\mathbin\{\\pm\}0\.01170\.9135±0\.01090\.9135\\mathbin\{\\pm\}0\.01090\.9159±0\.01250\.9159\\mathbin\{\\pm\}0\.01250\.9166±0\.01240\.9166\\mathbin\{\\pm\}0\.01240\.9081±0\.01250\.9081\\mathbin\{\\pm\}0\.01250\.9150±0\.01280\.9150\\mathbin\{\\pm\}0\.0128Frequency encoding0\.8619±0\.01370\.8619\\mathbin\{\\pm\}0\.01370\.9115±0\.01220\.9115\\mathbin\{\\pm\}0\.01220\.9140±0\.01170\.9140\\mathbin\{\\pm\}0\.01170\.9143±0\.01300\.9143\\mathbin\{\\pm\}0\.01300\.9168±0\.01220\.9168\\mathbin\{\\pm\}0\.01220\.9025±0\.01250\.9025\\mathbin\{\\pm\}0\.01250\.9135±0\.01260\.9135\\mathbin\{\\pm\}0\.0126Target encoding0\.8937±0\.01160\.8937\\mathbin\{\\pm\}0\.01160\.9107±0\.01230\.9107\\mathbin\{\\pm\}0\.01230\.9135±0\.01020\.9135\\mathbin\{\\pm\}0\.01020\.8776±0\.01630\.8776\\mathbin\{\\pm\}0\.01630\.9095±0\.01190\.9095\\mathbin\{\\pm\}0\.01190\.8843±0\.01100\.8843\\mathbin\{\\pm\}0\.01100\.9021±0\.01480\.9021\\mathbin\{\\pm\}0\.0148Categorical crosses0\.8885±0\.01370\.8885\\mathbin\{\\pm\}0\.01370\.9135±0\.01090\.9135\\mathbin\{\\pm\}0\.01090\.9142±0\.01130\.9142\\mathbin\{\\pm\}0\.01130\.9163±0\.01200\.9163\\mathbin\{\\pm\}0\.01200\.9143±0\.01210\.9143\\mathbin\{\\pm\}0\.01210\.8983±0\.01250\.8983\\mathbin\{\\pm\}0\.01250\.9135±0\.01030\.9135\\mathbin\{\\pm\}0\.0103Equal\-width binning———————Equal\-frequency binning———————Numeric interactions———————Group aggregation———————Variance filter0\.8832±0\.01180\.8832\\mathbin\{\\pm\}0\.01180\.9120±0\.01170\.9120\\mathbin\{\\pm\}0\.01170\.9135±0\.01090\.9135\\mathbin\{\\pm\}0\.01090\.9159±0\.01250\.9159\\mathbin\{\\pm\}0\.01250\.9166±0\.01240\.9166\\mathbin\{\\pm\}0\.01240\.9081±0\.01250\.9081\\mathbin\{\\pm\}0\.01250\.9150±0\.01280\.9150\\mathbin\{\\pm\}0\.0128Collinearity filter0\.8832±0\.01180\.8832\\mathbin\{\\pm\}0\.01180\.9120±0\.01170\.9120\\mathbin\{\\pm\}0\.01170\.9135±0\.01090\.9135\\mathbin\{\\pm\}0\.01090\.9159±0\.01250\.9159\\mathbin\{\\pm\}0\.01250\.9166±0\.01240\.9166\\mathbin\{\\pm\}0\.01240\.9081±0\.01250\.9081\\mathbin\{\\pm\}0\.01250\.9150±0\.01280\.9150\\mathbin\{\\pm\}0\.0128PCA———————Supervised selection0\.8832±0\.01180\.8832\\mathbin\{\\pm\}0\.01180\.9120±0\.01170\.9120\\mathbin\{\\pm\}0\.01170\.9135±0\.01090\.9135\\mathbin\{\\pm\}0\.01090\.9159±0\.01250\.9159\\mathbin\{\\pm\}0\.01250\.9166±0\.01240\.9166\\mathbin\{\\pm\}0\.01240\.9081±0\.01250\.9081\\mathbin\{\\pm\}0\.01250\.9150±0\.01280\.9150\\mathbin\{\\pm\}0\.0128TabPrep full0\.9016±0\.01280\.9016\\mathbin\{\\pm\}0\.01280\.9066±0\.01210\.9066\\mathbin\{\\pm\}0\.01210\.9052±0\.01210\.9052\\mathbin\{\\pm\}0\.01210\.9058±0\.01190\.9058\\mathbin\{\\pm\}0\.01190\.9060±0\.01230\.9060\\mathbin\{\\pm\}0\.01230\.9038±0\.01300\.9038\\mathbin\{\\pm\}0\.01300\.9058±0\.01200\.9058\\mathbin\{\\pm\}0\.0120TabPrep w/o groupby0\.8990±0\.01270\.8990\\mathbin\{\\pm\}0\.01270\.9028±0\.01650\.9028\\mathbin\{\\pm\}0\.01650\.9018±0\.01410\.9018\\mathbin\{\\pm\}0\.01410\.9012±0\.01400\.9012\\mathbin\{\\pm\}0\.01400\.9021±0\.01350\.9021\\mathbin\{\\pm\}0\.01350\.8998±0\.01110\.8998\\mathbin\{\\pm\}0\.01110\.9007±0\.01390\.9007\\mathbin\{\\pm\}0\.0139TabPrep w/o RSFC0\.8995±0\.01210\.8995\\mathbin\{\\pm\}0\.01210\.9115±0\.01120\.9115\\mathbin\{\\pm\}0\.01120\.9106±0\.01270\.9106\\mathbin\{\\pm\}0\.01270\.9117±0\.01250\.9117\\mathbin\{\\pm\}0\.01250\.9101±0\.01180\.9101\\mathbin\{\\pm\}0\.01180\.9027±0\.01100\.9027\\mathbin\{\\pm\}0\.01100\.9109±0\.01290\.9109\\mathbin\{\\pm\}0\.0129TabPrep w/o arithmetic0\.8995±0\.01410\.8995\\mathbin\{\\pm\}0\.01410\.9030±0\.01520\.9030\\mathbin\{\\pm\}0\.01520\.9031±0\.01380\.9031\\mathbin\{\\pm\}0\.01380\.9028±0\.01330\.9028\\mathbin\{\\pm\}0\.01330\.9035±0\.01330\.9035\\mathbin\{\\pm\}0\.01330\.9013±0\.01290\.9013\\mathbin\{\\pm\}0\.01290\.9042±0\.01290\.9042\\mathbin\{\\pm\}0\.0129TabPrep w/o cat\. interact\.0\.8999±0\.01390\.8999\\mathbin\{\\pm\}0\.01390\.9061±0\.01290\.9061\\mathbin\{\\pm\}0\.01290\.9029±0\.01250\.9029\\mathbin\{\\pm\}0\.01250\.9044±0\.01490\.9044\\mathbin\{\\pm\}0\.01490\.9055±0\.01420\.9055\\mathbin\{\\pm\}0\.01420\.9019±0\.01510\.9019\\mathbin\{\\pm\}0\.01510\.9055±0\.01360\.9055\\mathbin\{\\pm\}0\.0136TabPrep w/o OOF\-TE0\.8996±0\.01100\.8996\\mathbin\{\\pm\}0\.01100\.9041±0\.01390\.9041\\mathbin\{\\pm\}0\.01390\.9040±0\.01420\.9040\\mathbin\{\\pm\}0\.01420\.9041±0\.01430\.9041\\mathbin\{\\pm\}0\.01430\.9039±0\.01410\.9039\\mathbin\{\\pm\}0\.01410\.9024±0\.01380\.9024\\mathbin\{\\pm\}0\.01380\.9016±0\.01300\.9016\\mathbin\{\\pm\}0\.0130Shared\-context kNN0\.8830±0\.01180\.8830\\mathbin\{\\pm\}0\.01180\.9118±0\.01110\.9118\\mathbin\{\\pm\}0\.01110\.9136±0\.01090\.9136\\mathbin\{\\pm\}0\.01090\.9154±0\.01190\.9154\\mathbin\{\\pm\}0\.01190\.9169±0\.01180\.9169\\mathbin\{\\pm\}0\.01180\.9084±0\.01240\.9084\\mathbin\{\\pm\}0\.01240\.9151±0\.01290\.9151\\mathbin\{\\pm\}0\.0129OOF prediction feature0\.8823±0\.01270\.8823\\mathbin\{\\pm\}0\.01270\.9135±0\.01070\.9135\\mathbin\{\\pm\}0\.01070\.9142±0\.01060\.9142\\mathbin\{\\pm\}0\.01060\.9179±0\.01060\.9179\\mathbin\{\\pm\}0\.01060\.9163±0\.01190\.9163\\mathbin\{\\pm\}0\.01190\.9112±0\.01220\.9112\\mathbin\{\\pm\}0\.01220\.9155±0\.01330\.9155\\mathbin\{\\pm\}0\.0133Table 31:Complete TabPFN and TabICL raw metric results for Website phishing, metric macro f1\. Values are mean±\\mathbin\{\\pm\}sample standard deviation across the 30 paired splits\.ConditionPFN v1PFN v2PFN v2\.5PFN v2\.6PFN v3ICL v1ICL v2Identity0\.8433±0\.01950\.8433\\mathbin\{\\pm\}0\.01950\.8967±0\.01600\.8967\\mathbin\{\\pm\}0\.01600\.9024±0\.01240\.9024\\mathbin\{\\pm\}0\.01240\.9039±0\.01570\.9039\\mathbin\{\\pm\}0\.01570\.9059±0\.01460\.9059\\mathbin\{\\pm\}0\.01460\.8853±0\.01770\.8853\\mathbin\{\\pm\}0\.01770\.8998±0\.01710\.8998\\mathbin\{\\pm\}0\.0171Standard scaling———————Log transform———————Square\-root transform———————Box–Cox———————Min–max scaling———————One\-hot encoding0\.8776±0\.01810\.8776\\mathbin\{\\pm\}0\.01810\.8959±0\.01680\.8959\\mathbin\{\\pm\}0\.01680\.9059±0\.01360\.9059\\mathbin\{\\pm\}0\.01360\.8981±0\.01800\.8981\\mathbin\{\\pm\}0\.01800\.9072±0\.01350\.9072\\mathbin\{\\pm\}0\.01350\.8712±0\.01570\.8712\\mathbin\{\\pm\}0\.01570\.9034±0\.01430\.9034\\mathbin\{\\pm\}0\.0143Ordinal encoding0\.8433±0\.01950\.8433\\mathbin\{\\pm\}0\.01950\.8967±0\.01600\.8967\\mathbin\{\\pm\}0\.01600\.9024±0\.01240\.9024\\mathbin\{\\pm\}0\.01240\.9039±0\.01570\.9039\\mathbin\{\\pm\}0\.01570\.9059±0\.01460\.9059\\mathbin\{\\pm\}0\.01460\.8853±0\.01770\.8853\\mathbin\{\\pm\}0\.01770\.8998±0\.01710\.8998\\mathbin\{\\pm\}0\.0171Frequency encoding0\.7419±0\.04510\.7419\\mathbin\{\\pm\}0\.04510\.8969±0\.01820\.8969\\mathbin\{\\pm\}0\.01820\.9031±0\.01380\.9031\\mathbin\{\\pm\}0\.01380\.9011±0\.01530\.9011\\mathbin\{\\pm\}0\.01530\.9054±0\.01600\.9054\\mathbin\{\\pm\}0\.01600\.8687±0\.02540\.8687\\mathbin\{\\pm\}0\.02540\.8986±0\.01820\.8986\\mathbin\{\\pm\}0\.0182Target encoding0\.8582±0\.02030\.8582\\mathbin\{\\pm\}0\.02030\.8892±0\.02170\.8892\\mathbin\{\\pm\}0\.02170\.9013±0\.01510\.9013\\mathbin\{\\pm\}0\.01510\.7619±0\.06070\.7619\\mathbin\{\\pm\}0\.06070\.8869±0\.02170\.8869\\mathbin\{\\pm\}0\.02170\.7986±0\.03560\.7986\\mathbin\{\\pm\}0\.03560\.8578±0\.03660\.8578\\mathbin\{\\pm\}0\.0366Categorical crosses0\.8531±0\.02460\.8531\\mathbin\{\\pm\}0\.02460\.9064±0\.01340\.9064\\mathbin\{\\pm\}0\.01340\.9059±0\.01240\.9059\\mathbin\{\\pm\}0\.01240\.9084±0\.01280\.9084\\mathbin\{\\pm\}0\.01280\.9052±0\.01360\.9052\\mathbin\{\\pm\}0\.01360\.8616±0\.02070\.8616\\mathbin\{\\pm\}0\.02070\.9015±0\.01180\.9015\\mathbin\{\\pm\}0\.0118Equal\-width binning———————Equal\-frequency binning———————Numeric interactions———————Group aggregation———————Variance filter0\.8433±0\.01950\.8433\\mathbin\{\\pm\}0\.01950\.8967±0\.01600\.8967\\mathbin\{\\pm\}0\.01600\.9024±0\.01240\.9024\\mathbin\{\\pm\}0\.01240\.9039±0\.01570\.9039\\mathbin\{\\pm\}0\.01570\.9059±0\.01460\.9059\\mathbin\{\\pm\}0\.01460\.8853±0\.01770\.8853\\mathbin\{\\pm\}0\.01770\.8998±0\.01710\.8998\\mathbin\{\\pm\}0\.0171Collinearity filter0\.8433±0\.01950\.8433\\mathbin\{\\pm\}0\.01950\.8967±0\.01600\.8967\\mathbin\{\\pm\}0\.01600\.9024±0\.01240\.9024\\mathbin\{\\pm\}0\.01240\.9039±0\.01570\.9039\\mathbin\{\\pm\}0\.01570\.9059±0\.01460\.9059\\mathbin\{\\pm\}0\.01460\.8853±0\.01770\.8853\\mathbin\{\\pm\}0\.01770\.8998±0\.01710\.8998\\mathbin\{\\pm\}0\.0171PCA———————Supervised selection0\.8433±0\.01950\.8433\\mathbin\{\\pm\}0\.01950\.8967±0\.01600\.8967\\mathbin\{\\pm\}0\.01600\.9024±0\.01240\.9024\\mathbin\{\\pm\}0\.01240\.9039±0\.01570\.9039\\mathbin\{\\pm\}0\.01570\.9059±0\.01460\.9059\\mathbin\{\\pm\}0\.01460\.8853±0\.01770\.8853\\mathbin\{\\pm\}0\.01770\.8998±0\.01710\.8998\\mathbin\{\\pm\}0\.0171TabPrep full0\.8773±0\.01970\.8773\\mathbin\{\\pm\}0\.01970\.8895±0\.01820\.8895\\mathbin\{\\pm\}0\.01820\.8856±0\.01920\.8856\\mathbin\{\\pm\}0\.01920\.8861±0\.02070\.8861\\mathbin\{\\pm\}0\.02070\.8869±0\.02220\.8869\\mathbin\{\\pm\}0\.02220\.8810±0\.02140\.8810\\mathbin\{\\pm\}0\.02140\.8874±0\.01670\.8874\\mathbin\{\\pm\}0\.0167TabPrep w/o groupby0\.8672±0\.02330\.8672\\mathbin\{\\pm\}0\.02330\.8785±0\.02820\.8785\\mathbin\{\\pm\}0\.02820\.8743±0\.02350\.8743\\mathbin\{\\pm\}0\.02350\.8738±0\.02560\.8738\\mathbin\{\\pm\}0\.02560\.8755±0\.02530\.8755\\mathbin\{\\pm\}0\.02530\.8696±0\.02320\.8696\\mathbin\{\\pm\}0\.02320\.8743±0\.02420\.8743\\mathbin\{\\pm\}0\.0242TabPrep w/o RSFC0\.8795±0\.01650\.8795\\mathbin\{\\pm\}0\.01650\.8992±0\.01580\.8992\\mathbin\{\\pm\}0\.01580\.8980±0\.01740\.8980\\mathbin\{\\pm\}0\.01740\.8985±0\.01550\.8985\\mathbin\{\\pm\}0\.01550\.8920±0\.01890\.8920\\mathbin\{\\pm\}0\.01890\.8820±0\.01580\.8820\\mathbin\{\\pm\}0\.01580\.8958±0\.01890\.8958\\mathbin\{\\pm\}0\.0189TabPrep w/o arithmetic0\.8700±0\.02250\.8700\\mathbin\{\\pm\}0\.02250\.8775±0\.02190\.8775\\mathbin\{\\pm\}0\.02190\.8768±0\.02290\.8768\\mathbin\{\\pm\}0\.02290\.8776±0\.01940\.8776\\mathbin\{\\pm\}0\.01940\.8791±0\.02280\.8791\\mathbin\{\\pm\}0\.02280\.8736±0\.01980\.8736\\mathbin\{\\pm\}0\.01980\.8803±0\.01950\.8803\\mathbin\{\\pm\}0\.0195TabPrep w/o cat\. interact\.0\.8720±0\.02400\.8720\\mathbin\{\\pm\}0\.02400\.8876±0\.02090\.8876\\mathbin\{\\pm\}0\.02090\.8799±0\.02110\.8799\\mathbin\{\\pm\}0\.02110\.8843±0\.02380\.8843\\mathbin\{\\pm\}0\.02380\.8841±0\.02290\.8841\\mathbin\{\\pm\}0\.02290\.8765±0\.02580\.8765\\mathbin\{\\pm\}0\.02580\.8836±0\.02400\.8836\\mathbin\{\\pm\}0\.0240TabPrep w/o OOF\-TE0\.8729±0\.02060\.8729\\mathbin\{\\pm\}0\.02060\.8830±0\.02220\.8830\\mathbin\{\\pm\}0\.02220\.8816±0\.02270\.8816\\mathbin\{\\pm\}0\.02270\.8810±0\.02300\.8810\\mathbin\{\\pm\}0\.02300\.8814±0\.02060\.8814\\mathbin\{\\pm\}0\.02060\.8765±0\.02330\.8765\\mathbin\{\\pm\}0\.02330\.8788±0\.02290\.8788\\mathbin\{\\pm\}0\.0229Shared\-context kNN0\.8432±0\.01950\.8432\\mathbin\{\\pm\}0\.01950\.8969±0\.01560\.8969\\mathbin\{\\pm\}0\.01560\.9028±0\.01250\.9028\\mathbin\{\\pm\}0\.01250\.9030±0\.01420\.9030\\mathbin\{\\pm\}0\.01420\.9058±0\.01460\.9058\\mathbin\{\\pm\}0\.01460\.8857±0\.01760\.8857\\mathbin\{\\pm\}0\.01760\.9000±0\.01720\.9000\\mathbin\{\\pm\}0\.0172OOF prediction feature0\.8377±0\.02330\.8377\\mathbin\{\\pm\}0\.02330\.9043±0\.01310\.9043\\mathbin\{\\pm\}0\.01310\.9034±0\.01360\.9034\\mathbin\{\\pm\}0\.01360\.9093±0\.01440\.9093\\mathbin\{\\pm\}0\.01440\.9060±0\.01460\.9060\\mathbin\{\\pm\}0\.01460\.8944±0\.01650\.8944\\mathbin\{\\pm\}0\.01650\.9022±0\.01650\.9022\\mathbin\{\\pm\}0\.0165