Regression Benchmarks

Dataset Overview

Dataset	Instances	Features	Numeric	Categorical	Target
Boston housing	506	13	11	2	MEDV
California housing	20640	8	8	0	medianHouseValue
Geographical origin of music	1059	116	116	0	latitude
Health insurance	22272	11	4	7	whrswk
Pumadyn32nh	8192	32	32	0	thetadd6
Student performance por	649	30	13	17	G3
Superconductivity	21263	81	81	0	critical_temp

Quick Check

Dataset	Type	Family / Variant	Test RMSE	Test R²
Boston housing	Best classical	Trees / LightGBM	2.64293 ± 0.08667	0.92436 ± 0.00503
Boston housing	Best transformed	CNN+MLP / DistanceMatrix	2.39441 ± 0.14017	0.93780 ± 0.00728
California housing	Best classical	Trees / XGBoost	0.43989 ± 0.00403	0.85687 ± 0.00263
California housing	Best transformed	CNN / BIE	0.44662 ± 0.00312	0.85247 ± 0.00205
Geographical origin of music	Best classical	Trees / CatBoost	16.09875 ± 0.27347	0.28649 ± 0.02426
Geographical origin of music	Best transformed	CNN / REFINED	15.02703 ± 0.62945	0.37760 ± 0.05210
Health insurance	Best classical	Trees / CatBoost	14.24579 ± 0.00935	0.41469 ± 0.00077
Health insurance	Best transformed	ViT / REFINED	14.31386 ± 0.04021	0.40908 ± 0.00332
Pumadyn32nh	Best classical	Trees / CatBoost	0.02097 ± 0.00004	0.64498 ± 0.00135
Pumadyn32nh	Best transformed	ViT / REFINED	0.02185 ± 0.00008	0.61439 ± 0.00293
Student performance por	Best classical	Trees / LightGBM	2.07327 ± 0.01229	0.24692 ± 0.00894
Student performance por	Best transformed	ViT+MLP / REFINED	2.00620 ± 0.02164	0.29482 ± 0.01526
Superconductivity	Best classical	Trees / XGBoost	9.39012 ± 0.01083	0.92444 ± 0.00017
Superconductivity	Best transformed	CNN / TINTO	9.48401 ± 0.05426	0.92292 ± 0.00088

Boston housing

Source: Boston Housing (1978)

Leaderboard

Family	Best variant	Test RMSE	Test R²	Train time (s)	#Params	FLOPs
Trees	LightGBM	2.64293 ± 0.08667	0.92436 ± 0.00503	0.10473 ± 0.01010	—	—
MLP	MLP	3.01003 ± 0.21439	0.90158 ± 0.01395	4.23418 ± 0.73795	274,945 ± 0.00000	548,864 ± 0.00000
ViT	REFINED	2.57398 ± 0.21155	0.92793 ± 0.01177	29.41662 ± 0.19323	3,041,671 ± 0.00000	158,169,495 ± 0.00000
ViT+MLP	Combination	2.70160 ± 0.25837	0.92046 ± 0.01509	71.95644 ± 1.05371	16,894,937 ± 0.00000	23,145,874,912 ± 4,574,605,197.45434
CNN	REFINED	2.46685 ± 0.26438	0.93356 ± 0.01460	14.23677 ± 0.05346	192,825 ± 0.00000	3,284,400 ± 0.00000
CNN+MLP	DistanceMatrix	2.39441 ± 0.14017	0.93780 ± 0.00728	19.18030 ± 0.52748	623,881 ± 0.00000	123,184,480 ± 0.00000

Architecture Results

Tree Baselines

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	Train time (s)	#Params	FLOPs
CatBoost	0.27800 ± 0.10580	3.20287 ± 0.11571	2.73597 ± 0.08619	0.99896 ± 0.00083	0.87688 ± 0.00878	0.91895 ± 0.00514	2.99438 ± 0.03236	—	—
LightGBM	1.20464 ± 0.01442	3.25573 ± 0.10716	2.64293 ± 0.08667	0.98241 ± 0.00042	0.87281 ± 0.00851	0.92436 ± 0.00503	0.10473 ± 0.01010	—	—
XGBoost	1.23884 ± 0.02319	3.13241 ± 0.04323	2.79232 ± 0.04993	0.98140 ± 0.00069	0.88234 ± 0.00326	0.91562 ± 0.00301	0.44749 ± 0.00514	—	—

MLP

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
MLP	2.53665 ± 0.20504	3.49185 ± 0.03450	3.01003 ± 0.21439	0.92162 ± 0.01234	0.85380 ± 0.00288	0.90158 ± 0.01395	274,945 ± 0.00000	548,864 ± 0.00000	4.23418 ± 0.73795

ViT

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
TINTO	1.93251 ± 0.33082	3.49700 ± 0.08594	2.98962 ± 0.25167	0.95368 ± 0.01645	0.85331 ± 0.00728	0.90275 ± 0.01619	3,260,577 ± 0.00000	163,838,060 ± 0.00000	20.66712 ± 0.51800
IGTD	9.11893 ± 0.00307	9.13305 ± 0.00026	9.63393 ± 0.00221	-0.00768 ± 0.00068	-0.00005 ± 0.00006	-0.00413 ± 0.00046	512,743 ± 0.00000	27,155,815 ± 0.00000	23.42475 ± 1.20051
REFINED	1.50936 ± 0.30300	3.14998 ± 0.08060	2.57398 ± 0.21155	0.97150 ± 0.01229	0.88098 ± 0.00614	0.92793 ± 0.01177	3,041,671 ± 0.00000	158,169,495 ± 0.00000	29.41662 ± 0.19323
DistanceMatrix	1.47646 ± 0.47992	3.50178 ± 0.12724	3.54344 ± 0.17961	0.97135 ± 0.01783	0.85283 ± 0.01058	0.86388 ± 0.01358	14,234,905 ± 0.00000	2,308,646,228 ± 0.00000	67.32671 ± 15.22236
BarGraph	1.77073 ± 0.69186	3.24519 ± 0.07944	2.96469 ± 0.53319	0.95736 ± 0.03105	0.87368 ± 0.00617	0.90245 ± 0.03758	12,071,289 ± 0.00000	1,891,104,100 ± 0.00000	47.49440 ± 0.75261
Combination	1.80507 ± 0.46080	3.21779 ± 0.19262	2.74446 ± 0.16067	0.95846 ± 0.02236	0.87550 ± 0.01513	0.91829 ± 0.00950	16,580,473 ± 0.00000	2,754,888,892 ± 0.00000	60.89286 ± 0.79736
SuperTML	2.03421 ± 1.03974	4.45341 ± 0.56251	5.36638 ± 0.31885	0.93937 ± 0.06139	0.75918 ± 0.06113	0.68756 ± 0.03674	10,514,945 ± 0.00000	1,297,985,304 ± 0.00000	39.77714 ± 3.71406
FeatureWrap	4.57558 ± 0.30882	5.69138 ± 0.10345	6.32727 ± 0.19251	0.74537 ± 0.03399	0.61154 ± 0.01406	0.56656 ± 0.02669	943,513 ± 0.00000	19,181,964 ± 0.00000	29.16736 ± 0.36974
BIE	2.26520 ± 0.41759	4.88408 ± 0.42985	5.31738 ± 0.37801	0.93613 ± 0.02537	0.71223 ± 0.05027	0.69287 ± 0.04324	7,099,777 ± 0.00000	864,935,572 ± 0.00000	31.56232 ± 3.19591

ViT + MLP

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
TINTO	1.95366 ± 0.31369	3.27767 ± 0.10241	2.90662 ± 0.33039	0.95279 ± 0.01463	0.87110 ± 0.00805	0.90765 ± 0.02163	3,628,321 ± 0.00000	1,516,589,920 ± 299,742,401.47828	22.65244 ± 0.35614
IGTD	2.32634 ± 0.45024	3.51752 ± 0.06167	2.93851 ± 0.38052	0.93245 ± 0.02650	0.85162 ± 0.00522	0.90533 ± 0.02602	812,583 ± 0.00000	577,654,110 ± 50,741,741.31549	26.84440 ± 0.62645
REFINED	1.66692 ± 0.24461	3.19159 ± 0.12588	2.71211 ± 0.15036	0.96575 ± 0.01046	0.87772 ± 0.00975	0.92023 ± 0.00883	3,349,447 ± 0.00000	5,141,137,540 ± 290,316,149.83205	41.29689 ± 0.36799
DistanceMatrix	1.92433 ± 0.54507	3.49446 ± 0.19839	3.34396 ± 0.35498	0.95225 ± 0.02390	0.85322 ± 0.01669	0.87793 ± 0.02537	14,467,513 ± 0.00000	43,607,930,472 ± 3,830,566,231.60504	73.97143 ± 3.95586
BarGraph	2.00807 ± 0.36445	3.33908 ± 0.19814	3.13040 ± 0.46134	0.94985 ± 0.01879	0.86595 ± 0.01576	0.89214 ± 0.03165	11,797,241 ± 0.00000	15,869,381,664 ± 3,136,461,944.79706	54.16998 ± 1.31253
Combination	1.68597 ± 0.44069	3.21787 ± 0.15816	2.70160 ± 0.25837	0.96367 ± 0.01971	0.87562 ± 0.01204	0.92046 ± 0.01509	16,894,937 ± 0.00000	23,145,874,912 ± 4,574,605,197.45434	71.95644 ± 1.05371
SuperTML	1.96240 ± 0.13583	3.52269 ± 0.07090	2.73376 ± 0.13026	0.95315 ± 0.00648	0.85117 ± 0.00599	0.91900 ± 0.00778	10,368,001 ± 0.00000	24,675,806,448 ± 2,167,548,652.14303	45.29493 ± 1.17064
FeatureWrap	2.40244 ± 0.25579	3.51804 ± 0.04989	2.91964 ± 0.12322	0.92942 ± 0.01529	0.85159 ± 0.00420	0.90765 ± 0.00791	1,204,921 ± 0.00000	775,564,048 ± 43,795,515.41107	41.53267 ± 0.58403
BIE	2.03324 ± 0.11257	3.50626 ± 0.09037	2.78704 ± 0.09112	0.94978 ± 0.00543	0.85253 ± 0.00764	0.91589 ± 0.00556	6,843,905 ± 0.00000	7,346,259,872 ± 1,451,932,092.43856	50.24351 ± 0.52854

CNN

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
TINTO	1.34596 ± 0.40460	3.24922 ± 0.12831	3.21047 ± 0.37006	0.97646 ± 0.01350	0.87327 ± 0.01010	0.88730 ± 0.02593	74,193 ± 0.00000	9,381,952 ± 0.00000	20.19407 ± 1.37805
IGTD	2.59679 ± 0.64853	3.40121 ± 0.06535	2.86891 ± 0.35293	0.91421 ± 0.03901	0.86126 ± 0.00532	0.90988 ± 0.02135	440,377 ± 0.00000	8,526,440 ± 0.00000	18.95521 ± 0.12599
REFINED	1.10799 ± 0.32747	3.16947 ± 0.07643	2.46685 ± 0.26438	0.98408 ± 0.00954	0.87951 ± 0.00585	0.93356 ± 0.01460	192,825 ± 0.00000	3,284,400 ± 0.00000	14.23677 ± 0.05346
DistanceMatrix	1.15015 ± 0.18339	3.18025 ± 0.15685	2.50715 ± 0.09029	0.98364 ± 0.00525	0.87850 ± 0.01182	0.93193 ± 0.00494	185,353 ± 0.00000	122,308,640 ± 0.00000	18.11340 ± 0.76780
BarGraph	1.36435 ± 0.42157	3.40128 ± 0.14756	2.57906 ± 0.11596	0.97572 ± 0.01488	0.86109 ± 0.01224	0.92792 ± 0.00659	4,517,969 ± 0.00000	1,276,193,664 ± 0.00000	23.68178 ± 0.48813
Combination	1.07358 ± 0.30007	3.21128 ± 0.13433	2.63395 ± 0.15525	0.98516 ± 0.00682	0.87619 ± 0.01046	0.92473 ± 0.00911	9,952,017 ± 0.00000	8,098,979,136 ± 0.00000	34.41181 ± 0.25650
SuperTML	0.80803 ± 0.34971	4.01001 ± 0.14316	4.40619 ± 0.21669	0.99090 ± 0.00702	0.80701 ± 0.01384	0.78955 ± 0.02032	10,729,409 ± 0.00000	3,039,419,264 ± 0.00000	35.81777 ± 0.39223
FeatureWrap	3.49106 ± 0.44523	4.21044 ± 0.27441	6.18150 ± 0.37800	0.85039 ± 0.03802	0.78673 ± 0.02836	0.58537 ± 0.05072	154,961 ± 0.00000	2,986,320 ± 0.00000	19.31483 ± 0.15387
BIE	2.61601 ± 0.74975	5.84682 ± 0.31769	6.00553 ± 0.34949	0.91162 ± 0.05373	0.58918 ± 0.04365	0.60875 ± 0.04584	1,713,897 ± 0.00000	42,145,024 ± 0.00000	17.52854 ± 0.69925

CNN + MLP

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
TINTO	1.00499 ± 0.18957	3.33411 ± 0.15143	2.80304 ± 0.19099	0.98741 ± 0.00490	0.86650 ± 0.01227	0.91468 ± 0.01137	755,025 ± 0.00000	10,741,920 ± 0.00000	20.57700 ± 0.04900
IGTD	1.91775 ± 0.87132	3.31963 ± 0.12105	2.64527 ± 0.58132	0.94807 ± 0.05127	0.86774 ± 0.00984	0.92137 ± 0.03789	919,625 ± 0.00000	9,483,560 ± 0.00000	20.53250 ± 0.03646
REFINED	1.08777 ± 0.12727	3.17508 ± 0.18180	2.52415 ± 0.15201	0.98550 ± 0.00356	0.87882 ± 0.01413	0.93087 ± 0.00827	543,129 ± 0.00000	3,983,920 ± 0.00000	15.40566 ± 0.02158
DistanceMatrix	1.09828 ± 0.22947	3.11373 ± 0.11421	2.39441 ± 0.14017	0.98487 ± 0.00660	0.88364 ± 0.00856	0.93780 ± 0.00728	623,881 ± 0.00000	123,184,480 ± 0.00000	19.18030 ± 0.52748
BarGraph	1.21987 ± 0.29213	3.35928 ± 0.07035	2.71507 ± 0.11511	0.98114 ± 0.00891	0.86466 ± 0.00563	0.92013 ± 0.00680	4,695,697 ± 0.00000	1,276,548,448 ± 0.00000	24.80602 ± 0.15945
Combination	1.31655 ± 0.40520	3.19004 ± 0.12060	2.65254 ± 0.16080	0.97740 ± 0.01219	0.87785 ± 0.00942	0.92366 ± 0.00940	9,992,017 ± 0.00000	8,099,058,752 ± 0.00000	38.09345 ± 0.57019
SuperTML	1.30682 ± 0.39233	3.50697 ± 0.14106	3.44490 ± 0.28056	0.97781 ± 0.01313	0.85235 ± 0.01205	0.87093 ± 0.02102	10,767,809 ± 0.00000	3,039,495,696 ± 0.00000	45.59449 ± 2.34726
FeatureWrap	1.89755 ± 0.42813	3.32663 ± 0.07192	2.95132 ± 0.30706	0.95459 ± 0.02022	0.86727 ± 0.00576	0.90495 ± 0.02093	568,513 ± 0.00000	3,812,240 ± 0.00000	26.58122 ± 0.89657
BIE	1.41576 ± 0.31580	3.89415 ± 0.16937	3.70350 ± 0.41509	0.97474 ± 0.00997	0.81791 ± 0.01586	0.85012 ± 0.03325	2,363,273 ± 0.00000	43,442,560 ± 0.00000	19.26801 ± 1.32583

California housing

Source: OpenML · Original

Leaderboard

Family	Best variant	Test RMSE	Test R²	Train time (s)	#Params	FLOPs
Trees	XGBoost	0.43989 ± 0.00403	0.85687 ± 0.00263	1.77672 ± 0.09260	—	—
MLP	MLP	0.48063 ± 0.00318	0.82914 ± 0.00226	32.84561 ± 4.31202	267,777 ± 0.00000	534,528 ± 0.00000
ViT	SuperTML	0.46974 ± 0.00584	0.83678 ± 0.00406	3,945.05697 ± 7.98396	20,544,577 ± 0.00000	8,297,965,816 ± 0.00000
ViT+MLP	SuperTML	0.46976 ± 0.01030	0.83673 ± 0.00718	3,826.40757 ± 6.33717	20,501,569 ± 0.00000	67,793,230,784 ± 13,398,813,701.18015
CNN	BIE	0.44662 ± 0.00312	0.85247 ± 0.00205	1,412.74217 ± 1.22171	9,703,809 ± 0.00000	11,479,253,760 ± 0.00000
CNN+MLP	SuperTML	0.44877 ± 0.00787	0.85101 ± 0.00523	1,041.1302 ± 6.74585	10,748,017 ± 0.00000	2,931,497,536 ± 0.00000

Architecture Results

Tree Baselines

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	Train time (s)	#Params	FLOPs
CatBoost	0.38883 ± 0.00063	0.46611 ± 0.00213	0.44749 ± 0.00144	0.88624 ± 0.00037	0.83570 ± 0.00150	0.85189 ± 0.00095	4.40361 ± 0.25380	—	—
LightGBM	0.34418 ± 0.00287	0.45971 ± 0.00735	0.44134 ± 0.00771	0.91087 ± 0.00149	0.84015 ± 0.00514	0.85591 ± 0.00506	0.53835 ± 0.15180	—	—
XGBoost	0.15339 ± 0.00078	0.45610 ± 0.00391	0.43989 ± 0.00403	0.98230 ± 0.00018	0.84267 ± 0.00270	0.85687 ± 0.00263	1.77672 ± 0.09260	—	—

MLP

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
MLP	0.45728 ± 0.00309	0.49768 ± 0.00339	0.48063 ± 0.00318	0.84266 ± 0.00213	0.81268 ± 0.00255	0.82914 ± 0.00226	267,777 ± 0.00000	534,528 ± 0.00000	32.84561 ± 4.31202

ViT

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
TINTO	0.61452 ± 0.01092	0.67810 ± 0.00610	0.64259 ± 0.00535	0.71580 ± 0.01016	0.65225 ± 0.00629	0.69459 ± 0.00510	11,232,121 ± 0.00000	108,435,870 ± 0.00000	152.55714 ± 1.35583
IGTD	1.15301 ± 0.00003	1.14998 ± 0.00002	1.16281 ± 0.00001	-0.00026 ± 0.00005	-0.00008 ± 0.00003	-0.00005 ± 0.00002	5,623,111 ± 0.00000	112,844,007 ± 0.00000	244.20150 ± 0.26949
REFINED	0.49388 ± 0.01815	0.58730 ± 0.00350	0.55546 ± 0.00741	0.81628 ± 0.01344	0.73916 ± 0.00311	0.77177 ± 0.00607	29,768,263 ± 0.00000	582,613,719 ± 0.00000	347.38482 ± 0.74021
DistanceMatrix	0.57667 ± 0.02208	0.62189 ± 0.01604	0.59709 ± 0.01012	0.74950 ± 0.01922	0.70738 ± 0.01509	0.73626 ± 0.00895	13,164,103 ± 0.00000	1,006,315,932 ± 0.00000	582.92142 ± 1.39248
BarGraph	0.76060 ± 0.00642	0.77849 ± 0.00347	0.76262 ± 0.00537	0.56471 ± 0.00737	0.54168 ± 0.00409	0.56984 ± 0.00607	4,282,777 ± 0.00000	552,650,732 ± 0.00000	276.27179 ± 1.85934
Combination	0.50753 ± 0.00676	0.57846 ± 0.00394	0.56286 ± 0.00440	0.80617 ± 0.00515	0.74695 ± 0.00344	0.76567 ± 0.00367	8,363,737 ± 0.00000	1,327,060,508 ± 0.00000	665.79443 ± 12.26785
SuperTML	0.30560 ± 0.05360	0.48128 ± 0.01008	0.46974 ± 0.00584	0.92800 ± 0.02454	0.82477 ± 0.00737	0.83678 ± 0.00406	20,544,577 ± 0.00000	8,297,965,816 ± 0.00000	3,945.05697 ± 7.98396
FeatureWrap	0.73306 ± 0.00395	0.79687 ± 0.00374	0.72596 ± 0.00532	0.59567 ± 0.00435	0.51978 ± 0.00451	0.61019 ± 0.00571	9,881,593 ± 0.00000	96,348,000 ± 0.00000	309.49389 ± 2.01000
BIE	0.36140 ± 0.13995	0.54439 ± 0.02087	0.52315 ± 0.01736	0.88994 ± 0.06953	0.77562 ± 0.01716	0.79740 ± 0.01342	8,180,225 ± 0.00000	1,050,607,440 ± 0.00000	534.41748 ± 2.41966

ViT + MLP

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
TINTO	0.45674 ± 0.01856	0.50312 ± 0.01007	0.49053 ± 0.01151	0.84284 ± 0.01308	0.80851 ± 0.00775	0.82196 ± 0.00846	11,166,297 ± 0.00000	1,547,193,712 ± 305,791,006.96316	195.80453 ± 8.04050
IGTD	0.44018 ± 0.00216	0.49436 ± 0.00251	0.48557 ± 0.00336	0.85421 ± 0.00143	0.81518 ± 0.00187	0.82561 ± 0.00241	5,907,207 ± 0.00000	2,868,051,006 ± 251,932,600.68048	273.95670 ± 10.23985
REFINED	0.49616 ± 0.06657	0.53301 ± 0.04684	0.51819 ± 0.04558	0.81211 ± 0.05092	0.78382 ± 0.03844	0.80017 ± 0.03550	29,355,847 ± 0.00000	6,521,062,584 ± 1,288,838,158.12144	426.45587 ± 6.52916
DistanceMatrix	0.45873 ± 0.01869	0.50332 ± 0.01002	0.48512 ± 0.00773	0.84146 ± 0.01325	0.80836 ± 0.00772	0.82590 ± 0.00560	13,433,031 ± 0.00000	8,953,046,752 ± 1,769,501,233.39329	640.70717 ± 6.26998
BarGraph	0.46115 ± 0.00951	0.50180 ± 0.00456	0.48732 ± 0.00523	0.83995 ± 0.00669	0.80956 ± 0.00348	0.82434 ± 0.00379	3,629,433 ± 0.00000	10,406,511,576 ± 914,118,863.2519	290.97938 ± 5.03423
Combination	0.45835 ± 0.02473	0.50601 ± 0.01339	0.49449 ± 0.01299	0.84157 ± 0.01759	0.80626 ± 0.01038	0.81905 ± 0.00965	8,344,665 ± 0.00000	11,140,806,368 ± 2,201,895,193.36175	690.97560 ± 4.01270
SuperTML	0.28491 ± 0.08209	0.47589 ± 0.00321	0.46976 ± 0.01030	0.93487 ± 0.03562	0.82873 ± 0.00231	0.83673 ± 0.00718	20,501,569 ± 0.00000	67,793,230,784 ± 13,398,813,701.18015	3,826.40757 ± 6.33717
FeatureWrap	0.44808 ± 0.00268	0.49684 ± 0.00235	0.48778 ± 0.00450	0.84894 ± 0.00181	0.81332 ± 0.00176	0.82401 ± 0.00325	9,868,409 ± 0.00000	1,385,440,768 ± 273,821,774.38331	352.41515 ± 7.03545
BIE	0.44728 ± 0.02423	0.49988 ± 0.01102	0.48701 ± 0.01109	0.84912 ± 0.01688	0.81096 ± 0.00845	0.82451 ± 0.00808	8,349,761 ± 0.00000	8,927,987,328 ± 1,764,548,429.85005	587.75184 ± 4.40892

CNN

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
TINTO	0.56667 ± 0.01547	0.65894 ± 0.00063	0.62572 ± 0.00551	0.75826 ± 0.01312	0.67164 ± 0.00063	0.71041 ± 0.00513	11,020,865 ± 0.00000	414,831,744 ± 0.00000	175.04771 ± 5.54457
IGTD	0.40991 ± 0.03802	0.52349 ± 0.00403	3.14827 ± 2.10974	0.87271 ± 0.02464	0.79275 ± 0.00319	-8.96428 ± 11.03792	2,673,489 ± 0.00000	48,097,808 ± 0.00000	91.82369 ± 3.08409
REFINED	0.48096 ± 0.02209	0.59928 ± 0.00618	0.56371 ± 0.00368	0.82566 ± 0.01639	0.72838 ± 0.00559	0.76497 ± 0.00308	1,317,361 ± 0.00000	22,116,784 ± 0.00000	76.05887 ± 0.69582
DistanceMatrix	0.44172 ± 0.05716	0.58654 ± 0.01273	0.56900 ± 0.01700	0.85123 ± 0.03660	0.73974 ± 0.01141	0.76038 ± 0.01452	6,857,993 ± 0.00000	1,746,277,344 ± 0.00000	416.32115 ± 0.45420
BarGraph	0.75427 ± 0.00182	0.77748 ± 0.00095	0.75653 ± 0.00102	0.57194 ± 0.00206	0.54288 ± 0.00112	0.57670 ± 0.00115	26,209 ± 0.00000	981,248 ± 0.00000	70.14003 ± 0.61764
Combination	0.47767 ± 0.03061	0.56438 ± 0.00552	0.55096 ± 0.01109	0.82776 ± 0.02251	0.75910 ± 0.00472	0.77542 ± 0.00905	5,920,849 ± 0.00000	1,336,089,664 ± 0.00000	302.19510 ± 0.27329
SuperTML	0.01378 ± 0.00479	0.47443 ± 0.00373	0.45087 ± 0.00592	0.99984 ± 0.00012	0.82977 ± 0.00268	0.84963 ± 0.00397	10,645,233 ± 0.00000	2,931,292,480 ± 0.00000	1,031.57336 ± 17.72613
FeatureWrap	0.68080 ± 0.01616	0.69323 ± 0.00730	0.67850 ± 0.01115	0.65112 ± 0.01665	0.63655 ± 0.00764	0.65944 ± 0.01126	37,993 ± 0.00000	458,436 ± 0.00000	70.02285 ± 0.28436
BIE	0.02773 ± 0.01455	0.46976 ± 0.00469	0.44662 ± 0.00312	0.99929 ± 0.00063	0.83311 ± 0.00333	0.85247 ± 0.00205	9,703,809 ± 0.00000	11,479,253,760 ± 0.00000	1,412.74217 ± 1.22171

CNN + MLP

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
TINTO	0.42472 ± 0.00838	0.51350 ± 0.00796	0.50416 ± 0.00665	0.86423 ± 0.00541	0.80055 ± 0.00620	0.81198 ± 0.00498	10,725,505 ± 0.00000	414,241,120 ± 0.00000	175.60802 ± 2.91739
IGTD	0.38630 ± 0.03014	0.50047 ± 0.01254	1.42743 ± 0.59698	0.88718 ± 0.01817	0.81049 ± 0.00948	-0.71785 ± 1.50272	2,941,265 ± 0.00000	48,632,336 ± 0.00000	105.17529 ± 11.15271
REFINED	0.38848 ± 0.04257	0.53286 ± 0.00510	0.51555 ± 0.00643	0.88536 ± 0.02445	0.78526 ± 0.00413	0.80340 ± 0.00491	1,535,089 ± 0.00000	22,551,536 ± 0.00000	83.51049 ± 4.73300
DistanceMatrix	0.42044 ± 0.03069	0.49810 ± 0.00470	0.49232 ± 0.00715	0.86643 ± 0.01931	0.81236 ± 0.00353	0.82071 ± 0.00520	6,648,841 ± 0.00000	1,745,859,040 ± 0.00000	421.32265 ± 4.17418
BarGraph	0.43451 ± 0.00282	0.49357 ± 0.00311	0.48584 ± 0.00419	0.85794 ± 0.00184	0.81577 ± 0.00232	0.82541 ± 0.00302	326,273 ± 0.00000	45,517,184 ± 0.00000	158.89147 ± 1.23917
Combination	0.40111 ± 0.03899	0.50397 ± 0.00353	0.49452 ± 0.00943	0.87804 ± 0.02303	0.80792 ± 0.00269	0.81908 ± 0.00687	5,662,801 ± 0.00000	1,335,573,568 ± 0.00000	307.60273 ± 0.98531
SuperTML	0.06800 ± 0.02138	0.47212 ± 0.00471	0.44877 ± 0.00787	0.99625 ± 0.00236	0.83142 ± 0.00337	0.85101 ± 0.00523	10,748,017 ± 0.00000	2,931,497,536 ± 0.00000	1,041.1302 ± 6.74585
FeatureWrap	0.42977 ± 0.01018	0.50982 ± 0.00162	0.49455 ± 0.00228	0.86097 ± 0.00665	0.80344 ± 0.00125	0.81911 ± 0.00167	340,281 ± 0.00000	1,061,952 ± 0.00000	82.07914 ± 0.56705
BIE	0.04854 ± 0.02221	0.48339 ± 0.00198	0.45310 ± 0.00374	0.99793 ± 0.00203	0.82329 ± 0.00145	0.84815 ± 0.00252	10,430,465 ± 0.00000	11,480,705,536 ± 0.00000	1,423.09332 ± 1.15410

Geographical origin of music

Source: OpenML · Original

Leaderboard

Family	Best variant	Test RMSE	Test R²	Train time (s)	#Params	FLOPs
Trees	CatBoost	16.09875 ± 0.27347	0.28649 ± 0.02426	5.40574 ± 0.01840	—	—
MLP	MLP	16.82875 ± 0.58908	0.21974 ± 0.05508	6.15275 ± 0.54803	224,257 ± 0.00000	447,616 ± 0.00000
ViT	BarGraph	16.91933 ± 0.91566	0.21024 ± 0.08402	59.57013 ± 7.93472	6,900,631 ± 0.00000	223,482,786 ± 0.00000
ViT+MLP	Combination	16.10768 ± 0.12356	0.28583 ± 0.01098	52.62258 ± 1.54688	9,753,271 ± 0.00000	6,869,758,986 ± 603,446,815.89358
CNN	REFINED	15.02703 ± 0.62945	0.37760 ± 0.05210	17.44302 ± 0.11142	3,738,049 ± 0.00000	120,195,072 ± 0.00000
CNN+MLP	REFINED	15.29549 ± 0.55394	0.35539 ± 0.04664	18.31227 ± 0.12764	3,843,265 ± 0.00000	120,404,960 ± 0.00000

Architecture Results

Tree Baselines

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	Train time (s)	#Params	FLOPs
CatBoost	0.05557 ± 0.00772	16.06202 ± 0.18918	16.09875 ± 0.27347	0.99999 ± 0.00000	0.34184 ± 0.01551	0.28649 ± 0.02426	5.40574 ± 0.01840	—	—
LightGBM	0.16624 ± 0.03577	16.21642 ± 0.25397	16.98768 ± 0.27991	0.99991 ± 0.00004	0.32907 ± 0.02109	0.20553 ± 0.02620	0.28268 ± 0.01466	—	—
XGBoost	0.33621 ± 0.00319	16.37622 ± 0.32143	16.30701 ± 0.36834	0.99965 ± 0.00001	0.31570 ± 0.02669	0.26778 ± 0.03284	1.55595 ± 0.01979	—	—

MLP

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
MLP	10.69368 ± 1.91871	15.51013 ± 0.46948	16.82875 ± 0.58908	0.63755 ± 0.13473	0.38591 ± 0.03751	0.21974 ± 0.05508	224,257 ± 0.00000	447,616 ± 0.00000	6.15275 ± 0.54803

ViT

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
TINTO	13.70347 ± 2.51237	17.03049 ± 0.48423	18.52677 ± 0.28237	0.40415 ± 0.21213	0.25968 ± 0.04228	0.05509 ± 0.02876	5,811,351 ± 0.00000	190,865,164 ± 0.00000	46.01703 ± 4.92198
IGTD	4.38130 ± 2.75908	15.54277 ± 0.44909	17.99486 ± 0.78529	0.92187 ± 0.10129	0.38336 ± 0.03551	0.10737 ± 0.07837	18,975,257 ± 0.00000	187,320,724 ± 0.00000	98.01576 ± 3.22877
REFINED	12.73110 ± 3.20448	17.47121 ± 0.58240	17.68148 ± 0.54004	0.47380 ± 0.24188	0.22068 ± 0.05152	0.13886 ± 0.05282	4,072,967 ± 0.00000	1,237,334,920 ± 0.00000	50.97426 ± 1.32109
DistanceMatrix	11.53372 ± 2.91193	16.06591 ± 0.18580	17.57294 ± 0.84132	0.56799 ± 0.18100	0.34152 ± 0.01526	0.14847 ± 0.08357	24,509,305 ± 0.00000	228,074,320 ± 0.00000	51.79272 ± 2.42832
BarGraph	11.66409 ± 1.05832	17.42122 ± 0.35203	16.91933 ± 0.91566	0.57684 ± 0.07260	0.22557 ± 0.03103	0.21024 ± 0.08402	6,900,631 ± 0.00000	223,482,786 ± 0.00000	59.57013 ± 7.93472
Combination	11.55673 ± 2.67506	16.69437 ± 0.38998	17.58062 ± 1.12846	0.56962 ± 0.17848	0.28876 ± 0.03341	0.14649 ± 0.11207	9,560,503 ± 0.00000	314,769,189 ± 0.00000	43.79353 ± 0.88633
SuperTML	15.00412 ± 1.59699	19.24220 ± 0.30550	19.04030 ± 0.12776	0.29807 ± 0.14780	0.05533 ± 0.03011	0.00213 ± 0.01335	5,039,297 ± 0.00000	168,272,312 ± 0.00000	71.57072 ± 0.39260
FeatureWrap	15.36428 ± 0.55970	18.35840 ± 0.28669	18.77633 ± 0.23099	0.26981 ± 0.05265	0.14012 ± 0.02685	0.02952 ± 0.02381	2,223,271 ± 0.00000	22,210,476 ± 0.00000	32.03794 ± 0.18428
BIE	17.83038 ± 0.36524	19.74467 ± 0.09284	19.09284 ± 0.02706	0.01731 ± 0.04006	0.00553 ± 0.00933	-0.00335 ± 0.00284	20,250,457 ± 0.00000	190,315,952 ± 0.00000	50.08791 ± 1.41411

ViT + MLP

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
TINTO	11.27870 ± 0.31786	15.67644 ± 0.16878	16.16954 ± 0.32113	0.60668 ± 0.02228	0.37307 ± 0.01343	0.28014 ± 0.02850	5,800,087 ± 0.00000	1,888,211,296 ± 373,190,524.93865	45.43299 ± 1.59490
IGTD	11.49398 ± 1.82290	15.90038 ± 0.40134	17.39535 ± 0.77172	0.58357 ± 0.13235	0.35476 ± 0.03226	0.16581 ± 0.07515	19,047,193 ± 0.00000	2,692,426,912 ± 532,137,592.21586	54.17768 ± 0.81412
REFINED	10.88294 ± 0.70574	15.46777 ± 0.30883	16.18275 ± 0.41792	0.63280 ± 0.04735	0.38951 ± 0.02433	0.27881 ± 0.03704	4,107,015 ± 0.00000	22,952,799,504 ± 2,016,197,919.71731	41.30654 ± 0.10477
DistanceMatrix	10.69971 ± 1.13039	15.59085 ± 0.23527	16.26941 ± 0.43020	0.64309 ± 0.07573	0.37984 ± 0.01857	0.27105 ± 0.03890	23,906,425 ± 0.00000	3,014,266,752 ± 595,746,775.72737	55.16051 ± 0.52730
BarGraph	8.79557 ± 1.46960	15.62614 ± 0.41414	16.46694 ± 0.35351	0.75562 ± 0.08199	0.37679 ± 0.03272	0.25338 ± 0.03206	6,862,999 ± 0.00000	7,575,609,720 ± 427,788,953.20912	69.28047 ± 1.21371
Combination	12.21999 ± 1.18632	15.81405 ± 0.25097	16.10768 ± 0.12356	0.53511 ± 0.08945	0.36195 ± 0.02026	0.28583 ± 0.01098	9,753,271 ± 0.00000	6,869,758,986 ± 603,446,815.89358	52.62258 ± 1.54688
SuperTML	7.93616 ± 1.83935	15.33343 ± 0.54975	16.71844 ± 0.29170	0.79702 ± 0.09977	0.39964 ± 0.04318	0.23050 ± 0.02715	5,360,865 ± 0.00000	1,577,520,064 ± 311,784,778.55341	81.53160 ± 1.05610
FeatureWrap	9.21742 ± 0.92978	15.51625 ± 0.51796	16.67730 ± 0.72491	0.73534 ± 0.05056	0.38532 ± 0.04116	0.23331 ± 0.06575	2,517,607 ± 0.00000	731,278,872 ± 64,236,301.11885	41.72618 ± 1.19304
BIE	11.16109 ± 1.23325	15.92937 ± 0.75222	16.55521 ± 0.17354	0.61133 ± 0.08502	0.35158 ± 0.06225	0.24557 ± 0.01578	19,967,065 ± 0.00000	8,862,326,592 ± 500,448,882.12496	67.69650 ± 3.22348

CNN

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
TINTO	11.42706 ± 5.63796	17.50269 ± 0.46048	18.69147 ± 1.01999	0.51795 ± 0.33917	0.21813 ± 0.04067	0.03610 ± 0.10680	1,064,865 ± 0.00000	112,489,856 ± 0.00000	22.07763 ± 0.29004
IGTD	3.40363 ± 1.57712	15.76505 ± 0.74902	17.51502 ± 0.49999	0.95805 ± 0.03678	0.36488 ± 0.05951	0.15508 ± 0.04785	283,521 ± 0.00000	12,525,632 ± 0.00000	23.86034 ± 0.15064
REFINED	1.45952 ± 0.31864	15.26121 ± 0.31388	15.02703 ± 0.62945	0.99317 ± 0.00279	0.40569 ± 0.02440	0.37760 ± 0.05210	3,738,049 ± 0.00000	120,195,072 ± 0.00000	17.44302 ± 0.11142
DistanceMatrix	5.26771 ± 4.56349	15.72246 ± 0.50765	16.66954 ± 0.89513	0.86278 ± 0.18246	0.36891 ± 0.04026	0.23341 ± 0.08207	1,203,209 ± 0.00000	137,155,464 ± 0.00000	29.85507 ± 1.14905
BarGraph	5.41248 ± 4.20403	17.10003 ± 0.67535	17.98593 ± 0.71919	0.86579 ± 0.16321	0.25317 ± 0.05967	0.10848 ± 0.07187	86,545 ± 0.00000	90,185,728 ± 0.00000	28.58858 ± 0.19662
Combination	2.21433 ± 1.04818	15.95586 ± 0.17249	16.76053 ± 0.27255	0.98213 ± 0.01559	0.35052 ± 0.01405	0.22664 ± 0.02509	2,976,641 ± 0.00000	991,275,840 ± 0.00000	27.91533 ± 0.61218
SuperTML	14.58648 ± 1.90400	18.78454 ± 0.51314	19.16329 ± 0.47282	0.33360 ± 0.17012	0.09937 ± 0.04895	-0.01126 ± 0.04976	277,457 ± 0.00000	279,559,680 ± 0.00000	34.35937 ± 0.34717
FeatureWrap	15.37580 ± 1.24064	18.89610 ± 0.46891	19.02199 ± 0.44515	0.26569 ± 0.11599	0.08874 ± 0.04542	0.00364 ± 0.04705	36,769 ± 0.00000	3,266,144 ± 0.00000	13.14731 ± 0.89654
BIE	4.88207 ± 4.02859	19.64237 ± 0.61272	19.34129 ± 0.51306	0.88623 ± 0.13971	0.01506 ± 0.06071	-0.03021 ± 0.05498	19,046,097 ± 0.00000	1,580,752,896 ± 0.00000	38.22191 ± 0.87412

CNN + MLP

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
TINTO	10.11680 ± 2.57885	15.85264 ± 0.61112	17.19357 ± 0.86346	0.66731 ± 0.15259	0.35819 ± 0.04981	0.18469 ± 0.08119	1,354,913 ± 0.00000	113,068,800 ± 0.00000	24.04323 ± 0.43570
IGTD	3.37414 ± 3.68402	16.04367 ± 0.78891	17.85496 ± 0.89318	0.93127 ± 0.13106	0.34214 ± 0.06378	0.12078 ± 0.08993	505,473 ± 0.00000	12,968,736 ± 0.00000	23.35832 ± 0.13444
REFINED	3.90924 ± 2.74580	15.06717 ± 0.42406	15.29549 ± 0.55394	0.93414 ± 0.07172	0.42054 ± 0.03240	0.35539 ± 0.04664	3,843,265 ± 0.00000	120,404,960 ± 0.00000	18.31227 ± 0.12764
DistanceMatrix	2.46382 ± 1.43092	16.01207 ± 0.36239	16.19995 ± 0.35934	0.97618 ± 0.02643	0.34573 ± 0.02997	0.27738 ± 0.03198	1,472,777 ± 0.00000	137,693,672 ± 0.00000	30.08562 ± 0.68356
BarGraph	13.46694 ± 0.92622	17.15620 ± 0.49037	17.43264 ± 0.60262	0.43749 ± 0.07690	0.24870 ± 0.04300	0.16275 ± 0.05797	318,865 ± 0.00000	90,649,472 ± 0.00000	31.54327 ± 0.74361
Combination	2.69676 ± 0.48890	15.55850 ± 0.28827	16.38854 ± 0.14145	0.97694 ± 0.00809	0.38235 ± 0.02296	0.26070 ± 0.01276	3,013,761 ± 0.00000	991,349,664 ± 0.00000	28.90632 ± 1.47219
SuperTML	12.44674 ± 1.87392	16.39167 ± 0.44488	17.21217 ± 0.44550	0.51262 ± 0.14688	0.31422 ± 0.03778	0.18414 ± 0.04263	542,865 ± 0.00000	280,089,472 ± 0.00000	35.44523 ± 0.53667
FeatureWrap	11.59757 ± 3.70233	17.73740 ± 0.23283	18.04943 ± 0.44827	0.55051 ± 0.21409	0.19735 ± 0.02110	0.10287 ± 0.04485	257,745 ± 0.00000	3,707,280 ± 0.00000	13.81799 ± 1.11630
BIE	3.94150 ± 0.84846	18.73255 ± 0.55031	18.62305 ± 0.62363	0.95022 ± 0.01925	0.10427 ± 0.05202	0.04456 ± 0.06396	18,945,553 ± 0.00000	1,580,551,520 ± 0.00000	40.39863 ± 0.22127

Health insurance

Source: OpenML · Original

Leaderboard

Family	Best variant	Test RMSE	Test R²	Train time (s)	#Params	FLOPs
Trees	CatBoost	14.24579 ± 0.00935	0.41469 ± 0.00077	8.40559 ± 0.18532	—	—
MLP	MLP	14.41788 ± 0.05896	0.40045 ± 0.00491	23.59535 ± 0.16191	72,705 ± 0.00000	144,896 ± 0.00000
ViT	REFINED	14.31386 ± 0.04021	0.40908 ± 0.00332	112.10536 ± 6.41435	3,954,055 ± 0.00000	178,178,231 ± 0.00000
CNN	Combination	14.35479 ± 0.02489	0.40570 ± 0.00206	341.71894 ± 121.41553	14,729 ± 0.00000	30,507,467,000.4 ± 67,671,999,500.72966

Architecture Results

Tree Baselines

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	Train time (s)	#Params	FLOPs
CatBoost	14.00700 ± 0.01523	14.49204 ± 0.00387	14.24579 ± 0.00935	0.44059 ± 0.00122	0.40015 ± 0.00032	0.41469 ± 0.00077	8.40559 ± 0.18532	—	—
LightGBM	14.00577 ± 0.00000	14.50065 ± 0.00000	14.26687 ± 0.00000	0.44068 ± 0.00000	0.39944 ± 0.00000	0.41296 ± 0.00000	0.15978 ± 0.03133	—	—
XGBoost	13.96504 ± 0.00298	14.48740 ± 0.01172	14.25517 ± 0.00724	0.44393 ± 0.00024	0.40054 ± 0.00097	0.41392 ± 0.00060	0.66936 ± 0.03725	—	—

MLP

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
MLP	14.26401 ± 0.23963	14.66848 ± 0.04344	14.41788 ± 0.05896	0.41974 ± 0.01941	0.38545 ± 0.00364	0.40045 ± 0.00491	72,705 ± 0.00000	144,896 ± 0.00000	23.59535 ± 0.16191

ViT

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
TINTO	14.90667 ± 0.07405	14.99027 ± 0.02687	14.75547 ± 0.06309	0.36640 ± 0.00630	0.35820 ± 0.00230	0.37205 ± 0.00537	3,052,633 ± 0.00000	30,099,212 ± 0.00000	218.86890 ± 3.80415
IGTD	14.41499 ± 0.03905	14.74528 ± 0.05914	14.50579 ± 0.04380	0.40752 ± 0.00321	0.37900 ± 0.00498	0.39313 ± 0.00367	15,348,535 ± 0.00000	149,915,190 ± 0.00000	198.74354 ± 1.54255
REFINED	14.16646 ± 0.14277	14.56664 ± 0.07354	14.31386 ± 0.04021	0.42773 ± 0.01154	0.39395 ± 0.00613	0.40908 ± 0.00332	3,954,055 ± 0.00000	178,178,231 ± 0.00000	112.10536 ± 6.41435
DistanceMatrix	14.40996 ± 0.11359	14.64094 ± 0.06183	14.46737 ± 0.08837	0.40791 ± 0.00936	0.38775 ± 0.00518	0.39632 ± 0.00740	18,009,271 ± 0.00000	938,846,999 ± 0.00000	452.18137 ± 1.34062
BarGraph	14.29940 ± 0.07290	14.63614 ± 0.04308	14.36011 ± 0.01015	0.41697 ± 0.00595	0.38816 ± 0.00361	0.40526 ± 0.00084	17,784,983 ± 0.00000	901,498,431 ± 0.00000	463.53721 ± 1.41682
Combination	14.30616 ± 0.13358	14.59731 ± 0.01957	14.36827 ± 0.01376	0.41639 ± 0.01085	0.39141 ± 0.00163	0.40458 ± 0.00114	782,743 ± 0.00000	43,985,679 ± 0.00000	133.54671 ± 2.39014
SuperTML	14.32618 ± 0.09602	14.71468 ± 0.03609	14.43704 ± 0.03742	0.41478 ± 0.00783	0.38158 ± 0.00303	0.39887 ± 0.00312	1,228,673 ± 0.00000	128,519,616 ± 0.00000	849.08724 ± 16.28477
FeatureWrap	14.57555 ± 0.13783	14.90586 ± 0.03114	14.80843 ± 0.04887	0.39421 ± 0.01148	0.36540 ± 0.00265	0.36754 ± 0.00418	6,685,239 ± 0.00000	66,224,004 ± 0.00000	266.60863 ± 3.80443
BIE	14.34745 ± 0.16886	14.76377 ± 0.08510	14.56183 ± 0.08750	0.41300 ± 0.01387	0.37743 ± 0.00719	0.38841 ± 0.00736	2,595,745 ± 0.00000	25,652,424 ± 0.00000	296.86140 ± 3.08840

ViT + MLP

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
TINTO	—	—	—	—	—	—	—	—	—
IGTD	—	—	—	—	—	—	—	—	—
REFINED	—	—	—	—	—	—	—	—	—
DistanceMatrix	—	—	—	—	—	—	—	—	—
BarGraph	—	—	—	—	—	—	—	—	—
Combination	—	—	—	—	—	—	—	—	—
SuperTML	—	—	—	—	—	—	—	—	—
FeatureWrap	14.64419 ± 0.06402	14.92097 ± 0.05659	14.77694 ± 0.02616	0.38852 ± 0.00534	0.36411 ± 0.00482	0.37023 ± 0.00223	6,660,407 ± 0.00000	359,965,332,836 ± 793,197,824,645.23132	595.82048 ± 170.82780
BIE	14.06634 ± 0.42315	14.69208 ± 0.13668	14.46670 ± 0.09874	0.43543 ± 0.03352	0.38344 ± 0.01153	0.39637 ± 0.00826	2,781,441 ± 0.00000	113,740,118,660.8 ± 252,604,596,884.66263	673.43974 ± 153.13924

CNN

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
TINTO	14.20966 ± 0.12760	15.13582 ± 0.06853	14.90585 ± 0.06573	0.42424 ± 0.01037	0.34566 ± 0.00593	0.35918 ± 0.00566	137,193 ± 0.00000	97,100,106,840 ± 177,334,897,633.34714	273.75396 ± 91.47594
IGTD	14.07675 ± 0.56979	14.87647 ± 0.16764	14.77837 ± 0.23073	0.43426 ± 0.04490	0.36784 ± 0.01431	0.36999 ± 0.01973	379,921 ± 0.00000	23,514,255,340.8 ± 39,895,887,557.08404	310.17038 ± 109.96476
REFINED	14.20569 ± 0.26736	14.67801 ± 0.05755	14.42321 ± 0.06496	0.42444 ± 0.02152	0.38465 ± 0.00482	0.40001 ± 0.00541	22,721 ± 0.00000	2,127,251,420.8 ± 4,727,825,965.72182	287.14075 ± 106.06291
DistanceMatrix	14.07601 ± 0.31802	14.60251 ± 0.10019	14.37632 ± 0.06409	0.43483 ± 0.02523	0.39095 ± 0.00839	0.40391 ± 0.00532	1,306,657 ± 0.00000	1,648,572,144,089.6001 ± 2,860,193,866,394.75586	334.61430 ± 103.91823
BarGraph	14.37006 ± 0.07627	14.58942 ± 0.03359	14.35670 ± 0.03626	0.41120 ± 0.00626	0.39206 ± 0.00280	0.40554 ± 0.00301	5,417,457 ± 0.00000	1,405,065,174,595.19995 ± 3,112,648,869,247.36816	363.45893 ± 112.02614
Combination	14.28038 ± 0.06160	14.55864 ± 0.02904	14.35479 ± 0.02489	0.41853 ± 0.00501	0.39462 ± 0.00242	0.40570 ± 0.00206	14,729 ± 0.00000	30,507,467,000.4 ± 67,671,999,500.72966	341.71894 ± 121.41553
SuperTML	14.33471 ± 0.19071	14.67737 ± 0.11701	14.42643 ± 0.11644	0.41402 ± 0.01563	0.38468 ± 0.00986	0.39972 ± 0.00974	750,369 ± 0.00000	25,645,956,761.6 ± 15,726,805,509.29922	2,389.29581 ± 172.56997
FeatureWrap	14.29496 ± 0.19934	14.77070 ± 0.07971	14.81967 ± 0.08522	0.41726 ± 0.01626	0.37685 ± 0.00673	0.36656 ± 0.00728	48,337 ± 0.00000	8,641,717,884.8 ± 19,182,581,167.87682	492.14608 ± 184.11893
BIE	14.15244 ± 0.24928	14.79987 ± 0.04575	14.61196 ± 0.12369	0.42877 ± 0.01999	0.37439 ± 0.00387	0.38418 ± 0.01047	754,089 ± 0.00000	11,105,391,678,592 ± 24,719,605,984,413.71484	656.42623 ± 130.46665

CNN + MLP

Method
TINTO
IGTD
REFINED
DistanceMatrix
BarGraph
Combination
SuperTML
FeatureWrap
BIE

Pumadyn32nh

Source: OpenML · Original

Leaderboard

Family	Best variant	Test RMSE	Test R²	Train time (s)	#Params	FLOPs
Trees	CatBoost	0.02097 ± 0.00004	0.64498 ± 0.00135	5.07097 ± 0.12914	—	—
MLP	MLP	0.02233 ± 0.00010	0.59719 ± 0.00354	41.73644 ± 1.80933	49,665 ± 0.00000	98,880 ± 0.00000
ViT	REFINED	0.02185 ± 0.00008	0.61439 ± 0.00293	304.25574 ± 0.63485	11,354,503 ± 0.00000	822,779,180 ± 0.00000
ViT+MLP	REFINED	0.02185 ± 0.00020	0.61426 ± 0.00709	398.67869 ± 6.59992	11,339,975 ± 0.00000	7,294,636,896 ± 1,441,729,205.9538
CNN	SuperTML	0.02224 ± 0.00041	0.60049 ± 0.01498	1,138.71236 ± 0.75749	771,937 ± 0.00000	4,259,639,040 ± 0.00000
CNN+MLP	SuperTML	0.02254 ± 0.00014	0.58974 ± 0.00515	1,138.98998 ± 1.20643	804,961 ± 0.00000	4,259,704,704 ± 0.00000

Architecture Results

Tree Baselines

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	Train time (s)	#Params	FLOPs
CatBoost	0.01582 ± 0.00001	0.02058 ± 0.00004	0.02097 ± 0.00004	0.80792 ± 0.00016	0.67418 ± 0.00133	0.64498 ± 0.00135	5.07097 ± 0.12914	—	—
LightGBM	0.01771 ± 0.00003	0.02110 ± 0.00008	0.02134 ± 0.00003	0.75918 ± 0.00093	0.65733 ± 0.00272	0.63231 ± 0.00098	0.36394 ± 0.02792	—	—
XGBoost	0.01904 ± 0.00001	0.02104 ± 0.00002	0.02126 ± 0.00002	0.72162 ± 0.00028	0.65953 ± 0.00064	0.63497 ± 0.00060	1.47681 ± 0.03719	—	—

MLP

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
MLP	0.01956 ± 0.00009	0.02224 ± 0.00014	0.02233 ± 0.00010	0.70639 ± 0.00267	0.61939 ± 0.00493	0.59719 ± 0.00354	49,665 ± 0.00000	98,880 ± 0.00000	41.73644 ± 1.80933

ViT

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
TINTO	0.02239 ± 0.00036	0.02379 ± 0.00016	0.02407 ± 0.00008	0.61512 ± 0.01237	0.56450 ± 0.00589	0.53201 ± 0.00329	16,600,153 ± 0.00000	164,288,418 ± 0.00000	403.39934 ± 3.78837
IGTD	0.02482 ± 0.00133	0.02770 ± 0.00030	0.02836 ± 0.00012	0.52603 ± 0.05134	0.40978 ± 0.01275	0.35032 ± 0.00563	4,321,335 ± 0.00000	42,443,564 ± 0.00000	298.27538 ± 0.24385
REFINED	0.02113 ± 0.00029	0.02070 ± 0.00007	0.02185 ± 0.00008	0.65733 ± 0.00941	0.67046 ± 0.00238	0.61439 ± 0.00293	11,354,503 ± 0.00000	822,779,180 ± 0.00000	304.25574 ± 0.63485
DistanceMatrix	0.02414 ± 0.00072	0.02530 ± 0.00017	0.02587 ± 0.00028	0.55231 ± 0.02681	0.50772 ± 0.00673	0.45924 ± 0.01147	8,211,585 ± 0.00000	80,177,580 ± 0.00000	282.84231 ± 3.23933
BarGraph	0.02085 ± 0.00079	0.02169 ± 0.00052	0.02230 ± 0.00037	0.66587 ± 0.02565	0.63775 ± 0.01732	0.59840 ± 0.01328	8,346,497 ± 0.00000	81,331,920 ± 0.00000	343.30284 ± 29.30881
Combination	0.02088 ± 0.00063	0.02171 ± 0.00023	0.02256 ± 0.00027	0.66521 ± 0.02014	0.63735 ± 0.00778	0.58878 ± 0.00972	10,981,729 ± 0.00000	1,424,588,196 ± 0.00000	324.80838 ± 2.57464
SuperTML	0.02144 ± 0.00066	0.02119 ± 0.00027	0.02193 ± 0.00026	0.64674 ± 0.02186	0.65439 ± 0.00891	0.61166 ± 0.00933	975,649 ± 0.00000	510,261,742 ± 0.00000	359.72687 ± 6.97145
FeatureWrap	0.03487 ± 0.00010	0.03497 ± 0.00012	0.03410 ± 0.00008	0.06663 ± 0.00532	0.05901 ± 0.00618	0.06103 ± 0.00457	8,319,777 ± 0.00000	79,884,240 ± 0.00000	351.17434 ± 18.46822
BIE	0.02300 ± 0.00170	0.02463 ± 0.00178	0.02457 ± 0.00168	0.59212 ± 0.05938	0.53127 ± 0.06789	0.51071 ± 0.06812	8,493,217 ± 0.00000	285,350,020 ± 0.00000	402.58314 ± 10.93166

ViT + MLP

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
TINTO	0.01967 ± 0.00079	0.02241 ± 0.00012	0.02271 ± 0.00025	0.70245 ± 0.02377	0.61350 ± 0.00409	0.58337 ± 0.00929	16,585,497 ± 0.00000	2,359,058,576 ± 466,249,889.61959	948.19912 ± 16.09877
IGTD	0.02233 ± 0.00167	0.02336 ± 0.00105	0.02336 ± 0.00095	0.61561 ± 0.05807	0.57953 ± 0.03789	0.55871 ± 0.03576	4,273,463 ± 0.00000	609,931,104 ± 120,548,219.02632	378.72084 ± 15.63163
REFINED	0.02141 ± 0.00023	0.02070 ± 0.00010	0.02185 ± 0.00020	0.64801 ± 0.00749	0.67034 ± 0.00307	0.61426 ± 0.00709	11,339,975 ± 0.00000	7,294,636,896 ± 1,441,729,205.9538	398.67869 ± 6.59992
DistanceMatrix	0.01958 ± 0.00134	0.02227 ± 0.00018	0.02290 ± 0.00034	0.70462 ± 0.04016	0.61833 ± 0.00600	0.57650 ± 0.01266	8,154,241 ± 0.00000	1,138,069,728 ± 224,930,779.78552	366.64496 ± 20.56310
BarGraph	0.02113 ± 0.00039	0.02184 ± 0.00050	0.02263 ± 0.00036	0.65709 ± 0.01279	0.63282 ± 0.01687	0.58627 ± 0.01301	8,389,249 ± 0.00000	1,154,515,072 ± 228,181,076.28208	392.98477 ± 25.46348
Combination	0.02009 ± 0.00028	0.02126 ± 0.00009	0.02219 ± 0.00022	0.68993 ± 0.00857	0.65237 ± 0.00307	0.60229 ± 0.00784	10,917,793 ± 0.00000	12,113,008,160 ± 2,394,043,443.86283	402.76591 ± 31.83774
SuperTML	0.02055 ± 0.00065	0.02129 ± 0.00033	0.02191 ± 0.00034	0.67545 ± 0.02058	0.65114 ± 0.01092	0.61229 ± 0.01194	1,094,049 ± 0.00000	4,183,851,632 ± 826,906,284.33329	427.94311 ± 6.77084
FeatureWrap	0.02040 ± 0.00095	0.02279 ± 0.00010	0.02311 ± 0.00034	0.67989 ± 0.02992	0.60037 ± 0.00334	0.56848 ± 0.01276	8,058,593 ± 0.00000	1,139,654,272 ± 225,243,952.79132	409.11364 ± 16.84657
BIE	0.01961 ± 0.00120	0.02249 ± 0.00026	0.02258 ± 0.00047	0.70390 ± 0.03674	0.61072 ± 0.00903	0.58824 ± 0.01728	8,488,993 ± 0.00000	2,808,225,440 ± 555,024,285.85178	595.30145 ± 45.64617

CNN

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
TINTO	0.02170 ± 0.00068	0.02352 ± 0.00042	0.02431 ± 0.00084	0.63807 ± 0.02244	0.57441 ± 0.01520	0.52221 ± 0.03371	146,025 ± 0.00000	14,930,400 ± 0.00000	113.59447 ± 1.40437
IGTD	0.01990 ± 0.00137	0.02332 ± 0.00033	0.02404 ± 0.00027	0.69484 ± 0.04167	0.58135 ± 0.01186	0.53323 ± 0.01056	138,633 ± 0.00000	2,665,296 ± 0.00000	112.16792 ± 0.77712
REFINED	0.02033 ± 0.00044	0.02318 ± 0.00033	0.02404 ± 0.00089	0.68265 ± 0.01382	0.58668 ± 0.01185	0.53295 ± 0.03513	26,873 ± 0.00000	500,232 ± 0.00000	115.67679 ± 1.13143
DistanceMatrix	0.02227 ± 0.00095	0.02396 ± 0.00037	0.02471 ± 0.00054	0.61870 ± 0.03258	0.55838 ± 0.01347	0.50689 ± 0.02142	27,409 ± 0.00000	19,190,864 ± 0.00000	105.71885 ± 1.76016
BarGraph	0.01696 ± 0.00854	0.02249 ± 0.00061	0.02293 ± 0.00052	0.73433 ± 0.14888	0.61052 ± 0.02149	0.57509 ± 0.01944	6,591,201 ± 0.00000	648,924,672 ± 0.00000	182.02909 ± 4.87026
Combination	0.01703 ± 0.00843	0.02246 ± 0.00060	0.02320 ± 0.00070	0.73364 ± 0.14886	0.61179 ± 0.02081	0.56505 ± 0.02604	6,481,505 ± 0.00000	1,785,374,208 ± 0.00000	169.32325 ± 1.95742
SuperTML	0.02107 ± 0.00133	0.02146 ± 0.00023	0.02224 ± 0.00041	0.65795 ± 0.04197	0.64574 ± 0.00779	0.60049 ± 0.01498	771,937 ± 0.00000	4,259,639,040 ± 0.00000	1,138.71236 ± 0.75749
FeatureWrap	0.03429 ± 0.00082	0.03542 ± 0.00029	0.03464 ± 0.00027	0.09673 ± 0.04388	0.03468 ± 0.01560	0.03080 ± 0.01532	1,674,129 ± 0.00000	30,998,352 ± 0.00000	115.27792 ± 0.29258
BIE	0.00158 ± 0.00113	0.02676 ± 0.00054	0.02643 ± 0.00023	0.99730 ± 0.00392	0.44873 ± 0.02236	0.43585 ± 0.00987	417,041 ± 0.00000	133,454,208 ± 0.00000	333.18199 ± 12.26761

CNN + MLP

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
TINTO	0.02153 ± 0.00058	0.02305 ± 0.00021	0.02410 ± 0.00019	0.64403 ± 0.01900	0.59111 ± 0.00751	0.53085 ± 0.00756	183,209 ± 0.00000	15,004,432 ± 0.00000	138.96872 ± 8.46889
IGTD	0.02082 ± 0.00071	0.02283 ± 0.00045	0.02352 ± 0.00037	0.66693 ± 0.02229	0.59900 ± 0.01596	0.55299 ± 0.01415	253,529 ± 0.00000	2,894,352 ± 0.00000	225.15165 ± 38.38193
REFINED	0.02077 ± 0.00109	0.02244 ± 0.00057	0.02337 ± 0.00059	0.66801 ± 0.03549	0.61247 ± 0.01998	0.55876 ± 0.02209	129,881 ± 0.00000	705,488 ± 0.00000	235.78252 ± 48.03677
DistanceMatrix	0.02025 ± 0.00099	0.02334 ± 0.00019	0.02381 ± 0.00021	0.68442 ± 0.03115	0.58096 ± 0.00682	0.54196 ± 0.00821	84,241 ± 0.00000	19,304,016 ± 0.00000	141.11054 ± 2.98111
BarGraph	0.01396 ± 0.00919	0.02259 ± 0.00019	0.02326 ± 0.00039	0.79843 ± 0.17347	0.60745 ± 0.00670	0.56282 ± 0.01456	6,500,897 ± 0.00000	648,743,936 ± 0.00000	205.01951 ± 3.11489
Combination	0.02097 ± 0.00084	0.02217 ± 0.00051	0.02301 ± 0.00068	0.66205 ± 0.02684	0.62169 ± 0.01732	0.57206 ± 0.02532	6,266,401 ± 0.00000	1,784,944,208 ± 0.00000	188.25400 ± 4.97836
SuperTML	0.02049 ± 0.00099	0.02190 ± 0.00031	0.02254 ± 0.00014	0.67709 ± 0.03193	0.63105 ± 0.01051	0.58974 ± 0.00515	804,961 ± 0.00000	4,259,704,704 ± 0.00000	1,138.98998 ± 1.20643
FeatureWrap	0.02190 ± 0.00072	0.02484 ± 0.00053	0.02482 ± 0.00064	0.63140 ± 0.02422	0.52515 ± 0.02016	0.50201 ± 0.02569	1,726,161 ± 0.00000	31,101,984 ± 0.00000	121.36724 ± 0.28997
BIE	0.01741 ± 0.00180	0.02867 ± 0.00206	0.02894 ± 0.00189	0.76523 ± 0.04553	0.36506 ± 0.09236	0.32103 ± 0.08978	460,337 ± 0.00000	133,540,448 ± 0.00000	177.56438 ± 2.37141

Student performance por

Source: OpenML · Original

Leaderboard

Family	Best variant	Test RMSE	Test R²	Train time (s)	#Params	FLOPs
Trees	LightGBM	2.07327 ± 0.01229	0.24692 ± 0.00894	0.06854 ± 0.00324	—	—
MLP	MLP	2.09287 ± 0.08028	0.23174 ± 0.05981	3.05389 ± 0.51833	292,353 ± 0.00000	583,680 ± 0.00000
ViT	REFINED	2.13202 ± 0.06906	0.20300 ± 0.05223	19.78263 ± 0.04077	8,970,759 ± 0.00000	1,111,201,232 ± 0.00000
ViT+MLP	REFINED	2.00620 ± 0.02164	0.29482 ± 0.01526	24.76651 ± 0.31276	8,878,343 ± 0.00000	33,044,561,088 ± 1,866,001,380.69021
CNN	IGTD	2.08120 ± 0.15865	0.23765 ± 0.12046	8.71615 ± 0.05789	824,241 ± 0.00000	12,292,800 ± 0.00000
CNN+MLP	REFINED	2.03476 ± 0.06501	0.27407 ± 0.04684	20.00194 ± 0.48703	6,591,281 ± 0.00000	730,020,896 ± 0.00000

Architecture Results

Tree Baselines

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	Train time (s)	#Params	FLOPs
CatBoost	2.14322 ± 0.04256	2.61678 ± 0.00698	2.08151 ± 0.00951	0.60506 ± 0.01581	0.27242 ± 0.00387	0.24094 ± 0.00693	12.64899 ± 0.14024	—	—
LightGBM	2.68989 ± 0.00442	2.62963 ± 0.01526	2.07327 ± 0.01229	0.37808 ± 0.00204	0.26524 ± 0.00852	0.24692 ± 0.00894	0.06854 ± 0.00324	—	—
XGBoost	2.59119 ± 0.00514	2.60717 ± 0.00659	2.07417 ± 0.01860	0.42289 ± 0.00229	0.27775 ± 0.00365	0.24625 ± 0.01354	0.15527 ± 0.00400	—	—

MLP

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
MLP	2.20826 ± 0.92555	2.75390 ± 0.02522	2.09287 ± 0.08028	0.52195 ± 0.31138	0.19412 ± 0.01477	0.23174 ± 0.05981	292,353 ± 0.00000	583,680 ± 0.00000	3.05389 ± 0.51833

ViT

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
TINTO	2.93695 ± 0.05031	2.59890 ± 0.05789	2.23585 ± 0.02876	0.25842 ± 0.02535	0.28205 ± 0.03202	0.12409 ± 0.02259	903,703 ± 0.00000	29,203,002 ± 0.00000	18.44586 ± 0.19326
IGTD	2.81884 ± 0.16402	2.77916 ± 0.02253	2.28951 ± 0.07894	0.31518 ± 0.07729	0.17928 ± 0.01333	0.08080 ± 0.06307	2,774,881 ± 0.00000	27,840,536 ± 0.00000	11.72688 ± 0.10983
REFINED	2.88697 ± 0.08463	2.64711 ± 0.04207	2.13202 ± 0.06906	0.28312 ± 0.04193	0.25531 ± 0.02359	0.20300 ± 0.05223	8,970,759 ± 0.00000	1,111,201,232 ± 0.00000	19.78263 ± 0.04077
DistanceMatrix	2.64166 ± 0.17059	2.76243 ± 0.02828	2.15614 ± 0.07647	0.39819 ± 0.07808	0.18911 ± 0.01656	0.18473 ± 0.05856	17,054,305 ± 0.00000	1,703,980,720 ± 0.00000	32.18724 ± 0.15245
BarGraph	2.75222 ± 0.17286	2.65312 ± 0.05940	2.25989 ± 0.12131	0.34687 ± 0.07891	0.25177 ± 0.03342	0.10322 ± 0.09584	1,216,353 ± 0.00000	459,910,052 ± 0.00000	12.96350 ± 0.18219
Combination	2.80817 ± 0.11109	2.69432 ± 0.05642	2.21138 ± 0.12874	0.32134 ± 0.05331	0.22840 ± 0.03260	0.14096 ± 0.09914	4,855,105 ± 0.00000	456,591,504 ± 0.00000	14.19763 ± 0.12567
SuperTML	2.84375 ± 0.12419	2.69306 ± 0.06959	2.22813 ± 0.13748	0.30384 ± 0.06039	0.22898 ± 0.04003	0.12760 ± 0.11153	1,753,089 ± 0.00000	55,688,968 ± 0.00000	18.68712 ± 0.78474
FeatureWrap	3.05272 ± 0.12647	2.81339 ± 0.16254	2.26426 ± 0.03637	0.19789 ± 0.06629	0.15674 ± 0.09718	0.10163 ± 0.02890	22,093,623 ± 0.00000	442,033,759 ± 0.00000	40.14556 ± 4.76981
BIE	2.83558 ± 0.10440	2.70644 ± 0.05184	2.32541 ± 0.10244	0.30814 ± 0.05019	0.22148 ± 0.02998	0.05117 ± 0.08415	22,192,513 ± 0.00000	2,904,925,784 ± 0.00000	50.89112 ± 0.34698

ViT + MLP

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
TINTO	0.84497 ± 0.29635	2.67168 ± 0.04201	2.22408 ± 0.13201	0.93259 ± 0.04116	0.24142 ± 0.02398	0.13097 ± 0.10137	1,360,151 ± 0.00000	293,072,208 ± 57,923,481.01091	22.41009 ± 0.33038
IGTD	2.83420 ± 0.05077	2.75004 ± 0.03526	2.04088 ± 0.02291	0.30939 ± 0.02468	0.19633 ± 0.02060	0.27022 ± 0.01646	3,116,769 ± 0.00000	914,998,320 ± 80,374,409.62299	16.02527 ± 0.26102
REFINED	2.69505 ± 0.07157	2.68977 ± 0.03813	2.00620 ± 0.02164	0.37534 ± 0.03303	0.23114 ± 0.02191	0.29482 ± 0.01526	8,878,343 ± 0.00000	33,044,561,088 ± 1,866,001,380.69021	24.76651 ± 0.31276
DistanceMatrix	2.75605 ± 0.09744	2.77058 ± 0.05214	2.06605 ± 0.03636	0.34646 ± 0.04672	0.18415 ± 0.03092	0.25200 ± 0.02656	17,145,249 ± 0.00000	14,740,056,064 ± 2,913,259,375.05104	38.64666 ± 0.90085
BarGraph	2.78466 ± 0.08357	2.74530 ± 0.03297	2.04117 ± 0.01500	0.33301 ± 0.03986	0.19911 ± 0.01920	0.27005 ± 0.01072	1,436,097 ± 0.00000	17,873,390,744 ± 743,692,424.48962	18.48115 ± 0.51367
Combination	1.36122 ± 0.28026	2.68793 ± 0.03098	2.15356 ± 0.06181	0.83534 ± 0.07353	0.23224 ± 0.01782	0.18696 ± 0.04625	4,862,817 ± 0.00000	8,873,642,016 ± 779,469,997.54245	18.95864 ± 0.27732
SuperTML	2.67008 ± 0.10342	2.70077 ± 0.07558	2.06424 ± 0.05476	0.38647 ± 0.04665	0.22448 ± 0.04331	0.25307 ± 0.03928	2,078,081 ± 0.00000	1,683,872,736 ± 95,087,020.27892	21.70629 ± 1.15053
FeatureWrap	0.58956 ± 0.13245	2.68276 ± 0.05475	2.18022 ± 0.09262	0.96892 ± 0.01377	0.23502 ± 0.03111	0.16605 ± 0.06917	22,633,079 ± 0.00000	23,547,780,378 ± 979,797,629.41975	53.58027 ± 1.19315
BIE	2.71706 ± 0.11849	2.71004 ± 0.02256	2.10730 ± 0.07137	0.36449 ± 0.05558	0.21960 ± 0.01297	0.22131 ± 0.05285	22,625,345 ± 0.00000	24,682,275,008 ± 4,878,262,928.74567	57.14752 ± 1.44125

CNN

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
TINTO	2.71646 ± 0.07432	2.87997 ± 0.07242	2.20393 ± 0.05426	0.36536 ± 0.03457	0.11826 ± 0.04422	0.14863 ± 0.04235	44,137 ± 0.00000	9,609,200 ± 0.00000	9.40622 ± 0.28257
IGTD	2.14493 ± 0.79970	2.77638 ± 0.04811	2.08120 ± 0.15865	0.56058 ± 0.22509	0.18077 ± 0.02852	0.23765 ± 0.12046	824,241 ± 0.00000	12,292,800 ± 0.00000	8.71615 ± 0.05789
REFINED	0.51366 ± 0.57277	2.77123 ± 0.05204	2.13354 ± 0.11906	0.95476 ± 0.08806	0.18377 ± 0.03098	0.20055 ± 0.09002	6,492,657 ± 0.00000	66,168,768 ± 0.00000	14.35458 ± 0.06314
DistanceMatrix	0.39893 ± 0.31522	2.71516 ± 0.02309	2.12103 ± 0.06746	0.97949 ± 0.03148	0.21664 ± 0.01334	0.21121 ± 0.05013	1,405,713 ± 0.00000	487,848,704 ± 0.00000	24.99695 ± 0.21563
BarGraph	2.66685 ± 0.27506	2.85222 ± 0.06208	2.32736 ± 0.10340	0.38349 ± 0.13369	0.13528 ± 0.03775	0.04956 ± 0.08450	668,033 ± 0.00000	184,843,344 ± 0.00000	20.30143 ± 0.14342
Combination	2.18546 ± 0.55208	2.84263 ± 0.09573	2.21374 ± 0.12857	0.56851 ± 0.17633	0.14063 ± 0.05734	0.13913 ± 0.09999	1,710,385 ± 0.00000	1,457,369,280 ± 0.00000	16.30842 ± 0.07185
SuperTML	2.74824 ± 0.13166	2.78930 ± 0.05693	2.25473 ± 0.07110	0.34962 ± 0.06269	0.17305 ± 0.03400	0.10865 ± 0.05721	319,761 ± 0.00000	310,244,736 ± 0.00000	19.47898 ± 0.36295
FeatureWrap	2.43107 ± 0.45570	3.04510 ± 0.10817	2.58094 ± 0.12282	0.47773 ± 0.19317	0.01375 ± 0.07003	-0.16911 ± 0.11451	3,067,097 ± 0.00000	63,097,992 ± 0.00000	23.04521 ± 0.18939
BIE	1.87327 ± 1.04213	2.77007 ± 0.08068	2.30823 ± 0.17893	0.62370 ± 0.27079	0.18413 ± 0.04725	0.06211 ± 0.14743	2,692,721 ± 0.00000	256,454,400 ± 0.00000	21.22984 ± 1.06166

CNN + MLP

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
TINTO	2.62500 ± 0.28240	2.72197 ± 0.02301	2.10339 ± 0.05933	0.40224 ± 0.11990	0.21271 ± 0.01334	0.22442 ± 0.04448	537,033 ± 0.00000	116,529,336 ± 0.00000	12.84134 ± 0.07940
IGTD	1.54520 ± 0.77944	2.67039 ± 0.04854	2.16746 ± 0.10360	0.75300 ± 0.18841	0.24211 ± 0.02748	0.17547 ± 0.07799	1,066,417 ± 0.00000	140,541,632 ± 0.00000	12.30086 ± 0.17006
REFINED	0.50965 ± 0.32211	2.72013 ± 0.02272	2.03476 ± 0.06501	0.97054 ± 0.03899	0.21377 ± 0.01316	0.27407 ± 0.04684	6,591,281 ± 0.00000	730,020,896 ± 0.00000	20.00194 ± 0.48703
DistanceMatrix	1.79537 ± 0.91277	2.82054 ± 0.05529	2.20535 ± 0.11973	0.66565 ± 0.26016	0.15444 ± 0.03341	0.14593 ± 0.09290	1,836,817 ± 0.00000	488,709,824 ± 0.00000	27.69409 ± 1.14331
BarGraph	1.08430 ± 0.10465	2.70800 ± 0.09488	2.09846 ± 0.08224	0.89819 ± 0.01955	0.22005 ± 0.05495	0.22759 ± 0.06083	1,040,449 ± 0.00000	2,041,457,440 ± 0.00000	30.53304 ± 1.71425
Combination	1.06648 ± 0.58434	2.78186 ± 0.05249	2.21351 ± 0.13429	0.87876 ± 0.13340	0.17750 ± 0.03113	0.13910 ± 0.10258	1,969,073 ± 0.00000	1,457,885,888 ± 0.00000	18.47078 ± 0.45905
SuperTML	2.71874 ± 0.06915	2.73325 ± 0.02812	2.05940 ± 0.01953	0.36434 ± 0.03263	0.20615 ± 0.01637	0.25693 ± 0.01407	656,721 ± 0.00000	310,917,504 ± 0.00000	21.61322 ± 0.57559
FeatureWrap	1.61312 ± 0.65180	2.76541 ± 0.05730	2.08629 ± 0.08131	0.74712 ± 0.17348	0.18715 ± 0.03383	0.23653 ± 0.05844	3,502,169 ± 0.00000	63,967,080 ± 0.00000	24.74905 ± 0.23222
BIE	1.02344 ± 0.60519	2.78509 ± 0.03986	2.30793 ± 0.04552	0.88478 ± 0.09724	0.17568 ± 0.02354	0.06655 ± 0.03657	3,000,625 ± 0.00000	257,069,440 ± 0.00000	21.66396 ± 0.61913

Superconductivity

Source: OpenML · Original

Leaderboard

Family	Best variant	Test RMSE	Test R²	Train time (s)	#Params	FLOPs
Trees	XGBoost	9.39012 ± 0.01083	0.92444 ± 0.00017	14.42918 ± 0.71470	—	—
MLP	MLP	13.02278 ± 0.08713	0.85467 ± 0.00195	38.31988 ± 0.27649	206,337 ± 0.00000	411,776 ± 0.00000
ViT	Combination	9.85932 ± 0.03877	0.91670 ± 0.00065	1,081.16444 ± 256.86060	13,374,487 ± 0.00000	585,567,985,104.19995 ± 1,302,618,243,023.18262
CNN	TINTO	9.48401 ± 0.05426	0.92292 ± 0.00088	577.38758 ± 197.83984	10,741,857 ± 0.00000	710,159,859,724.80005 ± 1,271,392,566,165.7981

Architecture Results

Tree Baselines

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	Train time (s)	#Params	FLOPs
CatBoost	4.53931 ± 0.01369	9.27537 ± 0.06568	9.50490 ± 0.06107	0.98249 ± 0.00011	0.92601 ± 0.00105	0.92258 ± 0.00100	35.48475 ± 0.25031	—	—
LightGBM	5.75896 ± 0.03346	9.46416 ± 0.07228	9.78001 ± 0.12346	0.97182 ± 0.00033	0.92297 ± 0.00117	0.91803 ± 0.00207	1.28021 ± 0.04398	—	—
XGBoost	4.83724 ± 0.01133	9.06668 ± 0.03218	9.39012 ± 0.01083	0.98012 ± 0.00009	0.92931 ± 0.00050	0.92444 ± 0.00017	14.42918 ± 0.71470	—	—

MLP

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
MLP	12.18590 ± 0.07631	12.35558 ± 0.05771	13.02278 ± 0.08713	0.87381 ± 0.00158	0.86872 ± 0.00123	0.85467 ± 0.00195	206,337 ± 0.00000	411,776 ± 0.00000	38.31988 ± 0.27649

ViT

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
TINTO	7.42554 ± 0.13475	10.17726 ± 0.06878	10.23188 ± 0.14155	0.95313 ± 0.00171	0.91092 ± 0.00120	0.91028 ± 0.00247	11,288,857 ± 0.00000	106,213,732 ± 0.00000	424.71950 ± 6.58643
IGTD	7.20714 ± 0.10199	9.98521 ± 0.11446	10.02393 ± 0.11961	0.95585 ± 0.00124	0.91425 ± 0.00197	0.91389 ± 0.00206	3,641,431 ± 0.00000	35,974,944 ± 0.00000	490.10305 ± 2.71046
REFINED	6.81035 ± 0.43307	9.98932 ± 0.18200	10.14475 ± 0.17488	0.96046 ± 0.00519	0.91417 ± 0.00313	0.91179 ± 0.00305	3,035,031 ± 0.00000	59,100,759 ± 0.00000	228.89744 ± 8.49279
DistanceMatrix	6.56761 ± 0.30220	9.79910 ± 0.15459	9.91098 ± 0.08857	0.96328 ± 0.00343	0.91741 ± 0.00260	0.91582 ± 0.00150	20,136,423 ± 0.00000	20,714,923,423,581.60156 ± 43,332,096,532,550.5625	1,470.66296 ± 6.31309
BarGraph	6.14691 ± 0.09702	9.60107 ± 0.15526	9.95331 ± 0.12401	0.96789 ± 0.00102	0.92071 ± 0.00257	0.91510 ± 0.00211	21,098,263 ± 0.00000	400,874,159 ± 0.00000	637.27321 ± 1.90689
Combination	6.14398 ± 0.14685	9.41024 ± 0.04133	9.85932 ± 0.03877	0.96791 ± 0.00155	0.92385 ± 0.00067	0.91670 ± 0.00065	13,374,487 ± 0.00000	585,567,985,104.19995 ± 1,302,618,243,023.18262	1,081.16444 ± 256.86060
SuperTML	4.55318 ± 0.38427	10.55164 ± 0.18643	10.95439 ± 0.18499	0.98228 ± 0.00301	0.90423 ± 0.00340	0.89715 ± 0.00349	13,033,665 ± 0.00000	413,926,829,673.59998 ± 907,899,654,168.94824	3,195.55674 ± 161.28588
FeatureWrap	12.76631 ± 0.43769	16.11097 ± 0.41295	20.59555 ± 1.42934	0.86138 ± 0.00966	0.77667 ± 0.01144	0.63513 ± 0.05126	26,463,961 ± 0.00000	820,659,602,644.80005 ± 1,828,045,572,040.96899	951.38445 ± 310.15833
BIE	4.29548 ± 0.22002	10.70148 ± 0.08250	11.03662 ± 0.22029	0.98429 ± 0.00162	0.90151 ± 0.00152	0.89559 ± 0.00420	35,879,911 ± 0.00000	27,587,790,024,715.39844 ± 61,453,258,210,193.89844	2,437.28664 ± 6.34257

ViT + MLP

Method
TINTO
IGTD
REFINED
DistanceMatrix
BarGraph
Combination
SuperTML
FeatureWrap
BIE

CNN

Method	Train RMSE	Val RMSE	Test RMSE	Train R²	Val R²	Test R²	#Params	FLOPs	Train time (s)
TINTO	6.26595 ± 0.15267	9.62326 ± 0.07660	9.48401 ± 0.05426	0.96662 ± 0.00165	0.92036 ± 0.00127	0.92292 ± 0.00088	10,741,857 ± 0.00000	710,159,859,724.80005 ± 1,271,392,566,165.7981	577.38758 ± 197.83984
IGTD	6.19039 ± 0.22334	9.61344 ± 0.14718	9.85135 ± 0.11225	0.96740 ± 0.00233	0.92051 ± 0.00244	0.91683 ± 0.00189	4,507,673 ± 0.00000	309,129,657,280 ± 574,781,614,714.94189	509.33440 ± 180.92264
REFINED	5.94252 ± 0.19473	9.57097 ± 0.09981	9.57201 ± 0.11834	0.96997 ± 0.00197	0.92122 ± 0.00165	0.92148 ± 0.00194	1,654,833 ± 0.00000	166,022,193,100.79999 ± 280,016,749,242.1524	422.80904 ± 162.80911
DistanceMatrix	5.80147 ± 0.04815	9.53799 ± 0.14256	9.60631 ± 0.06818	0.97140 ± 0.00047	0.92175 ± 0.00233	0.92092 ± 0.00112	8,309,345 ± 0.00000	2,461,664,039,412.7998 ± 4,017,310,686,211.29297	1,089.20098 ± 310.99029
BarGraph	5.22966 ± 0.16871	9.79060 ± 0.06058	9.96486 ± 0.06396	0.97674 ± 0.00149	0.91756 ± 0.00102	0.91491 ± 0.00109	11,044,833 ± 0.00000	4,525,419,867,219.2002 ± 7,390,524,080,872.92383	866.04780 ± 203.89004
Combination	5.34537 ± 0.19032	9.55318 ± 0.07219	9.94313 ± 0.10081	0.97569 ± 0.00173	0.92151 ± 0.00118	0.91528 ± 0.00172	9,819,433 ± 0.00000	849,233,239,970.40002 ± 1,160,163,613,041.34424	535.82400 ± 72.16412
SuperTML	4.29412 ± 0.25653	10.48723 ± 0.08078	10.59245 ± 0.09414	0.98429 ± 0.00193	0.90541 ± 0.00146	0.90385 ± 0.00171	4,634,473 ± 0.00000	709,217,228,032 ± 1,564,581,382,185.67017	2,983.68161 ± 201.08062
FeatureWrap	13.77206 ± 2.12998	15.71511 ± 0.35545	21.06315 ± 0.83208	0.83574 ± 0.05462	0.78753 ± 0.00962	0.61936 ± 0.03016	5,460,577 ± 0.00000	1,030,081,193,107.19995 ± 1,820,098,138,320.47534	512.76986 ± 183.44309
BIE	4.55087 ± 0.51946	10.98117 ± 0.14843	11.21765 ± 0.17455	0.98222 ± 0.00407	0.89629 ± 0.00279	0.89215 ± 0.00336	11,563,073 ± 0.00000	15,283,835,263,308.80078 ± 21,448,598,033,060.51562	1,266.2391 ± 0.28499

CNN + MLP

Method
TINTO
IGTD
REFINED
DistanceMatrix
BarGraph
Combination
SuperTML
FeatureWrap
BIE