When Repeated Measurements Hurt Tabular Foundation Models
Organizations: National University of Singapore · Duke-NUS Medical School · Mohamed bin Zayed University of Artificial Intelligence
Abstract
Tabular foundation models (TFMs) achieve state-of-the-art performance on IID benchmarks, but how do they respond to repeated measurements at the same inputs? Across six TFMs, synthetic and semi-synthetic experiments show that additional measurements can improve predictions at measured inputs while degrading them elsewhere. Harm is most frequent at low noise, and irrelevant features amplify it in several models; real repeated-measurement datasets show similar patterns. Statistically, the IID rule targeted by PFN pretraining treats each repeated input as fresh evidence about the input distribution. When the prior links this distribution to the response function, the resulting protocol mismatch can outweigh the benefit of additional measurements, even under exact inference. Computationally, interventions identify row-count dependence in TabPFN-v3's attention scaling as a contributor to harm. Resetting the count largely reverses distortion in a noiseless linear diagnostic and attenuates amplification by irrelevant features. Finally, we evaluate ways to retain the benefits of repeated measurements while limiting their harm. Averaging measurements usually outperforms supplying them separately at larger repetition counts, whereas count reset can suppress both harm and useful gains. Code, saved results and reproduction instructions are available at https://github.com/drizmiz/PFN-Repeated-Measurement-Supp
Figures & tables
| noise SD | Single | Expanded | Mean | full reset | Mean wins |
|---|---|---|---|---|---|
| 0 | 0.0088 | 0.053 | 0.0088 | 0.0084 | 36 |
| 0.05 | 0.015 | 0.049 | 0.0094 | 0.0135 | 61 |
| 0.15 | 0.039 | 0.045 | 0.010 | 0.032 | 90 |
| 0.30 | 0.104 | 0.047 | 0.013 | 0.076 | 107 |
| 0.50 | 0.194 | 0.052 | 0.017 | 0.174 | 115 |
Appendix figures & tables31 assets
Supplementary material from the paper’s appendix.
Appendix
| dataset | a reading is | sites | context sites | ||
|---|---|---|---|---|---|
| SGEMM kernel timings | one run of a kernel configuration | 14 | 2,994 | 4 | 150 |
| Kernel Tuner convolution | one launch of a kernel configuration | 7 | 3,000 | 16 | 150 |
| Kernel Tuner dedispersion | one launch of a kernel configuration | 6 | 3,000 | 32 | 150 |
| FCNet slice localization | one training run with its own random seed | 9 | 3,000 | 4 | 150 |
| Bayes-factor surface | one Monte Carlo replicate | 2 | 80 | 4 | 40 |
| G. aparine bioassay | one pot at a dose and formulation | 2 | 21 | 8 | 10 |
| equal counts | unequal counts | |||
| learner | weighted | unweighted | weighted | unweighted |
| least squares | 440 (440) | 440 (440) | 440 (440) | 40 (40) |
| kernel ridge, fixed kernel | 440 (440) | 0 (0) | 440 (440) | 0 (0) |
| GP, fixed kernel and noise | 440 (440) | 0 (0) | 440 (440) | 0 (0) |
| regression tree | 241 (440) | 241 (440) | 240 (440) | 240 (438) |
| gradient boosting | 240 (440) | 240 (440) | 240 (440) | 0 (0) |
| setting | Single | Expanded | Mean | full reset | embedding only | mean better | |
|---|---|---|---|---|---|---|---|
| 1-D, | noise 0 | 0.0088 | 0.028 | 0.0088 | 0.0089 | 0.021 | 36 |
| noise 0.05 | 0.015 | 0.021 | 0.016 | 0.015 | 0.018 | 59 | |
| noise 0.15 | 0.039 | 0.028 | 0.031 | 0.028 | 0.029 | 64 | |
| noise 0.30 | 0.104 | 0.047 | 0.050 | 0.069 | 0.040 | 77 | |
| noise 0.50 | 0.194 | 0.084 | 0.082 | 0.176 | 0.076 | 94 | |
| 1-D, | noise 0 | 0.0088 | 0.053 | 0.0088 | 0.0084 | 0.038 | 36 |
| Expanded / Single | full/ Single | full wins | |
|---|---|---|---|
| 2 | 1.600 | 1.045 | 15/20 |
| 5 | 3.100 | 1.051 | 19/20 |
| 10 | 3.146 | 1.151 | 20/20 |
| Single | Expanded | Mean | ||||
|---|---|---|---|---|---|---|
| model | bias 2 | var | bias 2 | var | bias 2 | var |
| TabPFN-v3 | 0.023 | 0.013 | 0.041 | 0.0005 | 0.007 | 0.0005 |
| TabPFN-v3.5 | 0.100 | 0.016 | 0.240 | 0.0013 | 0.035 | 0.0006 |
| TabICLv2 | 0.072 | 0.018 | 0.107 | 0.0004 | 0.063 | 0.0005 |
| TabDPT | 0.082 | 0.015 | 0.064 | 0.0006 | 0.036 | 0.0004 |
| LimiX-2 | 0.041 | 0.014 | 0.200 | 0.0037 | 0.027 | 0.0013 |
| Single | Expanded | Mean | |||||
|---|---|---|---|---|---|---|---|
| designs | model | bias 2 | var | bias 2 | var | bias 2 | var |
| 1-D, noise 0.5 | TabPFN-v3 | 0.112 | 0.110 | 0.043 | 0.0033 | 0.012 | 0.0036 |
| TabPFN-v3.5 | 0.273 | 0.073 | 0.278 | 0.0028 | 0.049 | 0.0040 | |
| TabICLv2 | 0.121 | 0.126 | 0.147 | 0.0031 | 0.062 | 0.0045 | |
| TabDPT | 0.273 | 0.098 | 0.138 | 0.0033 | 0.047 | 0.0032 | |
| LimiX-2 | 0.118 | 0.093 | 0.318 | 0.0073 | 0.029 | 0.0046 | |
| Coverage | CRPS: MR/comparator | ||||||
| model | Single | Exp. | Mean | MR | Exp. | Single | Mean |
| One-dimensional | |||||||
| TabPFN-v3 | 0.87 | 0.91 | 0.43 | 0.92 | 0.926 | 0.810 | 0.906 |
| TabPFN-v3.5 | 0.96 | 0.99 | 0.68 | 0.94 | 0.684 | 0.808 | 0.983 |
| TabICLv2 | 0.67 | 0.98 | 0.57 | 0.92 | 0.819 | 0.835 | 0.948 |
| TabDPT | 0.93 | 0.90 | 0.65 | 0.96 | 0.966 | 0.853 | 0.988 |
| one-dimensional | semi-synthetic | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| model | scheme | mean | copies | Expanded | worse | mean | copies | Expanded | worse |
| TabPFN-v3 | random | 0.027 | 0.054 | 0.040 | 89 | 0.444 | 0.490 | 0.489 | 65 |
| clustered | 0.026 | 0.083 | 0.039 | 97 | 0.429 | 0.491 | 0.501 | 69 | |
| TabPFN-v3.5 | random | 0.078 | 0.169 | 0.163 | 83 | 0.473 | 0.491 | 0.524 | 61 |
| clustered | 0.070 | 0.182 | 0.128 | 90 | 0.473 | 0.482 | 0.492 | 54 | |
| LimiX-2 | random | 0.054 | 0.156 | 0.096 | 108 | 0.410 | 0.477 | 0.483 | 66 |
| fresh-input MSE | ||||||||
|---|---|---|---|---|---|---|---|---|
| noise SD | Single | Expanded | full | Exp. Single | full Exp. | Single | Expanded | full |
| 0.05 | 10.91 | 10.56 | 11.12 | 112/120 | 120/120 | 0.017 | 0.051 | 0.010 |
| 0.15 | 10.89 | 10.70 | 11.19 | 94/120 | 120/120 | 0.042 | 0.051 | 0.029 |
| noise SD | harm | gain | harm | gain |
|---|---|---|---|---|
| 0.05 | 74 | 38 | 6 | 2 |
| 0.15 | 43 | 51 | 11 | 15 |
| learner | MSE | MSE | worse |
|---|---|---|---|
| Gaussian process | 0.014 | 0.0002 | 0/20 |
| Gradient boosting | 0.172 | 0.158 | 6/20 |
| Random forest | 0.182 | 0.158 | 4/20 |
| MLP | 0.043 | 0.018 | 1/20 |
| TabPFN-v3 | 0.017 | 0.070 | 18/20 |
| TabPFN-v3.5 | 0.062 | 0.379 | 20/20 |
| family | LimiX-2 | TabICLv2 | TabPFN-v3.5 | TabPFN-v3 | TabFM | TabDPT | forest | GP (rows) | MLP | boosting |
|---|---|---|---|---|---|---|---|---|---|---|
| 1-D (60) | 39 | 26 | 35 | 14 | 8 | 4 | 10 | 0 | 0 | 0 |
| Real covariates (45) | 25 | 34 | 24 | 30 | 33 | 17 | 34 | 19 | 8 | 6 |
| Multivariate (9) | 9 | 9 | 4 | 8 | 7 | 4 | 9 | 3 | 0 | 0 |
| All (114) | 73 | 69 | 63 | 52 | 48 | 25 | 53 | 22 | 8 | 6 |
| scored at | TabPFN-v3 | TabPFN-v3.5 | LimiX-2 | TabICLv2 | TabDPT | TabFM | forest |
|---|---|---|---|---|---|---|---|
| measured sites | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| gap midpoints | 37 | 78 | 91 | 59 | 16 | 30 | 111 |
| fresh inputs | 50 | 93 | 102 | 70 | 29 | 22 | 57 |
| sites | spacing | ||||||
|---|---|---|---|---|---|---|---|
| model | 6 | 12 | 24 | 48 | 96 | even | random |
| TabPFN-v3 | 5 | 16 | 8 | 1 | 0 | 0.23 | 0.42 |
| TabPFN-v3.5 | 6 | 18 | 11 | 9 | 7 | 0.78 | 0.78 |
| LimiX-2 | 11 | 20 | 20 | 10 | 3 | 0.88 | 0.85 |
| TabICLv2 | 9 | 12 | 6 | 5 | 2 | 0.32 | 0.58 |
| TabDPT | 1 | 9 | 8 | 5 | 2 | 0.07 | 0.24 |
| model | Single | Expanded | Mean | ratio | worse | |
|---|---|---|---|---|---|---|
| TabPFN-v3 | 2 / 5 / 10 | 0.051 / 0.069 / 0.084 | 0.076 / 0.204 / 0.259 | 0.012 / 0.022 / 0.026 | 1.60 / 3.10 / 3.15 | 15 / 18 / 19 |
| TabPFN-v3.5 | 2 / 5 / 10 | 0.066 / 0.099 / 0.124 | 0.070 / 0.101 / 0.133 | 0.028 / 0.045 / 0.065 | 1.00 / 1.00 / 1.04 | 10 / 10 / 13 |
| LimiX-2 | 2 / 5 / 10 | 0.040 / 0.050 / 0.046 | 0.045 / 0.088 / 0.175 | 0.014 / 0.016 / 0.015 | 1.11 / 1.61 / 3.06 | 13 / 17 / 20 |
| TabICLv2 | 2 / 5 / 10 | 0.083 / 0.193 / 0.243 | 0.172 / 0.279 / 0.424 | 0.060 / 0.136 / 0.202 | 1.89 / 1.80 / 1.69 | 19 / 18 / 18 |
| TabDPT | 2 / 5 / 10 | 0.079 / 0.113 / 0.120 | 0.072 / 0.175 / 0.282 | 0.046 / 0.060 / 0.084 | 0.97 / 1.46 / 1.72 | 8 / 17 / 20 |
| TabFM | 2 / 5 / 10 | 0.138 / 0.182 / 0.211 | 0.172 / 0.256 / 0.297 | 0.118 / 0.145 / 0.164 | 1.11 / 1.31 / 1.30 | 15 / 18 / 17 |
| on the rows | means with variances | means only | |
|---|---|---|---|
| One-dimensional synthetic | 0 of 60 | 0 of 60 | 0 of 54 |
| Real covariates | 19 of 45 | 18 of 45 | 5 of 40 |
| Multivariate synthetic ( ) | 3 of 9 | 0 of 9 | 0 of 9 |
| harmed splits | relative MSE gap | ||
|---|---|---|---|
| dataset ( ) | rows | means+var. | median |
| SGEMM ( ) | 14/20 | 14/20 | |
| KT convolution ( ) | 19/20 | 19/20 | |
| KT dedispersion ( ) | 17/20 | 17/20 | |
| FCNet slice ( ) | 11/20 | 11/20 | |
| Expanded | Mean | |||||||
|---|---|---|---|---|---|---|---|---|
| model | Single | 4 | 64 | 256 | 4 | 64 | 256 | |
| one-dimensional | TabPFN-v3 | 0.039 | 0.028 | 0.045 | 0.049 | 0.031 | 0.010 | 0.010 |
| synthetic | TabPFN-v3.5 | 0.107 | 0.050 | 0.265 | 0.274 | 0.063 | 0.044 | 0.037 |
| LimiX-2 | 0.069 | 0.077 | 0.204 | 0.162 | 0.053 | 0.034 | 0.032 | |
| TabICLv2 | 0.109 | 0.105 | 0.131 | 0.136 | 0.096 | 0.073 | 0.075 | |
| TabDPT | 0.087 | 0.047 | 0.067 | 0.081 | 0.057 | 0.044 | 0.045 | |
| SGEMM ( ) | Kernel Tuner conv. ( ) | Hydraulic rig ( ) | ||||||||||
| S | E | M | worse | S | E | M | worse | S | E | M | worse | |
| TabPFN-v3 | 0.105 | 0.161 | 0.104 | 20 | 0.223 | 0.259 | 0.218 | 15 | 0.178 | 0.074 | 0.071 | 2 |
| TabPFN-v3.5 | 0.097 | 0.089 | 0.097 | 2 | 0.211 | 0.216 | 0.203 | 13 | 0.199 | 0.110 | 0.078 | 6 |
| LimiX-2 | 0.091 | 0.116 | 0.093 | 20 | 0.207 | 0.222 | 0.200 | 17 | 0.141 | 0.057 | 0.045 | 4 |
| TabICLv2 | 0.112 | 0.232 | 0.111 | 20 | 0.208 | 0.252 | 0.198 | 17 | 0.102 | 0.051 | 0.047 | 2 |
| TabDPT | 0.086 | 0.162 | 0.086 | 20 | 0.229 | 0.250 | 0.223 | 16 | 0.185 | 0.097 | 0.102 | 3 |
| Scope | Near slope | Middle slope | MSE |
|---|---|---|---|
| Native | 0.688 | 1.354 | 0.001345 |
| Embedding-only | 0.803 | 1.141 | 0.000203 |
| ICL only | 0.943 | 1.069 | 0.000196 |
| Full | 0.996 | 0.999 | 0.000065 |
| function | TabDPT | TabFM |
|---|---|---|
| quadratic | 1.243 | 1.000 |
| absolute value | 0.712 | 0.999 |
| linear | 1.420 | 1.009 |
| hyperbolic tangent | 1.023 | 1.007 |
| step | 0.932 | 1.003 |
| sine | 0.484 | 0.999 |
| Expanded | Mean | ||||
|---|---|---|---|---|---|
| trial | shipped | trained | shipped | trained | wins |
| Four ICL layers + count + head | 0.0648 | 0.0621 | 0.0079 | 0.0481 | 23/36 |
| All ICL layers + count + head | 0.0648 | 0.0730 | 0.0079 | 0.0307 | 17/36 |
| Values-only adapter | 0.0655 | 0.0727 | 0.0076 | 0.0076 | 17/36 |
Tabular Foundation Models
Tabular foundation models learn reusable representations or in-context prediction skills for structured data such as spreadsheets and databases.
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