An analyst perturbs a label to test how it influences a model. If the software first standardises all labels, the perturbation changes more than the analyst intended.
An October 6 paper shows how ordinary derivative tests can examine behaviour outside the standardised label set used by public tabular models. Its alternative certificates operate on valid inputs and find joint label processing in the evaluated systems. Read the research paper.
An intervention can leave the model's normal input domain
Tabular foundation models use labelled context examples to predict a new row. Simple explanations treat that process as fixed weighting: the features determine how much each label contributes. Testing the explanation with derivatives seems natural. But public packages often standardise the labels before the network receives them. An ordinary perturbation can then describe behaviour outside the set of standardised inputs the package actually presents.
The paper calls this a standardisation trap. A derivative test can reject a fixed-weight explanation even when every valid prediction agrees with one. The problem is not a lack of mathematical sophistication; it is a mismatch between the mathematical intervention and the operational input domain.
Two certificates test distinct explanations
The authors construct certificates based only on predictions at standardised labels. One can reject fixed-weight prediction. The other can reject a broader account in which labels undergo separate nonlinear transformations before being combined. Distinguishing the two matters: rejecting linearity alone would not show that labels interact with one another.
Across five public tabular models, both certificates indicate joint processing: changing one context label changes how another label influences the prediction. The evaluated models include several pretrained on synthetic tasks and TabDPT, trained on real tables, giving the result some architectural and training-data diversity without making it universal across all tabular systems.
The interaction is connected to training and attention
The experiments use a synthetic regression problem and three OpenML datasets, with two hundred and fifty-six context rows and repeated context-and-query samples. The synthetic control permits redrawing label noise and avoids some confounds associated with real datasets. The authors also compare randomly initialised copies, where the measured interaction is much weaker, suggesting that training helps produce the joint behaviour.
Blocking derivatives through attention scores removes most of the measured interaction while leaving predictions unchanged. This identifies where the interaction passes in the implemented networks; it is not an intervention demonstrating that removing attention preserves the same model function. The paper reports that twenty-three to ninety-two percent of curvature departing from fixed weights comes from interaction that independent label transformations cannot produce.
The certificates reject explanations rather than completing one
A nonzero certificate establishes that the corresponding restricted account cannot explain the observed predictions. It does not reconstruct a complete algorithm for the tabular model. Joint processing can encompass many possible mechanisms, and the attention analysis identifies a route for measured interaction without proving a unique conceptual explanation.
The distinction matters for interpretability reporting. Evidence against fixed weights is stronger when the test respects standardisation, but it should not be expanded into a detailed story about how every training example is represented. The paper deliberately separates fixed weighting, independent nonlinear label transformations and joint label effects. That hierarchy gives researchers a more precise set of hypotheses to test, while leaving a substantial explanatory gap after the simpler hypotheses are rejected.
The software pipeline belongs in the explanation
The analysis requires careful implementation choices, including standard attention that can be differentiated twice rather than deployment kernels that cannot. It also distinguishes individual estimators from package ensembles. Those details are not bookkeeping trivia: they determine which mathematical object the certificate is actually measuring.
A model explanation should specify its valid input domain, preprocessing and readout. A probe that moves outside that domain can reveal properties of an artificial extension rather than the deployed system. Here, correcting the intervention does not rescue the simple fixed-weight story; it produces stronger evidence for a more interesting result, namely that context labels jointly alter the influence of examples.
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