Linear regression and kernel smoothing give a tractable view of in‑context learning: features set the weight for each context label. Whether this fixed‑weight view holds for pretrained tabular foundation models (TFMs) is unclear. Using derivatives to test it falls into a standardization trap—public TFM packages standardize labels before the model sees them, while ordinary derivatives also reflect behavior outside the standardized label space, making the model appear nonlinear even if every prediction follows a fixed‑weight map. We introduce two certificates that rely only on predictions at standardized labels and can reject two alternative explanations: a fixed‑weight predictor and a sum of independent nonlinear label transformations. Evaluating five public TFMs, the certificates reveal that changing one context label alters how other labels affect the prediction, a phenomenon we call joint processing. Further analysis shows joint processing emerges during training and that attention scores carry most of the measured interaction. These findings suggest that explanations of TFMs should account for how context labels modulate each other's influence.
Review