Support-Compiled Feature Folding: More Evidence at Lower Memory Across Tabular Foundation Models

Wide tables offer tabular foundation models more evidence, but accessing it can exhaust their memory: full-width pairwise mixing grows quadratically with the number of columns, while feature selection makes inputs affordable by discarding evidence. We ask whether using more features requires interacting over all of them at once. We introduce Support-Compiled Feature Folding (SCFF), a training-free inference framework that encodes wide tables through bounded calls to a frozen backbone. SCFF organizes support-ranked features into a strong Core and a candidate Tail, folds them into narrow feature groups, and support-checks the Tail's added evidence before a single contextual prediction. This converts quadratic feature-interaction work into linear-in-width work with a bounded local working set, without ensembling predictions or training new parameters. On the exhaustive 18-dataset wide-table slice of fixed AMLB-29, TabZilla, and TabArena snapshots, SCFF improves dataset-macro accuracy and NLL on all six evaluated backbones. All four matched-width comparisons retain favorable 95% dataset-bootstrap intervals on locked folds, with relative error reductions up to 26.1%. Median paired GPU-memory savings are 2.09-2.36x, and the ratio of separately observed maximum peaks reaches 34.3x. Under a measured peak-memory ceiling, SCFF uses the saved budget to preserve more support-selected evidence, improving accuracy by 4.06 and 3.72 points over the widest feasible single leaf on predeclared wide-Core strata of TabICLv2 and TabPFN-3.