Useful Features Can Crowd Out Interactions in Tabular Foundation Models

Tabular foundation models (TFMs) can lose an interaction when other columns become informative, even though those columns remain useful at test time. We call this crowding out. The TFMs predict from labeled context rows with fixed pretrained weights. We add a known parity component to real regression targets and compare the original competing columns with permuted copies. The target, table width and column marginals stay fixed, separating crowding from dilution by uninformative columns. TabPFN-3, TabICLv2 and TabFM exhibit crowding; boosting and most networks trained by gradient descent benefit from the same columns. Weak additive or pairwise clues improve interaction learning without preventing crowding. Swapping labels used to construct column representations induces or releases crowding while prediction labels stay fixed. CrowdBench tests interaction retention on controlled tasks, known rules and measured systems. In selected measured systems, summaries improve RMSE while hiding component loss, or hurt prediction as context grows. These cases establish susceptibility rather than prevalence. Searching prediction residuals and refitting on the discovered columns restores planted interactions within the search dictionary.