What Do Tabular Foundation Models Compute In Context? In-Situ Representation Refinement through Attention-Gated Updates

A tabular foundation model must discover which distinctions matter for each new table without updating its parameters. We develop in-situ representation refinement: support labels guide changes to the episode's representations, improving the information available to later queries. A regularized leave-one-out objective yields a support correction and its query extension. The leading term separates attention-based reading from state-dependent scaling, motivating RefineICL: an attention-gated, FFN-free contextual stack with selected low-rank feature interaction and typed memory. A direct intervention tests the role of evolving support states: removing one intermediate support update while preserving the block's query output increases final query cross-entropy in all 72 tested episodes. RefineICL-L24 reaches 0.93836 OVR-AUC and 0.87173 accuracy on AMLB29. A benchmark-informed continuation reaches 1644.8 Elo on the 38-dataset TabArena snapshot, 31.4 Elo above TabPFN-3 under the same evaluation. It also improves all four reported metrics over TabPFN-v3 on both TabZilla views. In a matched 100K-update depth grid, an expanded FFN gives no consistent validation benefit and uses 60.2% more peak inference memory at L8. These results connect learning within a forward pass to representation refinement and show how this view guides a competitive, memory-efficient model.