Recurrent In-Context Learning for Tabular Foundation Models

Tabular foundation models using in-context learning have recently surpassed gradient-boosted trees on predictive tabular tasks. However, recent mechanistic insights suggest that parameters in these models are largely redundant. We introduce LoopICL, a looped transformer whose core design decouples parameter count from computational depth. LoopICL consists of a single block, processing data through two coupled streams: a cell stream capturing per-cell feature representations and a row stream capturing in-context example representations, jointly refined through within-column and cross-column attention. During pre-training, we vary loop counts, allowing the block to be unrolled for a varying number of iterations at test-time and use a learned exit-gate to automatically exit. In its standard setting, LoopICL performs competitively with TabICLv2 on TabArena and TALENT at the same computational cost (FLOPs), while using nearly 90% fewer parameters. Furthermore, its recurrent design enables users to also trade off inference cost and performance, providing a resource-aware TFM.

Transformer-based tabular foundation models (TFMs) dominate small to medium tabular predictive benchmark tasks, yet their inference mechanisms remain largely unexplored. We present the first large-scale mechanistic study of layerwise dynamics in 6 state-of-the-art tabular in-context learning models. We explore how predictions emerge across depth, identify distinct stages of inference and reveal latent-space dynamics that differ from those of language models. Our findings indicate substantial depthwise redundancy across multiple models, suggesting iterative refinement with overlapping computations during inference stages. Guided by these insights, we design a proof-of-concept, looped single-layer model that uses only 20% of the original model's parameters while achieving comparable performance. The code is available at https://github.com/amirbalef/is_one_layer_enough.

Transformer-based tabular foundation models (TFMs) achieve state-of-the-art performance on small to medium-sized tabular prediction tasks while processing diverse inputs through a shared stack of layers. Recent layerwise analyses identify strong predictive performance in early TFM representations and substantial overlap in computation across layers. However, early predictive accessibility alone does not establish whether later layers are dispensable for every input, and aggregate accuracy can obscure which inputs benefit from additional computation. We study all 24 in-context-learning layers of TabPFN-3 across 272 classification datasets, combining representation geometry, prediction trajectories, truncation, and structural interventions, while also examining related representation dynamics in four additional TFMs. We uncover a pronounced expansion-compression trajectory, with stronger late dimensional contraction associated with larger increases in class-prototype separation. A targeted analysis of early-stabilizing samples shows that substantial representational changes persist after predicted classes stabilize, while locally ambiguous queries obtain larger accuracy gains from shallow to late layers than well-separated queries. Repeating a single pretrained block or perturbing layer order reduces predictive performance on average, constraining simple post-hoc substitutions in the frozen model. These findings distinguish predictive accessibility, class stability, and the benefits of continuing computation, supporting an input-dependent assessment of depthwise redundancy in TFMs.