FTFM: Factorized Tabular Foundation Models

Tabular foundation models (TFMs) have recently emerged as a promising paradigm for machine learning on tabular data, offering the ability to generalize across datasets without task-specific training. Since many machine learning datasets can be represented as tables, this raises the question: does TFM capability extend beyond tasks traditionally regarded as tabular? We address this question by using TabPFN v3 on three non-tabular classification problems: handwritten digit recognition on MNIST, language identification of French and German words, and image classification on Tiny ImageNet. In each case, the original data are represented as rows of a table and classification is formulated as prediction of a missing label. We evaluate performance as a function of the number of context samples provided to the pretrained model, with no additional training or fine-tuning. Despite having no explicit access to the spatial or sequential structure characterizing the data, TabPFN v3 in some cases achieves accuracies comparable with that of models or methods geared specifically toward the corresponding tasks.

In-context-learning Tabular Foundation Models (TFMs) are uniquely suited to scenarios with limited resources or privacy constraints, as they solve new tasks without additional training. However, their architecture consists of multiple transformer blocks, resulting in high computational and memory footprints. Meanwhile, traditional alternatives like Gradient-Boosted Decision Trees (GBDTs) remain highly competitive and run efficiently on CPUs, suggesting that tabular tasks may not inherently require deep architectures. This contrast raises a fundamental question: can TFMs be simplified by removing architectural redundancies without sacrificing performance? To answer this, we introduce a closed-form, label-free affine translator that replaces a contiguous window of up to 96% of the blocks, leaving the rest unchanged. Evaluating eight frontier TFMs on 171 classification datasets, we reveal that tabular transformers are vastly overparameterized: replacing half of a model's blocks costs at most $0.002$ median AUROC across all architectures, with the half-depth TabFM still outperforming every other full-depth TFMs and tuned GBDTs. Furthermore, different model families are overparameterized in different ways: TabPFN-3 relies on its encoders, maintaining performance regardless of which single block is retained. Other single-axis models spread computation thinly, needing only their first block, while dual-axis models concentrate it in one critical block. Ultimately, removing depth saves up to 1.5B parameters, speeds up GPU inference by up to $6\times$ at a median cost of $0.03$ AUROC, while a single-block TabPFN-3 serves cached queries $2.4\times$ faster using $6\times$ less memory at negligible cost.

Tabular foundation models (TFMs) increasingly rival tree ensembles, but their performance is often compute-inefficient: with standard affine scalar tokenization, each feature injects value variation through an essentially one-dimensional channel, and feature IDs/positional signals cannot increase within-feature value degrees of freedom, yielding weak early-layer value sensitivity and redundant hidden states. We present a unified tokenize-and-route framework for strong TFMs: RaBEL expands each scalar into compact localized RBF features (optionally exponent-gated) to improve conditioning and shallow-layer effective rank, while a reordered bidirectional block S->N->F aligns computation with the readout by aggregating cross-sample context before feature mixing and using attention pooling. Together, these changes yield LimiX-2M, a 2M-parameter model that outperforms larger TabPFN-v2 and TabICL baselines on widely used tabular benchmarks while reducing training and inference costs. These results highlight value-aware tokenization and readout-aligned routing as key levers for improving the accuracy--efficiency trade-off in TFMs. Model checkpoints and inference code are available at https://github.com/limix-ldm-ai/LimiX.