LLMs on Tabular Data with Limited Semantics: Evidence from Industrial Car Retrofit Prediction

Large language models (LLMs) have become the default tool for a remarkable range of tasks, yet they have had conspicuously little success at one of the most common machine learning workloads: predictive analytics over tabular data. This gap is the founding premise of the fast-growing field of tabular foundation models, but the question of why generic LLMs fail has remained open. We study a frontier LLM in its purest inference regime - a single generation pass over a prompt containing the full training and test data, with no tools, no agentic scaffolding, and no fine-tuning - and systematically evaluate five hypotheses for the failure: (a) an inability to handle noisy or non-linearly-separable data; (b) the linearised CSV format obscuring column structure; (c) the tokenisation of numeric values; (d) the number of test points classified per query; and (e) the dimensionality of the input. Controlled experiments falsify (a)-(d). Dimensionality, in contrast, is decisive: sweeping random linear projections of thirty-one benchmark datasets, the LLM is the only method among nine whose accuracy decreases as dimensionality grows, while every classical baseline stays flat or improves. A behavioural comparison against 252 configured classical models finds that in two dimensions the LLM predicts like a local, distance-based method (up to 91.6% grid agreement), but in higher dimensions no classical model - even when augmented with tuned, dimension-dependent noise - reproduces its predictions. We do not claim to have identified the internal mechanism; our results show, more modestly, that the LLM's capability dissolves with dimension in a way no noise-corrupted classical learner mimics - which explains why LLMs, so capable elsewhere, keep losing to fifty-year-old baselines on tables, while leaving the mechanism of the prediction as an open question.

Every major data modality now has a foundation model that understands it natively: text has language models, images have vision models, audio has audio models. Tabular data, the modality on which many consequential real-world AI decisions are made, does not. Every approach to tabular AI today, from gradient-boosted trees to the latest tabular foundation models, requires a preprocessing pipeline before any model can consume the data. None of them understand tabular data as a modality. We introduce the Data Language Model (DLM), the missing foundation model for tabular data. A DLM understands tables the way a language model understands sentences: natively, without serialization or preprocessing, directly from raw cell values. It is the tabular data layer on which AI models, agents, and vertical AI applications can be built, eliminating the preprocessing pipelines that currently stand between raw data and every AI system that consumes it. We present Schema-1, the first DLM: a 140M parameter model trained on more than 2.3M synthetic and real-world tabular datasets. Schema-1 outperforms gradient-boosted ensembles, AutoML stacks, and the tabular foundation models we evaluate on established row-level prediction benchmarks. On missing value reconstruction it achieves lower reconstruction error than all classical statistical methods and frontier large language models on mean performance across conditions, establishing that structural understanding of a dataset's own distributional geometry is more useful for imputation than world knowledge encoded in language. It identifies the industry sector of any unseen dataset from raw cell values alone, reliably across any domain, a task no prior tabular model can perform. It is the native tabular understanding layer that has been missing from the AI stack.

Tabular prediction has long been dominated by gradient-boosted decision trees and specialized deep tabular models, while large language models (LLMs) remain difficult to make competitive despite their cross-task adaptability and transparent reasoning traces. We address this gap by incorporating tabular structural priors into LLM post-training. Specifically, we propose Permutation Relative Policy Optimization (PRPO), which operationalizes column-permutation invariance through label-preserving column permutations and two-level advantage estimation. This design converts sparse outcome rewards into denser and more stable optimization signals. Extensive experiments on 139 OpenML datasets show that our 8B model reaches a genuinely competitive regime against strong specialized tabular baselines. It achieves strong fully supervised performance, dominates zero-shot settings, and performs on par with 32-shot strong baselines. Moreover, it substantially outperforms much larger general-purpose and reasoning LLMs, including up to a 53.17% improvement over DeepSeek-R1 (685B). These results show that structural-prior RL post-training is an effective route for making LLMs competitive in tabular prediction.