Self-Improving Tabular Language Models via Iterative Reward-Guided Post-Training
Authors: Yunbo Long, Tejumade Afonja, Guangya Hao, Alexandra Brintrup, Mario Fritz
Organizations: Department of Engineering, University of Cambridge · CISPA Helmholtz Center for Information Security, Saarbrücken, Germany · The Alan Turing Institute, London
Abstract
Tabular language models can generate synthetic tables by modeling rows as token sequences, but they are typically trained once with supervised fine-tuning and then used as static synthesizers. This is limiting because next-token likelihood does not directly optimize the distributional, utility, and indistinguishability properties used to evaluate synthetic data. We study iterative reward-guided post-training for tabular language models through a generate--score--align protocol, where a generator samples synthetic rows, a task-specified reward ranks them, and the model is updated relative to a fixed supervised reference. Within this protocol, we propose \textbf{TabGRAA} (\textbf{Tab}ular \textbf{G}roup-\textbf{R}elative \textbf{A}dvantage \textbf{A}lignment), a group-relative alignment method that compares high- and low-reward generated groups using group-averaged policy/reference log-ratios rather than one-to-one preference pairs. Across five mixed-type benchmarks, TabGRAA improves a GReaT backbone beyond additional supervised fine-tuning and achieves the strongest average trade-off among adapted DPO, KTO, and NPO baselines on fidelity and downstream utility, while maintaining empirical privacy diagnostics near the supervised baseline. Ablations show that the gains depend on meaningful reward ranking and stable group-level updates rather than extra training alone. Reward-substitution and scorer-separation studies further show that the post-training loop can use both classifier-based and classifier-free rewards, and that proper scorer separation is important for preserving the fidelity--utility--privacy trade-off. These results position TabGRAA as a self-improving post-training method for tabular language-model generators, complementary to strong static tabular synthesizers.
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.
Tabular foundation models, such as TabPFNv2 and TabICL, have recently dethroned gradient-boosted trees at the top of predictive benchmarks, demonstrating the value of in-context learning for tabular data. We introduce TabICLv2, a new state-of-the-art foundation model for regression and classification built on three pillars: (1) a novel synthetic data generation engine designed for high pretraining diversity; (2) various architectural innovations, including a new scalable softmax in attention improving generalization to larger datasets without prohibitive long-sequence pretraining; and (3) optimized pretraining protocols, notably replacing AdamW with the Muon optimizer. On the TabArena and TALENT benchmarks, TabICLv2 without any tuning surpasses the performance of the current state of the art, RealTabPFN-2.5 (hyperparameter-tuned, ensembled, and fine-tuned on real data). With only moderate pretraining compute, TabICLv2 generalizes effectively to million-scale datasets under 50 GB GPU memory while being markedly faster than RealTabPFN-2.5. We provide extensive ablation studies to quantify these contributions and foster open research by releasing code for inference, pretraining, and synthetic data generation at https://github.com/soda-inria/tabicl.
What determines the quality of a tabular foundation model? Unlike language or vision, tabular foundation models acquire their inductive biases almost entirely from synthetic pretraining distributions, yet the design of these distributions remains poorly understood. Standard synthetic priors are too well-behaved: they omit the irregularities and failure modes that determine deployment robustness. We introduce O'Prior, a compositional realism prior built around four coupled components: a hierarchical SCM meta-generator spanning diverse functional families; a modular realism engine covering heterogeneous marginals, missingness, and target transforms; an explicit stress module injecting confounding and support-query mismatch; and a curriculum-governed, leakage-safe generation protocol. To isolate prior design as the scientific variable, we hold architecture, optimizer, and compute budget fixed and vary only the synthetic task distribution. O'Prior yields consistent and substantial improvements in downstream accuracy and robustness across real tabular benchmarks, with gains concentrated in regimes characterized by distributional irregularities. Ablations confirm that mechanism diversity, realism composition, and shift-aware stress each contribute independently, their effects are not interchangeable. These results establish synthetic prior construction as a first-order and largely overlooked determinant of tabular foundation model quality