TLRD: Teaching LLMs to Reason over Tabular Data with Tri-Level Rationale Distillation

Large Language Models (LLMs) fine-tuned on serialized tabular data are emerging as powerful alternatives to traditional tree-based models, particularly for heterogeneous or context-rich datasets. However, their deployment in high-stakes domains is hindered by a lack of faithful interpretability; existing methods often rely on global linear proxies or scalar probability shifts that fail to capture the model's full probabilistic uncertainty. In this work, we introduce TabSHAP, a model-agnostic interpretability framework designed to directly attribute local query decision logic in LLM-based tabular classifiers. By adapting a Shapley-style sampled-coalition estimator with Jensen-Shannon divergence between full-input and masked-input class distributions, TabSHAP quantifies the distributional impact of each feature rather than simple prediction flips. To align with tabular semantics, we mask at the level of serialized key:value fields (atomic in the prompt string), not individual subword tokens. Experimental validation on the Adult Income and Heart Disease benchmarks demonstrates that TabSHAP isolates critical diagnostic features, achieving significantly higher faithfulness than random baselines and XGBoost proxies. We further run a distance-metric ablation on the same test instances and TabSHAP settings: attributions are recomputed with KL or L1 replacing JSD in the similarity step (results cached per metric), and we compare deletion faithfulness across all three.

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.

Large language models (LLMs) perform table-centric prediction through in-context learning, making demonstration selection critical to performance. Existing retrieval methods prioritize similarity to the query, but similar demonstrations often reinforce the model's likely prediction rather than reveal the distinctions needed for difficult decisions. We propose EdgeLM, a retrieval framework that instead selects edge evidence, demonstrations that are both relevant to the query and informative about the decision boundary. EdgeLM retrieves two complementary forms of edge evidence by selecting data edges, nearby examples with different ground-truth labels, and model edges, similar examples previously misclassified by the deployed model. EdgeLM requires neither model retraining nor task-specific engineering. Across five data wrangling tasks, fifteen datasets, and five open-weight and proprietary LLMs, EdgeLM consistently achieves the best or near-best performance in every setting, while ablations show that the two forms of edge evidence provide complementary benefits. Our code and datasets are publicly available at https://github.com/soroushomidvar/EdgeLM.