Large Language Models have achieved remarkable success and are increasingly deployed in critical applications involving tabular data, such as Table Question Answering. However, their robustness to the structure of this input remains a critical, unaddressed question. This paper demonstrates that modern LLMs exhibit a significant vulnerability to the layout of tabular data. Specifically, we show that semantically-invariant permutations of rows and columns - rearrangements that do not alter the table's underlying information - are sometimes sufficient to cause incorrect or inconsistent model outputs. To systematically probe this vulnerability, we introduce Adversarial Table Permutation, a novel, gradient-based attack that efficiently identifies worst-case permutations designed to maximally disrupt model performance. Our extensive experiments demonstrate that ATP significantly degrades the performance of a wide range of LLMs. This reveals a pervasive vulnerability across different model sizes and architectures, including the most recent and popular models. Our findings expose a fundamental weakness in how current LLMs process structured data, underscoring the urgent need to develop permutation-robust models for reliable, real-world applications.
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.
While large language models (LLMs) perform well on table tasks, they still make data referencing errors (DREs), i.e., incorrectly citing or omitting table values, despite understanding the table structure. Beyond final-answer accuracy, DREs directly compromise the correctness and reliability of intermediate reasoning steps. Yet prior studies have only offered limited, small-scale analyses. In this work, we present the first systematic evaluation of tabular data referencing errors across different models and tasks. Our results show that DREs occur across all tested models (1.7B to 20B parameters). Furthermore, we demonstrate that incorporating data referencing as a critic significantly improves answer accuracy up to 12.0%, through critic-based filtering and rejection sampling. Finally, we trained a lightweight 4B-parameter critic model that achieves an average F1 score of 78.2% in detecting both in-distribution and out-of-distribution DREs, and effectively assists inference for larger models.
Large Language Models (LLMs) and Vision-Language Models (VLMs) are increasingly evaluated on table reasoning tasks, but the role of table representation remains under-explored. In practice, the same table content may appear in different structural formats, such as HTML, Markdown, and LaTeX, or as rendered images. However, existing evaluations often let content, format, layout, and modality vary together, making it difficult to isolate representation effects. We introduce TABVERSE, a controlled multimodal table benchmark that aligns the same table content across multiple structural formats and rendered images, with question category and difficulty tags. This design enables systematic evaluation of representation effects while holding table content fixed. We evaluate LLMs and VLMs across three tasks: Question Answering (QA), Structural Understanding Capability (SUC), and Structure Reconstruction (SR). Our results show that representation choice substantially affects table understanding. Models generally perform better with structured text than with rendered images, but the size of this gap depends on the task, model, and format. HTML is often the most robust text format, while row-sensitive structural tasks and syntactically usable LaTeX reconstruction remain challenging. These findings show that table representation is a key factor in reliable table evaluation.