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.
LLMs can generate fluent descriptions from tables, but their outputs may remain logically unsupported by the structured data. We introduce STAT-TO-TEXT, a controlled task in which LLMs generate quantified natural language inferences from statistical tables using quantified constructions such as all, some, no, and most. To evaluate these inferences, we use an LLM generated Python checker code which when executed verifies the corresponding truth conditions against the table. We compare four open-weight LLMs across model families and scales, evaluating faithfulness, logical accuracy, table coverage, and diversity. Our results show that model scale and family matter, with the largest model (GPT-OSS-120B) consistently producing the most faithful inferences without sacrificing greater table coverage and quantifier diversity, as opposed to smaller models. These findings are supported by human annotation, which shows that the automated checker closely aligns with human judgments.
When a language model answers a table question, users have no way to verify which cells informed which reasoning steps. We introduce RSAT, a method that trains small language models (SLMs, 1-8B) to produce step-by-step reasoning with cell-level citations grounded in table evidence. Phase 1 (SFT) teaches a structured JSON output format from verified reasoning traces. Phase 2 (GRPO) optimizes a composite reward centered on NLI-based faithfulness, alongside citation validity and parsimony. Across six models from two families-Qwen 2.5 (1.5B/3B/7B) and Llama 3 (1B/3B/8B)-RSAT improves faithfulness 3.7× over SFT alone (0.224→0.826), with near-perfect citation validity (0.992). Post-hoc attribution collapses below 13% format success, confirming that attribution must be integrated into reasoning, not retrofitted. Ablations show the faithfulness reward is essential: removing it drops faithfulness from 0.97 to 0.03.
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.