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.
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.
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.
Statistical reasoning is multidimensional, yet evaluations of large language models (LLMs) typically emphasize response accuracy while overlooking how models construct and communicate statistical explanations. This study demonstrates the value of a multidimensional evaluation by combining response accuracy, response behavior, structural topic modeling, and lexical similarity analysis. The framework is applied to explanations generated by 15 current-generation LLMs responding to 90 questions drawn from four statistics examinations spanning high school, undergraduate, and graduate levels. Accuracy varied substantially across models, ranging from 55% to 78%. In contrast, structural topic modeling revealed a common conceptual organization of statistical reasoning across all models, while lexical similarity analysis identified modest but consistent vendor-specific differences in explanatory style. Models developed by the same vendor (e.g. Anthropic, OpenAI) produced explanations that were slightly more similar than models from different vendors. These findings demonstrate that statistical reasoning in contemporary LLMs cannot be characterized by accuracy alone and illustrate how complementary analyses of response behavior and model-generated explanations provide a more comprehensive evaluation of statistical reasoning in generative AI.