ProgramTab: Boosting Table Reasoning of LLMs via Programmatic Paradigm

Multi-step LLM reasoning over structured tables fails because planning and execution share no explicit cell-grounding contract. Existing methods constrain the planner to a left-to-right factorization at odds with table permutation invariance, and score intermediate states by generated content alone, overlooking cell grounding. We conduct a pilot study showing that diffusion language models (DLMs) produce more human-aligned and permutation-stable cell attention on tables than autoregressive models, with a 40.2% median reduction in attention-AUROC variability under row reordering. Motivated by this, we propose TABALIGN, a planned table reasoning framework that operationalizes the contract. TABALIGN pairs a masked DLM planner, whose bidirectional denoising emits plan steps as binary cell masks, with TABATTN, a lightweight verifier trained on 1,600 human-verified attention standards to score each step by its attention overlap with the plan-designated mask. Across eight benchmarks covering table question answering and fact verification, TABALIGN improves average accuracy by 15.76 percentage points over the strongest open-source baseline at comparable 8B-class scale, with a matched-backbone ablation attributing 2.87 percentage points of this gain to the DLM planner over an AR planner on a fixed reasoner. Cleaner DLM plans also accelerate downstream reasoning execution by 44.64%.

Large Language Models (LLMs) have shown promising results on NLP tasks, however, their performance on tabular data still needs research attention, because Table Question-Answering (TQA) requires precise cell retrieval and multi-step structured reasoning. Existing work improves TQA either by fine-tuning or training LLMs on task-specific tabular data, but often lacks verifiable control over how the model navigates tables and derives answers. In this work, we propose a training-free TQA approach with two structured prompting frameworks: TableGrid Navigation (TGN), which iteratively navigates rows and columns via a three-module loop to locate evidence and refine answers, and Progressive Inference Prompting (PIP), which enforces columns identification for explicit progressive row selection constraint according to the query. We evaluate 17 LLMs against 6 baselines on TableBench and FeTaQa dataset. On TableBench, TGN improves over the strongest baseline by 3.8 points, and on FeTaQa, PIP achieves SOTA performance over ReAct and Chain-of-Thought. Beyond inference-time gains, PIP and TGN can also serve as supervision templates to fine-tune small models, narrowing the performance gap to much larger architectures in resource-constrained settings, offering versatile and cost-efficient solution for TQA.

Tables are ubiquitous across diverse domains, yet reasoning over them remains a significant challenge for modern large language models (LLMs). Current approaches typically linearize tables into sequences, inherently overlooking their intrinsic two-dimensional and hierarchical structure. To address this, we propose H2Table (Hierarchical Hypergraph-Enhanced Table Reasoning), a novel framework that represents complex tables as hierarchical nested hypergraphs. To process this representation, we design a tailored hypergraph encoder to facilitate message passing between hyperedges (headers) and nodes (cells), thereby perceiving the semantic entailment relationships between them within complex tables. Furthermore, we introduce a set of learnable query vectors acting as a lightweight bridge to extract representative structural embeddings from the encoder into the LLM. Experimental results demonstrate that our approach effectively handles complex table question answering tasks with hierarchical nested headers. Notably, on the HiTab dataset, H2Table achieves an average improvement of 22.88% over state-of-the-art baselines on highly complex tables with a nesting depth of four. Our code is available at: https://github.com/lila120/h2table.