Table Reasoning

Large Language Models (LLMs) have shown strong capabilities in table reasoning, but their effectiveness degrades as tables grow in size and complexity due to irrelevant context and difficulty localizing the evidence required for reasoning. Existing approaches typically reason over either the full table or a single reduced view, which can still obscure important row-column relationships. We introducePARTAB (Partition-Aware Reasoning overTables), a framework that constructs a structured evidence interface between the LLM and the table. PARTAB represents query-relevant evidence as semantically coherent, row-linked table regions and performs hierarchical selection over column groups and row-level partitions before composing the selected evidence for answer generation. We evaluate PARTAB on multiple table reasoning benchmarks, covering question answering, fact verification, and numerical reasoning. PARTAB consistently improves over full-table prompting and several recent table reasoning methods, achieving strong performance on WikiTableQuestions and TabFact while remaining competitive on numerical reasoning. Additional analyses show that semantic partitioning and targeted evidence selection improve evidence localization, substantially reduce the reasoning context, and provide larger benefits on complex tables. These results demonstrate the value of structured, partition aware evidence construction for scalable table reasoning.

Table-based reasoning with large language models (LLMs), which requires reasoning based on natural language questions and structured tabular data, has gained widespread attention. However, a series of issues still constrain the application of this task. The previous approaches suffered from significant performance degradation when faced with large tables due to the difficulty of long text modeling and the limitation of input length for LLMs. The text-to-SQL approach is used to efficiently extract key information from tables and generate smaller sub-tables. However, tabular data, especially web tables, often lack the necessary structure and consistency, making them unsuitable for performing mathematical logic operations using SQL queries. We propose the ProgramTab framework, which guides LLMs employing in-context learning to perform tabular data preprocessing with Python code, as well as the momentous contents extraction with row and column extraction and SQL generation. The experiment results on table reasoning datasets demonstrate that the ProgramTab framework effectively deals with table-based reasoning tasks and outperforms all LLM-based baselines.

Spreadsheets and tables are widely used representations for structured data analysis, but effective analysis still requires substantial manual effort and domain expertise. Recent large language model (LLM) agents can automate parts of this process, but they often provide limited transparency into intermediate decisions, rely on implicit assumptions, struggle with multi-table comparison, and repeat similar workflows without adapting to a user's preferences. This paper presents TabClaw, an open-source interactive AI agent for spreadsheet manipulation and table reasoning. Users upload CSV or Excel files and issue natural-language requests; TabClaw clarifies ambiguous intent, exposes an editable execution plan, streams a ReAct-style tool-using analysis loop, dispatches specialist agents for parallel multi-table reasoning, and synthesizes findings with explicit consensus and uncertainty markers. Beyond one-off analysis, TabClaw records completed workflows, extracts persistent user memory, distills reusable skills from repeated tool-use patterns, supports package-style skill import, and upgrades skills from negative feedback. Experiments on spreadsheet manipulation and table reasoning benchmarks show that TabClaw improves executable task completion and reasoning performance while preserving an inspectable user workflow. This paper shows how TabClaw turns spreadsheets and tables into inspectable analytical workflows while gradually personalizing itself to recurring data-analysis tasks. Our code is available.

Large Reasoning Models (LRMs) achieve strong performance on table reasoning tasks but incur substantial inference cost due to long reasoning traces. Stepwise model routing mitigates this issue by dynamically assigning reasoning steps to smaller or larger models. However, stepwise model routing for table reasoning remains underexplored. Through empirical analysis, we find that reasoning steps involving tables contain two types of tokens with distinct uncertainty distributions: table tokens grounded in table structure, such as cell values and headers, and text tokens representing surrounding natural-language reasoning. The uncertainty of both token types is correlated with the risk that the model makes an error in the next reasoning step. However, existing methods fail to model them separately, leading to suboptimal routing decisions. To address this, we propose EcoTab, a table-aware stepwise routing framework for efficient table reasoning. At each reasoning step, EcoTab separately estimates the uncertainties of table tokens and text tokens, maps them to next-step failure risks for the small model, and combines the two risks for routing. Experiments on multiple table reasoning benchmarks show that EcoTab consistently outperforms strong baselines and achieves a better balance between accuracy and efficiency.

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%.

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$\times$ over SFT alone (0.224$\rightarrow$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.

Historical approaches to Table Representation Learning (TRL) have largely adopted the sequential paradigms of Natural Language Processing (NLP). We argue that this linearization of tables discards their essential geometric and relational structure, creating representations that are brittle to layout permutations. This paper introduces the Platonic Representation Hypothesis (PRH) for tables, positing that a semantically robust latent space for table reasoning must be intrinsically Permutation Invariant (PI). To ground this hypothesis, we first conduct a retrospective analysis of table-reasoning tasks, highlighting the pervasive serialization bias that compromises structural integrity. We then propose a formal framework to diagnose this bias, introducing two principled metrics based on Centered Kernel Alignment (CKA): (i) PI, which measures embedding drift under complete structural derangement, and (ii) rho, a Spearman-based metric that tracks the convergence of latent structures toward a canonical form as structural information is incrementally restored. Our empirical analysis quantifies an expected flaw in modern Large Language Models (LLMs): even minor layout permutations induce significant, disproportionate semantic shifts in their table embeddings. This exposes a fundamental vulnerability in RAG systems, in which table retrieval becomes fragile to layout-dependent noise rather than to semantic content. In response, we present a novel, structure-aware TRL encoder architecture that explicitly enforces the cognitive principle of cell header alignment. This model demonstrates superior geometric stability and moves towards the PI ideal. Our work provides both a foundational critique of linearized table encoders and the theoretical scaffolding for semantically stable, permutation invariant retrieval, charting a new direction for table reasoning in information systems.

Structured tables are essential for conveying high-density information in professional domains such as finance, healthcare, and scientific research. Despite the progress in Multimodal Large Language Models (MLLMs), reasoning performance remains limited for complex tables with hierarchical layouts. In this paper, we identify a critical Perception Bottleneck through quantitative analysis. We find that as task complexity scales, the number of involved discrete visual regions increases disproportionately. This processing density leads to an internal "Perceptual Overload," where MLLMs struggle to maintain accurate spatial attention during implicit generation. To address this bottleneck, we introduce TableVision, a large-scale, trajectory-aware benchmark designed for spatially grounded reasoning. TableVision stratifies tabular tasks into three cognitive levels (Perception, Reasoning, and Analysis) across 13 sub-categories. By utilizing a rendering-based deterministic grounding pipeline, the dataset explicitly couples multi-step logical deductions with pixel-perfect spatial ground truths, comprising 6,799 high-fidelity reasoning trajectories. Our empirical results, supported by diagnostic probing, demonstrate that explicit spatial constraints significantly recover the reasoning potential of MLLMs. Furthermore, our two-stage decoupled framework achieves a robust 12.3% overall accuracy improvement on the test set. TableVision provides a rigorous testbed and a fresh perspective on the synergy between perception and logic in document understanding.

Multimodal reasoning has emerged as a powerful framework for enhancing reasoning capabilities of reasoning models. While multi-turn table reasoning methods have improved reasoning accuracy through tool use and reward modeling, they rely on fixed text serialization for table state readouts. This introduces representation errors in table encoding that significantly accumulate over multiple turns. Such accumulation is alleviated by tabular grounding methods in the expense of inference compute and cost, rendering real world deployment impractical. To address this, we introduce TABQAWORLD, a table reasoning framework that jointly optimizes tabular action through representation and estimation. For representation, TABQAWORLD employs an action-conditioned multimodal selection policy, which dynamically switches between visual and textual representations to maximize table state readout reliability. For estimation, TABQAWORLD optimizes stepwise reasoning trajectory through table metadata including dimension, data types and key values, safely planning trajectory and compressing low-complexity actions to reduce conversation turns and latency. Designed as a training-free framework, empirical evaluations show that TABQAWORLD achieves state-of-the-art performance with 4.87% accuracy improvements over baselines, with 5.42% accuracy gain and 33.35% inference latency reduction over static settings, establishing a new standard for reliable and efficient table reasoning.