Thinking with Tables: Enhancing Multi-Modal Tabular Understanding via Neuro-Symbolic Reasoning

Table images preserve structural information that are often lost in text serialization, and reasoning over them requires locating relevant rows, columns, and cells step by step. Current multimodal large language models (MLLMs) encode the whole image once before reasoning, so they cannot pick up row-, column-, and cell-level evidence as the question unfolds. Encoder-side table structure and generic interleaved visual chain-of-thought still do not bind each reasoning step to that structure. We propose InterTab, an Interleaved structure-aware framework for CoT reasoning over Table images, interleaves chain-of-thought with tool calls that crop structure-aligned table regions. First, we build InterTab-22K, includes reasoning trajectories in which each step is tied to both a structural location and a bounding box. InterTab is trained in two stages: supervised structure-aware alignment (SSA) on InterTab-22K teaches the model to interleave reasoning with structure-aligned crops, and active localization optimization (ALO) further optimizes answer correctness, localization IoU, and output format, while penalizing missing or excessive tool calls. Experiments on nine table benchmarks show that InterTab improves the average accuracy of its backbone from 68.28% to 73.17% and achieves the best average performance among all compared methods. Code and data will be released soon.

Despite the success of Large Language Models (LLMs) in table understanding, their internal mechanisms remain unclear. In this paper, we conduct an empirical study on 16 LLMs, covering general LLMs, specialist tabular LLMs, and Mixture-of-Experts (MoE) models, to explore how LLMs understand tabular data and perform downstream tasks. Our analysis focus on 4 dimensions including the attention dynamics, the effective layer depth, the expert activation, and the impacts of input designs. Key findings include: (1) LLMs follow a three-phase attention pattern -- early layers scan the table broadly, middle layers localize relevant cells, and late layers amplify their contributions; (2) tabular tasks require deeper layers than math reasoning to reach stable predictions; (3) MoE models activate table-specific experts in middle layers, with early and late layers sharing general-purpose experts; (4) Chain-of-Thought prompting increases table attention, further enhanced by table-tuning. We hope these findings and insights can facilitate interpretability and future research on table-related tasks.

Reasoning over tabular data is a crucial capability for tasks like question answering and fact verification, as it requires models to comprehend both free-form questions and semi-structured tables. However, while methods like Chain-of-Thought (CoT) introduce reasoning chains, purely symbolic methodes are inherently limited by their blindness to holistic visual patterns. To address this, we propose the Coarse-to-Fine Multimodal Synthesis framework (CFMS), a novel two-stage paradigm that hierarchically decouples high-level visual perception from granular symbolic reasoning. In the Coarse Stage, CFMS leverages the Multimodal Large Language Models (MLLMs) to perform a one-time synthesis of a multi-perspective knowledge tuple. This tuple subsequently serves as a dynamic reasoning map to guide the fine stage, where a symbolic engine executes a targeted and efficient sequence of iterative operations over the table. Extensive experiments on the WikiTQ and TabFact benchmarks demonstrate that CFMS achieves competitive accuracy. The framework exhibits particular robustness when handling large tables and when instantiated with smaller backbone models, validating its effectiveness and generalizability.