Understanding tabular semantics is essential for intelligent data management, yet data lake tables often lack explicit annotations, hindering interpretation of their structure and relations. Column Relation Extraction (RE), which identifies semantic relations between table columns, is a key step toward schema matching, data integration, and knowledge construction. Existing closed-set methods rely on predefined relation labels, while LLM-based generation offers greater flexibility but suffers from semantic ambiguity, coarse supervision, and inefficient pair-wise inference.

We propose a table-specific reinforcement learning framework for open-world RE. Instead of forcing predictions into a fixed label space, our method trains LLMs to generate free-form relations under fine-grained semantic feedback. We introduce a hierarchy-aware reward that converts semantic proximity into graded supervision, allowing the model to learn from near-miss predictions rather than treating all errors equally. We further propose relation-level policy optimization to improve efficiency: the model predicts all column-pair relations in one structured response, and each relation-level reward is assigned only to its corresponding token span. This reduces repeated table encoding and aligns optimization with relation-level correctness. Experiments demonstrate consistent improvements over strong LLM and table-specific baselines, especially on unseen relations and domains, highlighting the robustness and practicality for real-world table interpretation.

Relation Extraction (RE) is a key task in table understanding, aiming to extract semantic relations between columns. However, complex tables with hierarchical headers are hard to obtain high-quality textual formats (e.g., Markdown) for input under practical scenarios like webpage screenshots and scanned documents, while table images are more accessible and intuitive. Besides, existing works overlook the need of mining relations among multiple columns rather than just the semantic relation between two specific columns in real-world practice. In this work, we explore utilizing Multimodal Large Language Models (MLLMs) to address RE in tables with complex structures. We creatively extend the concept of RE to include calculational relations, enabling multi-task learning of both semantic and calculational RE for mutual reinforcement. Specifically, we reconstruct table images into graph structure based on neighboring nodes to extract graph-level visual features. Such feature enhancement alleviates the insensitivity of MLLMs to the positional information within table images. We then propose a Chain-of-Thought distillation framework with self-correction mechanism to enhance MLLMs’ reasoning capabilities without increasing parameter scale. Our method significantly outperforms most baselines on wide datasets. Additionally, we release a benchmark dataset for calculational RE in complex tables.