Programmatic Reasoning with Structural Schema: A Unified Framework for Multi-Table Inference

Large language models (LLMs) have shown strong performance in single-table reasoning but struggle to generalize to multi-table scenarios due to schema heterogeneity, long input contexts, and the lack of structural awareness. We introduce StrucTab-R1, a schema-centric reasoning framework that decouples relational reasoning from raw data exposure. Our approach encodes relational databases as heterogeneous schema graphs, where tables, columns, and foreign-key constraints form distinct node and edge types, and employs a heterogeneous graph encoder with question-conditioned cross-attention pooling to distill compact, semantically grounded schema tokens. Rather than serializing table rows into the context, the LLM plans over the schema representation and emits a Chain-of-Execution: an executable reasoning trace that first identifies the relevant schema subgraph and then performs a sequence of composable tool-function calls (e.g., filter, join, aggregate). These calls are executed externally, with compact observations returned to support subsequent reasoning steps. This design confines the model's attention to relevant subgraphs, mitigating hallucinations in multi-hop join reasoning. To further improve reliability, we train the model with supervised traces followed by structure-aware reinforcement learning, where the reward jointly optimizes answer correctness, schema-region precision, and execution consistency. Experiments on single-table and multi-table benchmarks show that StrucTab-R1 improves execution accuracy over strong general-purpose and table-specialized LLMs and remains effective on large-schema settings where raw-context baselines fail.