HCVR: Hypothesize, Compose, and Verify for Precise Multi-Table Retrieval

Text-to-SQL is increasingly deployed over a *pool* of tables, a data-lake-style repository that consolidates many source systems without database boundaries or declared foreign keys. Answering a query then starts with retrieval, which must find both the tables that hold the requested information and the tables needed to join them. Pooled-table retrievers to date rank candidates by how well each table matches the query, and a match alone cannot tell whether a table adds information or a connection that the tables already selected do not. We instead ask what role each table plays in answering the query: a table is a *provider* if it supplies one information requirement, a *connector* if it joins providers that would otherwise remain unjoined, and is excluded if it serves neither role. Under this criterion, competing providers of the same requirement and competing connectors of the same providers are resolved rather than all retained. We propose HCVR (**H**ypothesize, **C**ompose, and **V**erify for multi-table **R**etrieval), a training-free framework that treats every candidate as a hypothesis about its role. HCVR parses the query into typed requirements and retrieves provider candidates for each; it composes providers by bounded beam search and adds the connectors between them along minimum-hop paths in an inferred join graph; and it declares a role absent only after cross-verifying the composed set against an independent LLM selection. The whole procedure takes two to three LLM calls per query. On pooled BIRD, Spider, and MMQA with two retrieval LLMs, HCVR exceeds the best baseline in every setting by 10.7 to 31.2 precision points and 8.0 to 25.5 F1 points, while the fraction of queries whose gold tables are all retrieved stays within 3.9 points of the best baseline. With the retrieved tables frozen, the execution accuracy of two downstream SQL-generation LLMs improves on every corpus, by up to 11.8 points.