Neural Scalable Symbolic Search Framework for Complex Logical Queries with Multiple Free Variables

arXiv:2605.25985v2 Announce Type: replace
Abstract: Complex Query Answering (CQA) is a fundamental knowledge representation and reasoning task over incomplete knowledge graphs (KGs). Answering existential first-order queries with $k$ free variables (i.e., $textEFO_k$ queries) is a crucial yet challenging problem, as it requires ranking answer tuples in $mathcalE^k$, where $mathcalE$ denotes the entity set of a KG. This quickly becomes intractable as $k$ grows. Consequently, existing benchmarks and methods rely on marginal rankings over individual variables; however, marginal rankings are a poor proxy for the true joint ranking of tuples. Building on neural symbolic search for $textEFO_1$ queries, we propose Neural Scalable Symbolic Search (NS3), a budgeted framework that approximates joint ranking without enumerating $mathcalE^k$. NS3 (i) answers marginalized sub-queries to obtain necessary candidate sets, (ii) merges multiple free variables into hypernodes whose domains are pruned and controlled by a dynamic budget $B$, and (iii) progressively reduces an $textEFO_k$ query to an $textEFO_k-1$ query over a budgeted reduced domain. Across three standard KG datasets, NS3 substantially improves joint ranking performance while retaining strong marginal accuracy. We further release a joint-ranking benchmark that extends existing $textEFO_1$ datasets to $k=3$, enabling systematic evaluation of multi-variable queries. Our code is provided in https://github.com/HKUST-KnowComp/NS3_KDD2026.