DPNL: A DPLL-based Algorithm for Probabilistic Neurosymbolic Learning

Probabilistic Neurosymbolic Learning (PNL) combines neural predictions with symbolic reasoning, enabling end-to-end learning from final-output supervision without labels for intermediate concepts. A central challenge is probabilistic inference: state-of-the-art approaches often rely on materializing the logical provenance of a query, which can itself become a major computational bottleneck. We introduce Dynamic Probabilistic Neurosymbolic Learning (DPNL), an oracle-guided framework that avoids requiring complete provenance materialization before inference. DPNL lazily explores the space of intermediate assignments, while oracles resolve entire regions that can already be certified to produce or exclude the target output. We establish conditions ensuring soundness and termination. ApproxDPNL extends the same search with early termination while maintaining certified bounds on the exact output probability, providing controlled approximation guarantees. The oracle interface decouples inference from the representation of the symbolic component, enabling problem-specific reasoning within the same framework. Experiments on several neurosymbolic tasks show that DPNL and ApproxDPNL substantially extend the range of problem instances tractable by probabilistic neurosymbolic inference.