Title: ANDRE: An Attention-based Neuro-symbolic Differentiable Rule Extractor for Inductive Logic Programming

Abstract: Inductive Logic Programming (ILP) seeks to derive interpretable first-order rules from data; however, current symbolic and neuro-symbolic techniques face significant challenges in scaling to environments characterized by noise and probability. Traditional ILP methods depend on discrete combinatorial searches for rules, rendering them fragile when handling uncertainty. Meanwhile, differentiable ILP approaches often rely on fixed rule templates or imprecise fuzzy operators, which can lead to vanishing gradients or inadequate approximations of logical structures during reasoning with probabilistic predicate values. To address these limitations, this study introduces ANDRE (Attention-based Neuro-symbolic Differentiable Rule Extractor), a new ILP framework designed to learn first-order logic programs by optimizing across a continuous rule space using attention-based logical operators. ANDRE substitutes traditional rule templates and logical operators with fully differentiable, attention-driven mechanisms for conjunction and disjunction that mimic logical min-max semantics. This approach facilitates accurate, stable, and interpretable reasoning over probabilistic datasets. By employing soft selection, negation, or exclusion of predicates within rules, ANDRE enables flexible rule induction while maintaining symbolic integrity. Comprehensive experiments conducted on standard ILP benchmarks, large-scale knowledge bases, and synthetic datasets featuring probabilistic predicates and noisy supervision reveal that ANDRE delivers competitive or enhanced predictive performance. Crucially, it reliably extracts correct symbolic rules even under uncertainty. Notably, ANDRE demonstrates robustness to moderate label noise, significantly surpassing existing differentiable ILP methods in both the quality of extracted rules and overall stability.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC