ADVENT: LLM-Driven Automatic Predicate Invention for ILP

Inductive Logic Programming (ILP) aims to learn interpretable first-order rules from data, but existing symbolic and neuro-symbolic approaches struggle to scale to noisy and probabilistic settings. Classical ILP relies on discrete combinatorial rule search and is brittle under uncertainty, while differentiable ILP methods typically depend on predefined rule templates or inaccurate fuzzy operators that suffer from vanishing gradients or poor approximation of logical structure when reasoning over probabilistic predicate valuations. This paper proposes an Attention-based Neuro-symbolic Differentiable Rule Extractor (ANDRE), a novel ILP framework that learns first-order logic programs by optimizing over a continuous rule space with attention-based logical operators. ANDRE replaces both rule templates and logical operators with fully differentiable, attention-driven conjunction and disjunction operators that approximate logical min-max semantics, enabling accurate, stable, and interpretable reasoning over probabilistic data. By softly selecting, negating, or excluding predicates within each rule, ANDRE supports flexible rule induction while preserving symbolic structure. Extensive experiments on classical ILP benchmarks, large-scale knowledge bases, and synthetic datasets with probabilistic predicates and noisy supervision demonstrate that ANDRE achieves competitive or superior predictive performance while reliably recovering correct symbolic rules under uncertainty. In particular, ANDRE remains robust to moderate label noise, substantially outperforming existing differentiable ILP methods in both rule extraction quality and stability.

Large Language Models (LLMs) can propose rules in natural language, sidestepping the need for a predefined predicate space in traditional rule learning. Yet many LLM-based approaches ignore interactions among rules, and the opportunity to couple LLMs with probabilistic rule learning for robust inference remains underexplored. We present RLIE, a unified framework that integrates LLMs with probabilistic modeling to learn a set of weighted rules. RLIE has four stages: (1) Rule generation, where an LLM proposes and filters candidates; (2) Logistic regression, which learns probabilistic weights for global selection and calibration; (3) Iterative refinement, which updates the rule set using prediction errors; and (4) Evaluation, which compares the weighted rule set as a direct classifier with methods that inject rules into an LLM. We evaluate multiple inference strategies on real-world datasets. Applying rules directly with their learned weights yields superior performance, whereas prompting LLMs with the rules, weights, and logistic-model outputs surprisingly degrades accuracy. This supports the view that LLMs excel at semantic generation and interpretation but are less reliable for precise probabilistic integration. RLIE clarifies the potential and limitations of LLMs for inductive reasoning and couples them with classic probabilistic rule combination methods to enable more reliable neuro-symbolic reasoning.

First-order concept synthesis asks a system to infer one formula that classifies labeled objects consistently across several finite relational structures. Every candidate can be evaluated exactly, but quantified first-order formulas form a vast search space, and LLM outputs are often semantically promising without being fully correct. We introduce Hypothesis Frontier, a verifier-guided neurosymbolic framework that evaluates each LLM formula on every training object, retains the strongest verified hypothesis across rounds, and uses its remaining errors to guide subsequent generation. Symbolic processing repairs invalid formulas while remaining anchored to the LLM-generated hypothesis, and simplifies train-valid formulas without changing any training prediction. Under matched models, problem sets, and LLM-round budgets, Hypothesis Frontier solves substantially more problems than repeated original-prompt generation. After the final formulas are selected, exact simplification shortens many train-valid formulas while preserving every training prediction. Exact symbolic reasoning therefore helps both to solve more induction problems and to compress many of the resulting formulas.