Neuro-symbolic Weak Supervision: Theory and Semantics

TL;DR

This work addresses learning under weak supervision in multi-instance partial label learning (MI-PLL) by proposing an ILP-based neuro-symbolic semantics that constrains neural learning with explicit relational knowledge. It formalizes CP, TP, and OP predicates and defines hypothesis spaces for the Transition Predicate and Classifier Predicate, linking predictions, observed weak labels, and object-relational structure. Through two scenarios—inferring TP and inferring CP—the paper provides a principled, logic-guided framework that enhances interpretability, robustness, and accountability in uncertain, partially observable environments. The approach holds promise for high-stakes applications by enabling explicit logical reasoning to accompany neural predictions, with future work focusing on differentiable ILP and broader applicability across domains.

Abstract

Weak supervision allows machine learning models to learn from limited or noisy labels, but it introduces challenges in interpretability and reliability - particularly in multi-instance partial label learning (MI-PLL), where models must resolve both ambiguous labels and uncertain instance-label mappings. We propose a semantics for neuro-symbolic framework that integrates Inductive Logic Programming (ILP) to improve MI-PLL by providing structured relational constraints that guide learning. Within our semantic characterization, ILP defines a logical hypothesis space for label transitions, clarifies classifier semantics, and establishes interpretable performance standards. This hybrid approach improves robustness, transparency, and accountability in weakly supervised settings, ensuring neural predictions align with domain knowledge. By embedding weak supervision into a logical framework, we enhance both interpretability and learning, making weak supervision more suitable for real-world, high-stakes applications.