Learning Reasoning Strategies in End-to-End Differentiable Proving

Abstract

Attempts to render deep learning models interpretable, data-efficient, and robust have seen some success through hybridisation with rule-based systems like Neural Theorem Provers (NTPs). These neuro-symbolic reasoning models can induce interpretable rules and learn representations from data via back-propagation, while providing logical explanations for their predictions. However, they are restricted by their computational complexity, as they need to consider all possible proof paths for explaining a goal, thus rendering them unfit for large-scale applications. We present Conditional Theorem Provers (CTPs), an extension to NTPs that learns an optimal rule selection strategy via gradient-based optimisation. We show that CTPs are scalable and yield state-of-the-art results on the CLUTRR dataset, which tests systematic generalisation of neural models by learning to reason over smaller graphs, and evaluating on larger ones. Finally, CTPs show better link prediction results on standard benchmarks in comparison with other neuro-symbolic reasoning models, while retaining their explainability properties.