Learning Reasoning Strategies in End-to-End Differentiable Proving

TL;DR

This paper introduces Conditional Theorem Provers (CTPs), a scalable neural-symbolic reasoning model that learns optimal rule selection, achieving state-of-the-art results and better explainability in logical reasoning tasks.

Contribution

The paper proposes CTPs, an extension of Neural Theorem Provers, that learns rule selection strategies via gradient-based optimization, improving scalability and performance.

Findings

CTPs achieve state-of-the-art results on the CLUTRR dataset.

CTPs outperform other neural-symbolic models in link prediction benchmarks.

CTPs are scalable and provide interpretable reasoning processes.

Abstract

Attempts to render deep learning models interpretable, data-efficient, and robust have seen some success through hybridisation with rule-based systems, for example, in Neural Theorem Provers (NTPs). These neuro-symbolic 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 neural-symbolic models, while being explainable. All source code and datasets are available online, at https://github.com/uclnlp/ctp.