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.

本文提出了一种名为Conditional Theorem Provers（CTPs）的方法，它是Neural Theorem Provers（NTPs）的扩展，可以通过基于梯度的优化学习出最优规则选择策略以实现可解释性和可扩展性，并且在大规模任务中表现优异。CTPs在CLUTRR数据集上取得了表现最优结果，并在标准基准测试中展现了比其他神经符号模型更好的链接预测结果。

端到端可导证明中学习推理策略