Learning Reasoning Strategies in End-to-End Differentiable Proving

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.Comment: Proceedings of the 37th International Conference on Machine Learning (ICML 2020

Measuring Systematic Generalization in Neural Proof Generation with Transformers

We are interested in understanding how well Transformer language models (TLMs) can perform reasoning tasks when trained on knowledge encoded in the form of natural language. We investigate systematic generalization abilities on an inductive logical reasoning task in natural language, which involves reasoning over relationships between entities grounded in first-order logical proofs. Specifically, we perform soft theorem-proving by leveraging TLMs to generate logical proofs represented in natural language. We systematically test proof generation capabilities, along with inference capabilities leveraging the generated proofs. We observe length-generalization issues in proof generation and inference when evaluated on longer-than-trained sequences. However, we observe TLMs improve their generalization performance after being exposed to longer, exhaustive proofs. In addition, we discover that TLMs are able to generalize better using backward-chaining proofs compared to their forward-chaining counterparts, while they find it easier to generate forward chaining proofs. We observe that models that are not trained to generate proofs are better at generalizing to problems based on longer proofs. This result suggests that Transformers have efficient, yet not interpretable reasoning strategies internally. These results also highlight the systematic generalization issues in TLMs in the context of logical reasoning, and we believe this work will motivate deeper inspection of their underlying reasoning strategies.Comment: NeurIPS 2020; 17 pages; 9 figures; 6 table

Complex Query Answering on Eventuality Knowledge Graph with Implicit Logical Constraints

Querying incomplete knowledge graphs (KGs) using deep learning approaches can naturally leverage the reasoning and generalization ability to learn to infer better answers. Traditional neural complex query answering (CQA) approaches mostly work on entity-centric KGs. However, in the real world, we also need to make logical inferences about events, states, and activities (i.e., eventualities or situations) to push learning systems from System I to System II, as proposed by Yoshua Bengio. Querying logically from an EVentuality-centric KG (EVKG) can naturally provide references to such kind of intuitive and logical inference. Thus, in this paper, we propose a new framework to leverage neural methods to answer complex logical queries based on an EVKG, which can satisfy not only traditional first-order logic constraints but also implicit logical constraints over eventualities concerning their occurrences and orders. For instance, if we know that ``Food is bad'' happens before ``PersonX adds soy sauce,'' then ``PersonX adds soy sauce'' is unlikely to be the cause of ``Food is bad'' due to implicit temporal constraint. To facilitate consistent reasoning on EVKGs, we propose Complex Eventuality Query Answering (CEQA), a more rigorous definition of CQA that considers the implicit logical constraints governing the temporal order and occurrence of eventualities. In this manner, we propose to leverage theorem provers for constructing benchmark datasets to ensure the answers satisfy implicit logical constraints. We also propose a Memory-Enhanced Query Encoding (MEQE) approach to significantly improve the performance of state-of-the-art neural query encoders on the CEQA task