[Paper Review] Learning Reasoning Strategies in End-to-End Differentiable Proving

Pasquale Minervini, Sebastian Riedel+3 more|arXiv (Cornell University)|Jul 13, 2020

Intelligent Tutoring Systems and Adaptive Learning30 citations

TL;DR

The paper introduces Conditional Theorem Provers (CTPs), an extension of Neural Theorem Provers (NTPs) that learns adaptive, differentiable rule selection to enable scalable, interpretable neuro-symbolic reasoning, achieving state-of-the-art results on CLUTRR and competitive link prediction performance.

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.

Motivation & Objective

• Address limitations of Neural Theorem Provers (NTPs) in scalability due to exhaustive rule consideration.
• Develop a differentiable, goal-conditioned rule selection mechanism to prune the search space.
• Achieve state-of-the-art results on CLUTRR, testing systematic generalisation over graph-based reasoning tasks.
• Improve neural-symbolic reasoning performance on standard link prediction benchmarks while retaining explainability.

Proposed method

• Extend NTPs with a select module that generates a goal-conditioned, small set of rules for proving a given goal.
• Represent predicates and constants as continuous embeddings and use differentiable similarity measures for unification.
• Define select(G) to produce a head and body for a rule that is conditioned on the goal, enabling end-to-end differentiability.
• Introduce neural goal reformulation and memory-based reformulation options to generate or retrieve rules.
• Incorporate an attentive prior over predicates to prefer relations existing in the KB, via softmax attention over predicate embeddings.
• Provide a differentiable memory alternative for storing rules and indexing them via attention over memory, enabling inspectable reasoning paths.

Experimental results

Research questions

• RQ1 Can a differentiable, goal-conditioned selector reduce the need to consider all KB rules and improve scalability?
• RQ2 Does learning adaptive rule selection improve systematic generalisation on reasoning tasks like CLUTRR?
• RQ3 Do Conditional Theorem Provers (CTPs) yield better performance than traditional NTPs on standard benchmarks?
• RQ4 Can memory-based or attention-guided goal reformulation provide interpretable and competitive reasoning?

Key findings

• CTPs learn adaptive rule selection and scale to larger datasets where NTPs struggle.
• CTPs achieve state-of-the-art results on CLUTRR, demonstrating improved systematic generalisation.
• CTPs show better link prediction results on standard benchmarks compared with other neural-symbolic models while remaining explainable.
• The approach supports end-to-end differentiable training, enabling joint optimization of rule selection and reasoning.
• Code and datasets for CTPs are made available online, promoting reproducibility.