Learning Reasoning Strategies in End-to-End Differentiable Proving (2007.06477v3)

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.

• The paper introduces Conditional Theorem Provers (CTPs), enhancing neuro-symbolic reasoning with goal-conditioned rule selection.
• It employs differentiable goal reformulation via linear transformations, attention mechanisms, and memory-based methods to reduce the proof search space.
• CTPs achieved state-of-the-art performance on benchmarks such as CLUTRR, demonstrating improved scalability and efficiency in logical inference.

Learning Reasoning Strategies in End-to-End Differentiable Proving

The paper "Learning Reasoning Strategies in End-to-End Differentiable Proving" addresses one of the central challenges in neuro-symbolic reasoning—scaling up differentiable logic-based models for practical use. The work primarily extends Neural Theorem Provers (NTPs) by introducing Conditional Theorem Provers (CTPs), which leverage differentiable optimization techniques to make the rule selection process more computationally efficient.

Overview of Neuro-Symbolic Reasoning

Neuro-symbolic models, such as NTPs, aim to incorporate the advantages of deep learning with logical reasoning capabilities. NTPs operate by converting symbolic reasoning processes into neural network structures that can be trained end-to-end via backpropagation. They achieve this by allowing for soft unification between symbolic entities through their continuous vector embeddings. While advantageous in terms of producing interpretable models and potentially robust rule-based explanations, NTPs inherently require consideration of all potential proof paths, a limitation in terms of scalability.

Innovations in Conditional Theorem Provers

CTPs innovate by introducing a mechanism that selectively compiles rules during the reasoning process based on the specific subgoal in question. This selectivity is implemented through:

1. Differentiable Goal Reformulation: CTPs conditionally generate the minimal set of required rules via neural network architectures, conditioned specifically on the goal being addressed. This results in a significant reduction of the proof search space.
2. Implementation Strategies:
   • Linear Transformation: Utilizing linear mappings from goal predicates to rule predicates.
   • Attention Mechanisms: Adopting attention mechanisms to weigh predicate possibilities against a set of known relations.
   • Memory-Based Methods: Storing rules in a differentiable memory format, allowing for an efficient retrieval mechanism that scales more naturally to larger datasets.

Performance on Benchmark Datasets

The CTP framework was evaluated across various tasks, notably systematic generalization with the CLUTRR dataset and link prediction tasks in standard Knowledge Graph (KG) benchmarks. CTPs achieved state-of-the-art performance in reasoning over family relationship graphs, showcasing their ability to generalize beyond the training set size by leveraging learned reasoning strategies. In link prediction tasks, CTPs outperformed or were on par with existing neuro-symbolic and logical reasoning architectures, indicating significant improvements in both efficiency and scalability.

Implications and Future Directions

The implications of this research extend to creating AI systems that can make complex reasoning tasks interpretable, data-efficient, and scalable. The ability to learn reasoning rules and strategies dynamically, conditioned on specific goals, presents broad applicability across domains requiring logical inference, such as biomedical datasets or large-scale knowledge systems.

Future research could focus on integrating CTPs with textual data inputs to handle reasoning directly from natural language, addressing tasks where relationships are not pre-defined but inferred from raw text. The continued refinement of attention-based goal reformulation strategies could further enhance the robustness and versatility of neuro-symbolic AI applications.

This paper not only contributes to the field by alleviating scalability issues in neuro-symbolic reasoning but also provides a structured pathway for future developments that blend learning-based models with classical logic reasoning methodologies.