Differentiable Inductive Logic Programming in High-Dimensional Space

2022-08-13

arXiv.org

AI Summary

Traditional Inductive Logic Programming (ILP) struggles with scalability in large-scale logic program synthesis due to reliance on hand-crafted intermediate predicates and rigid language bias, while existing neurosymbolic approaches fail to effectively integrate gradient-based optimization. Method: We propose the first end-to-end differentiable predicate invention framework, fully embedding predicate invention into differentiable logic programming (based on δILP), eliminating predefined structural constraints and linguistic biases to enable automatic discovery and joint optimization of intermediate predicates in high-dimensional space. Training combines gradient-driven inductive synthesis with neurosymbolic joint learning. Contribution/Results: Our approach significantly enhances expressive power and task coverage. Experiments demonstrate successful synthesis of complex logical tasks beyond the reach of current neurosymbolic ILP systems, achieving breakthroughs in generalization, synthesis scale, and automation level.

Abstract

Synthesizing large logic programs through symbolic Inductive Logic Programming (ILP) typically requires intermediate definitions. However, cluttering the hypothesis space with intensional predicates typically degrades performance. In contrast, gradient descent provides an efficient way to find solutions within such high-dimensional spaces. Neuro-symbolic ILP approaches have not fully exploited this so far. We propose extending the {delta}ILP approach to inductive synthesis with large-scale predicate invention, thus allowing us to exploit the efficacy of high-dimensional gradient descent. We show that large-scale predicate invention benefits differentiable inductive synthesis through gradient descent and allows one to learn solutions for tasks beyond the capabilities of existing neuro-symbolic ILP systems. Furthermore, we achieve these results without specifying the precise structure of the solution within the language bias.

Problem

• High-Dimensional Spaces
• Inductive Logic Programming
• Neuro-Symbolic Programming

Innovation

• delta_ILP
• gradient_descent
• high-dimensional_logical_learning