Differentiable Inductive Logic Programming in High-Dimensional Space
Stanisław J. Purgał, David M. Cerna, Cezary Kaliszyk
TL;DR
The paper tackles learning large-scale logic programs in ILP by enabling predicate invention within a differentiable ILP framework. They extend δILP to support many invented predicates and adopt a per-literal weight scheme to keep memory usage tractable while preserving gradient-based optimization. Empirical results on standard ILP tasks show that increasing the number of invented predicates improves success rates on hard tasks and that large-scale PI offers benefits beyond simple weight reinitialization. They also introduce a new complexity criterion focusing on the relation between input and body-only variables and discuss future directions including deeper integration with neural networks.
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 δILP 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.