Differentiable Inductive Logic Programming in High-Dimensional Space
This addresses a bottleneck in neuro-symbolic ILP for researchers, though it appears incremental as it builds on prior work.
The paper tackles the problem of synthesizing large logic programs in high-dimensional spaces by extending the δILP approach with large-scale predicate invention, enabling efficient gradient descent and learning solutions beyond existing neuro-symbolic ILP systems without specifying solution structure.
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.