  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.
