Synthesizing large logic programs through symbolic Inductive Logic Programming (ILP) typically requires intermediate definitions. However, cluttering the hypothesis space with invented predicates typically degrades performance. In contrast, gradient descent provides an efficient method to find solutions within high-dimensional spaces; a property not fully exploited by neuro-symbolic ILP approaches. We propose extending the differentiable ILP framework by large-scale (extending its small-scale) predicate invention to emulate search through a high-dimensional space, and thus allowing us to exploit the efficacy of gradient descent. We show that large-scale predicate invention is beneficial to differentiable inductive synthesis and results in learning capabilities beyond existing neuro-symbolic ILP systems. Furthermore, we achieve these results without specifying the precise structure of the solution within the inductive bias.