Solve the combinatorial search problem in symbolic regression and inductive logic programming

Solve the combinatorial search problem that limits symbolic regression and inductive logic programming, including the difficulty of searching increasingly large hypothesis spaces and learning recursive programs.

Background

The paper presents symbolic regression and inductive logic programming as approaches that can induce exact structures and execute them, thereby addressing the continuous and relational limitations of fitted neural approximations. Their shared weakness is the combinatorial growth of the relevant hypothesis spaces.

The authors describe heuristic search, language biases, satisfiability-based compilation, and clause-learning methods as ways to reduce the burden, but state that these methods do not eliminate the underlying growth with program length. Recursive program learning is identified as an especially difficult case.

References

These methods move the boundary without removing it: the hypothesis space still grows combinatorially with program length, and learning recursive programs is harder still \citep{cohen1995recursive, cropper2020inductive}. The size of the combinatorial space is the main weakness the two paradigms share, and it is not yet solved.

— Exactness at Inference: A Representational Criterion for Out-of-Distribution Generalization  (2609.24942 - Rocha et al., 21 Sep 2026) in Section 9.3, “The combinatorial space, for both”