Formal guarantees for PSN reflection and refactoring

Establish formal theoretical guarantees for the reflection and refactoring process in Programmatic Skill Networks (PSN), including a well-defined projection operator in the symbolic program space and rigorous proofs of convergence and optimality for the resulting learning dynamics.

Background

The paper introduces Programmatic Skill Networks (PSN), where skills are executable programs connected in a compositional network. Learning is driven by a reflection mechanism for fault localization and an online structural refactoring module that reorganizes the network.

While empirical results show stable improvements, the authors explicitly note the absence of formal guarantees. Specifically, they highlight the lack of a formal projection guarantee in the symbolic program space and that theoretical properties such as projection, convergence, and optimality have not yet been established.