Determine whether nested recursive states provide complementary functions

Determine whether the persistent fast and intermediate states in Fractal Recursion learn useful, complementary functions when recursively updated through a shared operator across computational scales.

Background

Fractal Recursion augments recursive architectures with a persistent intermediate state that integrates repeated updates of a faster state and subsequently conditions further refinement. The proposed organisation is intended to support computation at different temporal or computational scales while preserving parameter sharing.

The paper explicitly distinguishes this question from the broader hypothesis that nesting improves predictive performance: the experiments do not establish what functions the persistent states learn or whether those functions are complementary. The issue remains unresolved because the evaluated HRM-F, TRM-F, and URM-F configurations also alter state coupling, input injection, gradient propagation, or computational schedules.