Rapid convergence of FCM iterations

Establish a theoretical explanation for why the fast committor machine typically requires only a few iterations to successfully converge when updating the scaling matrix M via the recursive feature machine approach.

Background

The FCM alternates between optimizing kernel coefficients and updating a scaling matrix M based on gradients, inspired by the recursive feature machine. Empirically, few iterations (e.g., 3–6) suffice, but the authors explicitly identify this as a challenging, unresolved question.

A theoretical understanding of this rapid convergence would clarify the algorithm’s behavior and potentially lead to improved convergence guarantees or parameter choices.