Automorphic Nelson Dilations for Contractions and Invariant Subspace Tracking

What the math gives to ML

The paper constructs an analytic matrix-valued lift of a strict contraction by replacing each singular value with a disk automorphism. The transferable asset is a stable rational filter that agrees with the original matrix at z=0, is contractive inside the disk, and is unitary on the unit circle. This suggests recurrent and state-space neural layers with tunable memory and explicit non-expansive frequency behavior, avoiding exploding hidden dynamics without forcing the transition matrix itself to be unitary.