Mixing for Free Semigroup Actions of Blaschke Products on the Circle
arXiv:2608.13876
2026
Dynamics
1 ideas extracted · analyzed Sep 1, 2026
What the math gives to ML
The paper identifies a sharp mechanism for double-exponential mixing in analytic dynamics: a common fixed point with minimal local degree p greater than one causes correlations of analytic observables to decay like exp(-c p^t). The exponent is log p, while a nonzero multiplier produces only exponential mixing, giving a measurable regime boundary. A transferable neural-network construction is a bounded analytic latent recurrence with a shared superattracting fixed point, used as a controllable memory-erasure or state-mixing module; its usefulness must be tested through the predicted correlation-decay slope rather than benchmark accuracy alone.
Ideas from this paper
Unverified
2026
Replace or augment the transition map of a recurrent state-space model with bounded analytic maps of a latent complex coordinate, using several finite Blaschke generators that share a fixed point. Enforcing a superattracting fixed point of local degree p creates a tunable hierarchy of memory erasure: the theory predicts double-exponential decorrelation with exponent log p, while a merely attracting fixed point gives ordinary exponential decay.
Useful5/10
Difficulty7/10
Novelty9/10