Decay of Correlations for Partially Hyperbolic Skew-Products

What the math gives to ML

The paper develops a sectional transfer-operator framework for skew-products whose fibre dynamics contract only in an averaged logarithmic sense. Its main transferable mechanism is that pointwise contraction is unnecessary: a negative mean log-Lipschitz rate can still produce a unique invariant section, forgetting of fibre initialization, and exponential statistical control. In neural networks, this suggests separating an expressive base state from an input-conditioned auxiliary fibre state and regularizing only the fibre's average log-Jacobian gain. The key falsifiable prediction is a sharp stability transition when the measured average log gain crosses zero, with exponential perturbation decay below that boundary.