Differential positivity and dynamical order in noisy oscillators under unidirectional coupling

What the math gives to ML

The paper provides a nonstandard mechanism for extracting an asymptotically one-dimensional dynamical order from noisy, unidirectionally coupled oscillators. Its key asset is differential positivity: a suitable state-dependent random cone field is preserved by the tangent flow, while horizontal or conal curves contract toward an ordered one-dimensional structure. A transferable neural-network construction is a recurrent or state-space layer with nonnegative directed coupling plus a Jacobian-cone regularizer, designed to preserve order under perturbations and produce a measurable dominant tangent direction. The main falsifiable signature is near-zero cone violations and exponential decay of transverse tangent components, with a sharp loss of order when coupling or regularization crosses a computable threshold.