arXiv:2608.17652 2026 Dynamics 1 ideas extracted · analyzed Sep 1, 2026
The paper formulates behavior assignment as asymptotic reproduction of a reference system's input-output behavior without requiring an explicit tracking error. Its transferable mechanism is a synchrony-detection coordinate whose zero set defines an invariant manifold; asymptotic stability of this manifold guarantees that the plant reproduces the reference behavior for every admissible open input. For neural networks, this suggests coupling a learned latent dynamical system to a reference dynamical system and explicitly stabilizing the transverse synchronization dynamics. The main falsifiable signature is a negative transverse Lyapunov exponent together with exponential decay of the synchronization residual, even from different initial attractors.
Pair a neural latent dynamical system with a reference latent system driven by the same external input, and train a coupling or controller so that a synchrony residual converges to zero. The target is transverse stabilization of a behavior-equivalence manifold rather than pointwise tracking of one selected trajectory or equilibrium.