Dynamics to decision: A mathematical theory of Lyapunov spectra and decision boundaries in deep classifiers
A deep classifier is defined not only by the decision it produces, but also by the sequence of transformations through which that decision is formed. Treating this evolution as a dynamical system across layers provides a natural framework for asking how decision geometry emerges through depth and how far back we can trace a boundary's dynamical signature. We model a feed-forward classifier as a finite, nonautonomous discrete dynamical system, with layers playing the role of discrete time steps. We study the Finite-Time Maximum Lyapunov Exponent (FTMLE) of the data samples' dynamical trajectory through depths of the classifier. The FTMLE measures the rate of convergence/divergence of nearb...
| Authors | Shirin Panahi, Amirhossein Nazerian, Ali Pezeshki |
|---|---|
| Primary category | cs.LG |
| Published | 30 September 2026 |
| Last updated at source | 30 September 2026 |
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