arXiv Machine Learning September 7, 2026 By Rae Chipera, Jenny Du, Irene Tsapara

Fractal and Chaotic Activation Functions in Echo State Networks: Preprocessing Topology Governs the Echo State Property

Read the original on arXiv Machine Learning →

The study explores non‑smooth activation functions—chaotic, stochastic, and fractal—in echo state networks, testing 36,610 reservoir configurations. It finds that functions like the Cantor function preserve the Echo State Property (ESP) even at spectral radii up to 10, outperforming traditional smooth activations in convergence speed. The authors introduce a theoretical framework for quantized activations, defining a Degenerate Echo State Property (d‑ESP) that implies the traditional ESP, and show that preprocessing topology, rather than continuity, governs stability.

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