פונקציות פראקטליות וקאוסטיות ברשתות Echo State: טופולוגיה של עיבוד קודם קובעת את התכונה Echo State

תקציר מקורי באנגליתarXiv:2512.14675v2 Announce Type: replace Abstract: Contemporary reservoir computing relies heavily on globally Lipschitz, well-behaved activation functions, limiting applications in defense, disaster response, and pharmaceutical modeling where robust operation under extreme conditions is critical. We systematically investigate non-smooth activation functions, including chaotic, stochastic, and fractal variants, in echo state networks. Through parameter sweeps across 36,610 reservoir configurations, we demonstrate that several non-smooth functions not only maintain behavior consistent with the Echo State Property (ESP) but outperform traditional smooth activations in convergence speed and spectral radius tolerance. Notably, the Cantor function (continuous everywhere, zero derivative almost