Stability of interval translation maps is characterized by absence of critical connections and matching.
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A transversality theorem is proved for dynamically defined vector subspaces of interval translation maps, yielding a perturbation result that controls first-return dynamics while preserving global behavior.
Functionals of infinite-width random neural networks on the sphere exhibit phase transitions in fluctuations as depth grows, converging to a limiting Gaussian field functional, a Gaussian, or a Qth Wiener chaos distribution depending on covariance fixed points.
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Phase Transitions in the Fluctuations of Functionals of Random Neural Networks
Functionals of infinite-width random neural networks on the sphere exhibit phase transitions in fluctuations as depth grows, converging to a limiting Gaussian field functional, a Gaussian, or a Qth Wiener chaos distribution depending on covariance fixed points.