AI RESEARCH
Activation Saturation and Floquet Spectrum Collapse in Neural ODEs
arXiv CS.LG
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ArXi:2604.00543v1 Announce Type: cross We prove that activation saturation imposes a structural dynamical limitation on autonomous Neural ODEs $\dot{h}=f_\theta(h)$ with saturating activations ($\tanh$, sigmoid, etc.): if $q$ hidden layers of the MLP $f_\theta$ satisfy $|\sigma'|\le\delta$ on a region~$U$, the input Jacobian is attenuated as $\norm{Df_\theta(x)}\le C(U)$ (for activations with $\sup_{x}|\sigma'(x)|\le 1$, e.g.\ $\tanh$ and sigmoid, this reduces to $C_W\delta^q$), forcing every Floquet (Lyapuno) exponen along any $T$-periodic orbit $\gamma\subset U$ into the interval.