 Furthermore, we relate the norms of the local linear operators to the energy stored in the dissipated system with supply rates represented by their aggregate bias terms. Finally, empirically, we analyze the variance in dynamical behavior and eigenvalue spectra of these local linear operators with varying weight factorizations, activation functions, bias terms, and depths. This article was authored by Jan Drogona, Aaron Tuer, Somia Vasisht, and others.