Hyperbolicity violation conjecture for high-dimensional neural networks

Let $f$ be a mapping (neural network) as defined in the paper, with sufficiently high dimension $d$. A hyperbolicity violation conjecture asserts that there exists at least one bifurcation chain subset $U$. The conjecture is motivated by the expected passage through bifurcations and neutral Lyapunov directions as the network dimension and parameters vary, but the supplied text gives no resolution.