Periodic-window probability conjecture for high-dimensional neural networks

Let $f$ be a mapping (neural network) and let $U$ be a bifurcation chain set as in the hyperbolicity violation conjecture. The periodic-window probability conjecture asserts that, in the asymptotic high-dimensional limit, the length $l=|a_n-a_1|$ of the bifurcation-chain-set interval increases, the cardinality of $U$ tends to $m$, where $m$ is the maximum number of positive Lyapunov exponents of $f$, and the probability, with respect to Lebesgue measure, of a periodic window on an interval such as $s\in(a_1,a_n)\sim(0.1,4)$ tends to zero. The paper treats this as an experimentally testable claim about the disappearance of periodic windows; the supplied status evidence does not resolve this exact conjecture.