On the model attractor in a high-dimensional neural network dynamics of reservoir computing

The paper establishes (A)–(C) only empirically: it computes Lyapunov spectra across spectral radii ρ and observes that λ1 ≈ Λ1 for all tested ρ, that λ2 ≈ Λ2 for small ρ while for larger ρ one finds λ3 ≈ Λ2, and that exponents restricted to the two-dimensional manifold match the actual ones; it then summarizes these observations broadly (e.g., “for any spectral radius ρ”) without a proof or quantified hypotheses about training limits, manifold existence, or normal hyperbolicity . The candidate model gives a plausible mechanism via an invariant graph and C^1-conjugacy, but it relies on unproven assumptions (exact readout P∘Ψ=Id, an implicit bound ‖A‖≤ρ, and persistence of the manifold for all ρ) and does not verify the domination needed for persistence. Hence both are directionally consistent but incomplete.