Explain the anomalous performance at γ=9 for standard map parameter inference using recurrence plots

Determine why, in the Chirikov standard map parameter inference using recurrence plots with initial conditions (q0, p0) = (δ × 10^{-γ}, π) and k in [0.1, 0.971635), the case γ = 9 exhibits worse regression accuracy (higher RMSE and lower c(m)) than γ = 7–8, contrary to the expected improvement as γ increases; identify the dynamical or methodological factors responsible for this anomaly.

Background

Appendix B investigates how the choice of γ in the initial conditions (q0, p0) = (δ × 10^{-γ}, π) for the standard map affects CNN-based regression of the nonlinearity parameter k from recurrence plots. The expectation was that bringing the initial condition closer to the unstable fixed point (increasing γ) would monotonically improve inference accuracy, reflected by lower RMSE and higher c(m).

Empirical results showed that while performance improved up to γ = 8, the case γ = 9 unexpectedly degraded (higher RMSE and lower c(m)), contradicting the anticipated trend. The authors explicitly note that the reason for this behavior is unclear and defer its resolution to future work.