Asymptotic residual floor of the dP2 neural-network approximation

Determine the asymptotic residual floor of the neural-network approximation to the Sasaki–Einstein metric on the dP2 cone at the irregular volume-minimizing Reeb vector.

Background

The paper compares polynomial and neural-network parametrizations for approximating the dP2 Sasaki–Einstein metric. The neural-network runs at the irregular Reeb vector terminate because they exhaust the available evaluation budget rather than because they satisfy the optimizer’s convergence criterion. The reported residual therefore does not establish the best value attainable by the network class, and the limiting residual remains undetermined.

References

On the pentagon at $b{\ast}$ the network is still capped at $4.1\times10{-10}$, so its floor there is not known, and we make no extrapolation for it.

— Numerical Sasaki--Einstein metrics and harmonic forms on del Pezzo links  (2609.25857 - Kim et al., 22 Sep 2026) in Appendix B, Section “Robustness, convergence, and cost”