Initialization Locking in Neural Heston Calibration: A Validation Hierarchy for Learned Inverse Maps

Calibrating a stochastic-volatility model is an inverse problem: its parameters are inferred from observed option prices, and learned pricing maps are used to make that inversion fast and differentiable. A Deep Galerkin (DGM) Heston calibrator trained at one parameter point and retained on one at-the-money contract can lock to its initialization. In a crossed 16-initialization by 3-seed warm design, recovered parameters track their starting guesses almost one-for-one (slopes 0.96–1.01; R² ≥ 0.94), with initialization accounting for over 99.99% of endpoint variance across the designed starts. Three controlled contrasts separate pricing-map fidelity from parameter-update behavior. Bounded trust-region least squares on a validated characteristic-function pricer converges from all 16 starts to a common 3.33%-error fit; matched-budget Adam on the same pricer partially tracks its starts; and two Jacobian-based least-squares solvers through the frozen surrogate yield median parameter errors of 109.0% and 122.5%. Among the tested arms, recovery occurs only with the validated map and a trust-region update. A four-level validation hierarchy locates the first failed gate. The checkpoint, selected for a 0.178% discrepancy on one contract, has 85.0% relative RMSE over the 42-contract surface at its training parameters. Under the actual relative-residual objective, one deep-out-of-the-money quote carries 99.5% of the surrogate's squared Jacobian norm, against 12.8% for the most influential quote of the validated map, whose own geometry is full rank but severely ill-conditioned. Single-contract accuracy is a screening metric rather than an inverse-use certificate: full-surface accuracy and objective-weighted sensitivity fidelity are necessary gates before optimizer comparisons can be interpreted parametrically.