Definition. Parameterization-stable training intervention [ftip-00BU]
Definition. Parameterization-stable training intervention [ftip-00BU]
Fix a factorized objective, an update algorithm, hyperparameter schedule, randomness coupling, stopping rule, and initial optimizer state. The resulting training intervention is parameterization-stable on an orthogonal orbit when every two gauge-related initial states have identical represented trajectories:
\[ \widetilde U_t\widetilde V_t^{\mathsf T}=U_tV_t^{\mathsf T} \qquad \hbox {at every compared step }t. \]This is a local stability property of a fully declared intervention. It does not say that arbitrary objective-equivalent pairs outside the orbit must agree.