Characterize convergence as the lifted representation grows

Characterize how the SALTO lifted model converges as the number of lifted channels or the capacity of its representation increases, including whether and under what conditions its finite-amplitude predictions approach the measurements and sensitivities generated by the nonlinear solver.

Background

The SALTO construction uses a finite-dimensional learned lift whose physical-state block is anchored to the solver's tangent propagator and whose learned observables encode the nonlinear remainder. Numerical experiments compare a small number of channel counts and show improvements in some settings, but they do not establish a general convergence theory or limiting behavior.

The authors explicitly identify convergence of the lift as an open question. Resolving it would clarify whether increasing lifted dimension systematically improves forward measurements, gradients, and source-inference accuracy, and what notion of convergence is appropriate for the learned propagator and its transpose.