Certified benefits of cross-solver-trained correctors

Determine whether a learned corrector trained on candidates generated by numerical schemes other than zero-start conjugate gradient produces additional certified solver-frontier displacement beyond the improvement provided by those numerical schemes alone.

Background

The paper develops a bounded machine-learning corrector specifically for defects produced by zero-start conjugate-gradient gain computation in recursive Kalman estimation. The corrector operates within a prescribed gain-space subspace and norm budget, while residual certification and verified fallback independently determine whether the corrected candidate is executed.

The authors emphasize that the repairability and certification framework itself is not tied to conjugate gradient: preconditioned, warm-started, or otherwise generated gain candidates can be evaluated through the same interface. However, the learned map studied in the paper is fitted specifically to zero-start conjugate-gradient defects. It is therefore unresolved whether training correctors on candidates from other numerical schemes would yield certified solver-frontier improvements beyond the gains attributable to the alternative schemes themselves.