Bridge-Preserving Gradient Calibration for Replay in Neural Schrödinger Bridges

Replay reduces simulation costs in neural Schrödinger bridge training, but stale endpoint pairs can distort gradient updates. Matching intermediate-state distributions alone does not resolve this mismatch and may alter conditional bridge laws. We propose Bridge-Preserving Gradient Calibration (BPGC), which reweights intact replay endpoint pairs through a bounded convex gradient-matching objective and generates independent training bridges. We establish conditional bridge preservation and a finite calibration certificate, and derive update-error bounds that expose sampling noise and unmeasured gradient components. The analysis distinguishes projected calibration from full-gradient accuracy and identifies limitations from replay support and parameter drift. We specify an evaluation protocol that separates gradient fidelity from downstream quality and compares calibration with direct fresh-data use under matched computational budgets.