The Half-Life of Repairs: Why Fixes Fail under Continued Training and How to Make Them Last

Post-hoc repairs to a trained differentiable audio synthesizer—a frozen gain, an inserted filter, a reverb reparameterization—are routine and physically verifiable, yet continued training silently undoes them. We formulate repair persistence as an engineering objective and measure it with a pre-registered four-arm paired- continuation protocol and tri-state verdicts: unrepaired training, immediate re- pair, repair under continuation, and repair with behavioral anchoring. In a con- trolled cello-vocoder experiment, a +5.03 dB gain restores the median loudness drift from −5.03 to −0.0006 dB; after 15,000 continued-training steps the unan- chored arm degrades to −5.25 dB (R = −0.27, the repair-retention ratio; direc- tional, within the seed-variance band), the benefit halving within 500–1,000 steps (single-seed). Three instruments localize the cancellation to the harmonic and noise branches; output-level gradient pressure falls in all 12 instrumented runs. Anchoring is a fuse, not a retainer—no stable persistence advantage over plain repair (1/3 vs 1/3 seeds)—and the repair-plus-anchor package backfires on both URMP seeds. A 34-run, 13-arm, two-domain matrix shows erasure replicating at the gradient-instrument level; persistence tracks the calibration source (3/3 vs 1/3 seeds; not separable, Fisher p = 0.20). Claims cover the loudness-defect domain only. Contributions: a repair-visibility taxonomy; a persistence-time / compensation-path detection protocol; a constructive candidate route to durable repair.