Data-Free Continual Model Merging: Arrival Order, Not Missing Data, Is the Bottleneck

Continual model merging folds a stream of task experts into one deployed model, one at a time, with neither joint retraining nor the data any expert was trained on, and without revisiting one already absorbed. The merge step is denied what one-shot merging takes for granted: the data and the whole pool. However, the gap is read as a data problem, and the remedy is not free: calibration needs labelled samples at every arrival, which raises the merge cost, and data saturates within a few samples per task. In addition, arrival order goes unpriced, though taking the stream in order costs a data-free rule up to 18.9 points. To address those issues, we hold pool, backbone and evaluator fixed, price each constraint on its own, and propose SCOPE (Sign-Conflict, Order-scaled, Parameter-class Estimation), a merge-time-data-free operator of three scalars. Moreover, the constraints interact rather than add: the order penalty is large for a data-free rule and nearly vanishes for a calibrated one. On eight CLIP ViT-B/32 experts over thirty arrival orders, SCOPE improves on the machine-designed operator of our earlier search by a small but consistent margin. Two results bound the claim: parity on longer streams needs the damping scaled by stream length, and automated discovery is blocked by the fitness signal. These results argue for measuring the order constraint on its own terms, since a data-free number need not transfer from a pool to a stream.