Factorized Initialization for Few-Step Adaptation in Time-Series Forecasting

Few-step adaptation in time-series forecasting leaves little optimization time to repair a poor start. We ask whether reusable transfer and current-support evidence should be encoded by one complete conditional update or by two explicit initialization paths. Statistical Sequence-Conditioned Initialization (SSCI) implements the latter: a learned shared displacement provides the reusable start, and a bounded support-conditioned correction specializes it before a fixed adaptation procedure. Shared-5, our reference, adapts the pretrained shared base for five support updates. Under a matched complete-update projection, factorization improves Shared-5-relative query gain over a complete conditional generator by 3.88 percentage points (pp) on External-7 and 4.59 pp on a temporal-split Monash replication. Within one jointly trained checkpoint, enabling the correction improves all six held-out real sources, with a source-equal mean of 3.44 pp. Statistics alone provide a competitive conditioning signal on External-7; the real-suite branch effect persists from zero to 20 support updates and recurs across three host architectures. The results show that explicitly separating shared transfer from support-conditioned specialization can improve the starting point supplied to a constrained optimizer.