Prior-residual learning for ranking future influential nodes in temporal networks

Whether temporal learning adds anything to a strong structural forecast is rarely tested directly. We recast future influential-node ranking as a prior–residual problem: a chronologically selected centrality prior plus a learned correction whose weight is fixed on validation data before the test period is seen. Across nine networks the correction raises mean Kendall agreement by 0.0203 under the original protocol and by 0.0120 when tied scores are preserved, with a zero median and four positive networks. Because five of the nine differences are exactly zero, the adjusted test cannot discriminate, so we evaluate the correction as a decision rather than an average. Validation abstains in 26 of 45 fits and returns the prior unchanged; in the 19 fits where it opens, 17 gain. Residual structure is predictable out of sample (positive squared-error skill in 45 of 45 fits), yet head-node retrieval and graph-filtered features gain nothing. The contribution is an auditable rule for when a learned correction should be trusted.