Readable Factors, Unresolved Combinations: Support-Aware Correction for Warm-Start Recommendation

A warm item can combine factors a user has seen separately but never together, even when that combination occurs elsewhere in training. Standard warm-start metrics mix these cases with repeated combinations, while tests of globally unseen combinations study a different setting. We define a pre-cutoff evaluation cohort and use an independently fitted audit to test whether pair features add held-out ranking value beyond a frozen ranker and the individual factors. On H&M fashion and M3L movies, the audit finds a positive increment from purified pair features; pair permutations and equal-capacity random controls are near zero. We introduce Support-Aware Compositional Factor Residual (SCFR), which removes declared lower-order variation from pair features and uses train-only pairwise-logistic curvature to shrink weakly supported comparison directions. One correction scores every eligible warm-catalog item. The analysis states when a target comparison is identifiable and locally stable and gives a conditional squared-risk result for shrinkage when signal aligns with support. On the two confirmatory anchors, SCFR improves target NDCG@20 over the strongest matched-input control selected on validation by +0.0074 [0.0015, 0.0081] and +0.0083 [0.0014, 0.0094], corresponding to relative gains of 20.1% and 6.7%, while passing prespecified overall and non-target non-inferiority checks. Amazon Sports replicates the target-gain direction; controlled anti-alignment and weak-support tests show where the advantage vanishes or reverses.