Gradient Conflict Is Frequent But Rarely Decisive: A Reproducible Boundary-Condition Study of Prioritized Gradient Projection in Multi-Behavior Recommendation

Industrial recommenders train on several behavioral signals at once (clicks, carts, purchases) by summing per-behavior contrastive losses over one shared embedding space. We ask a focused, reproducible question: does correcting gradient conflict between these objectives actually improve ranking quality or embedding geometry, and under what conditions? We run an empirical study -- proposing no new method -- comparing naive gradient summation, PCGrad, and an A-GEM-style asymmetric priority-preserving variant that shields a primary behavior (purchase) from modification and projects only non-primary gradients away from it on conflict. We evaluate two backbones: a shared lookup-embedding matrix-factorization model, where each behavior's minibatch touches a mostly disjoint (~18%-overlapping) subset of embedding rows, and a dense-encoder model (shared MLP over base ID embeddings), giving ~100% parameter overlap by construction. We test on two public multi-behavior benchmarks, Beibei and Tmall, measuring Recall@20/NDCG@20 alongside gradient-conflict frequency and effective rank. On the sparse backbone, gradient-sign conflict is frequent (39-49% of steps) on both datasets, yet PCGrad and our priority variant are statistically indistinguishable from naive summation on every metric. On the dense backbone, conflict for the primary-behavior pair rises to ~85%, and at 10 seeds both PCGrad and priority show an identical +3.7% relative Recall@20 gain over summation -- within about one standard error, not conventionally significant. More tellingly, effective rank moves in opposite directions for the two methods despite the identical ranking-quality gain, arguing against a single embedding-geometry mechanism explaining either effect. We report two findings without overclaiming: a clean, scale-invariant null result for sparse embedding architectures, and a precisely-measured but mechanistically inconsistent signal for dense encoders.