Bridging the Information Gap: Semantic Densification and Hindsight Distillation for Cold-Start Prediction

New-user cold-start is a critical bottleneck for e-commerce platforms: predicting user lifetime value (LTV) and conversion rate (CVR) for users with sparse interaction history. Two prior directions -- LLM-based semantic augmentation and learning using privileged information (LUPI) -- each face a key limitation. First, LLM augmentation produces unstructured rationales that are noisy and hard to operationalize in production. Second, naive student-teacher distillation can be brittle due to an information gap between the privileged teacher and the sparse student; moreover, this gap is heterogeneous across users. We propose SemRaD, a Semantic Reasoning-aware Distillation framework addressing both limitations. First, a Structured Semantic Reasoning Pipeline replaces free-form rationales with a structured schema built via a discover-curate-audit workflow, producing per user a Densified Semantic Profile (consumed by the deployed student via a Semantic-Gated Encoder that focuses on the most informative dimensions) and a Hindsight Distillation Target reconciled from pre- and post-conversion reasoning (used only at training). Second, to bridge this gap and handle its heterogeneity, a Hindsight-Aware Distillation Network transfers privileged knowledge via the hindsight target, with Distillation Experts improving transfer under per-user variability. On a large-scale industrial dataset, SemRaD lifts +1.9% LTV (Gini) and +1.0% CVR (AUROC) over a production-grade base; a four-week online A/B at Keeta confirms +1.0% LTV / +0.43% CVR. SemRaD also matches the production system's LTV using only 9% of the training data while improving CVR by 0.8%.