LinkedIn's engineering team details how they built MUSE (Member Understanding Semantic Embeddings), the semantic search system powering Hiring Assistant across 1.3B+ member profiles. The system uses a dual-tower Siamese LLM architecture producing Matryoshka embeddings (2048-dim for ANN retrieval, 4096-dim for L2 ranking). A scalable LLM-as-judge teacher system generates millions of qualification-match labels to fine-tune the embedding model with InfoNCE contrastive loss. Infrastructure uses a Lambda architecture with CDC-driven daily delta inference, IVFPQ indexing, and Apache Iceberg tables. Online A/B results show +2.7% highly-relevant candidate rate, +4.1% InMail sends per seat, and +1.8% InMail accepts — with fewer but better candidates surfaced. Key lessons: high-confidence LLM labels outperform human annotators on technical qualifications, contrastive post-training alignment matters more than model size for embedding tasks, and ANN approximation losses compound with post-filter losses.