Dimensionality reduction compresses high-dimensional embeddings to lower dimensions while preserving similarity structure. Why reduce: Lower storage costs, faster similarity search, reduce noise, enable visualization. Methods: PCA: Linear projection to principal components. Fast, effective for linear structure. UMAP: Preserves local and global structure. Good for visualization. t-SNE: Preserves local structure. Primarily for 2D/3D visualization. Autoencoders: Learn nonlinear compression. Can be fine-tuned. Random projection: Fast, simple, works via Johnson-Lindenstrauss lemma. Trade-offs: Information loss, reconstruction error, changed similarity rankings. Validate that downstream task performance is acceptable. Typical reductions: 1536-dim to 256-dim or 512-dim common. Aggressive reduction (to 64) may hurt quality. For vector search: Smaller vectors = faster search, less memory. But may need to evaluate more candidates to maintain recall. Training on data: PCA, autoencoders need to be fit on representative data. Matryoshka embeddings provide built-in reduction. Evaluation: Compare retrieval quality at different dimensions. Find acceptable trade-off point.