Dot product similarity measures vector similarity as their inner product, fundamental to attention and retrieval. Formula: A dot B = sum(a_i * b_i). Unbounded range. Interpretation: Higher = more similar (for unit vectors, equals cosine). Magnitude matters - longer vectors have higher products. Relation to cosine: For normalized vectors, dot product equals cosine similarity. Many systems normalize embeddings. In attention: Query dot key determines attention weight. High dot product = strong attention. Scaled by sqrt(d_k) for stability. For retrieval: Fast to compute, hardware-optimized (BLAS), works well for normalized embeddings. Maximum Inner Product Search (MIPS): Find vectors with highest dot product with query. Common retrieval formulation. When to use dot product vs cosine: Dot product when magnitude is meaningful (confidence, importance). Cosine when only direction matters. Implementation: Highly optimized in linear algebra libraries. GPUs excel at batch dot products. Vector databases: Support dot product and cosine, often convert between using normalization.