Under what specific conditions would 'dot product' be a more appropriate vector similarity metric than 'cosine similarity' for retrieval in a RAG system?

Dot product is a mathematical operation that takes two vectors and returns a single scalar number representing their similarity, incorporating both their directional alignment and their magnitudes, which are their lengths. Cosine similarity, conversely, measures only the directional alignment between two vectors by first normalizing their magnitudes to unit length before calculating their dot product. Therefore, cosine similarity focuses purely on the angle between vectors, disregarding how long or short they are. Dot product becomes a more appropriate vector similarity metric than cosine similarity for retrieval in a Retrieval Augmented Generation (RAG) system under specific conditions where the magnitude of the embedding vectors is intentionally designed or trained to encode additional meaningful information beyond mere semantic direction. This means the embedding model explicitly assigns semantic relevance to vector length. One primary condition is when vector magnitude represents the import....