Vector Embedding is a vector, a list of floating point numbers, that represents a piece of data so that the distance between two such vectors measures how related the underlying items are.
Google's Machine Learning Crash Course describes embeddings as lower-dimensional representations of sparse data and defines an embedding as a vector representation of data in embedding space. In that space, according to the course, words that are used in similar contexts will be closer to each other.
OpenAI's embeddings guide states that small distances suggest high relatedness and large distances suggest low relatedness. It recommends cosine similarity for comparing vectors, while noting that the choice of distance function typically doesn't matter much. The guide lists common uses: search ranked by relevance to a query string, clustering text strings by similarity, recommending items with related text, identifying outliers with little relatedness, analyzing similarity distributions to measure diversity, and classifying text strings by their most similar label.
📝Semantic Search applies embeddings to retrieval. As the Sentence Transformers documentation describes it, the entries of a corpus are embedded into a vector space, the query is embedded into the same space, and the closest corpus embeddings are found. In 📝MythOS, the 📝semantic search feature splits memos into chunks and embeds them with OpenAI's text-embedding-3-small model.