What is the difference between sparse and dense embeddings?

Dense embeddings are low-dimensional vectors, typically 384 to 3072 floats, where every dimension has a nonzero value and captures abstract semantic features. Sparse embeddings are high-dimensional vectors, often the size of the vocabulary, where most values are zero and nonzero entries correspond to specific terms with weights from algorithms like BM25 or learned methods like SPLADE. Dense embeddings excel at semantic similarity, while sparse embeddings handle exact keyword matches and rare terms better. Hybrid search combines both for best results.