The Theoretical Limitations of Embedding-Based Retrieval

Their idea is that capacity of even 4096-wide vectors limits their performance.

Sparse models like BM25 have a huge dimension and thus don’t suffer from this limit, but they don’t capture semantics and can’t follow instructions.

It seems like the holy grail is a sparse semantic model. I wonder how splade would do?

We already have "sparse" embeddings. Google's Matryoshka embedding schema can scale embeddings from ~150 dimensions to >3k, and it's the same embedding with layers of representational meaning. Imagine decomposing an embedding along principle components, then streaming the embedding vectors in order of their eigenvalue, kind of the idea.

Doesn't PCA compress the embeddings in this case, ie reduce the accuracy? It's similar to quantization.