The Problem of Multi-Vector Embeddings and High Dimensionality
A core theme in the discussion revolves around the practical challenges of using multi-vector or ColBERT-style embedding approaches. These methods, while sometimes offering improved retrieval performance, significantly increase computational costs due to the sheer dimensionality of the resulting vectors.
- trengrj highlights this issue: "When looking at multi-vector / ColBERT style approaches, the embedding per token approach can massively increase costs. You might go from a single 768 dimension vector to 128 x 130 = 16,640 dimensions. Even with better results from a multi-vector model this can make it unfeasible for many use-cases."
Muvera as a Solution: Compressing Multiple Vectors
Muvera is presented as a method to mitigate the cost and complexity of multi-vector embeddings by compressing them into a single, fixed-dimension vector. This allows existing ANN (Approximate Nearest Neighbor) indexing and quantization techniques to be utilized.
- trengrj explains Muvera's approach: "Muvera, converts the multiple vectors into a single fixed dimension (usually net smaller) vector that can be used by any ANN index. As you now have a single vector you can use all your existing ANN algorithms and stack other quantization techniques for memory savings."
- The perceived benefit is also stated: "In my opinion it is a much better approach than PLAID because it doesn't require specific index structures or clustering assumptions and can achieve lower latency."
The Nature of "Embedding of Embeddings" and Information Theory
Several users grapple with the theoretical implications of compressing multiple vectors into one. The core question is whether this compression sacrifices essential information, and if so, under what conditions it can still yield comparable performance.
- dinobones speculates on the effectiveness of such compression: "So this is basically an “embedding of embeddings”, an approximation of multiple embeddings compressed into one, to reduce dimensionality/increase performance. All this tells me is that: the majority of the value from ‘multiple embeddings’ is probably overlapping and the marginal value of each additional one is probably low, if you can represent them with a single embedding. I don’t otherwise see how you can keep comparable performance without breaking information theory."
- kevmo314 clarifies the underlying principle: "This is the point of the paper. Specifically, that single embedding vectors are sparse enough that you can compact more data from additional vectors together to improve retrieval performance." This counters the "overlapping" argument by suggesting sparsity allows for more efficient data packing.
Comparison to Other Dimensionality Reduction Techniques
Users draw parallels and distinctions between Muvera's approach and other dimensionality reduction methods like UMAP or feature hashing.
- bobosha inquires about alternative methods: "how is this different from generating a feature hash of the embeddings i.e reduce from many to one embedding reduction? Could a UMAP or such technique be helpful in reducing to a single vector?"
- dinkdonkbell points out a crucial difference with UMAP: "UMAP doesn't project values into the same coordinate space. While the abstract properties are the same between projections, where it projects it to in coordinate space won't be the same." This suggests that Muvera's approach might maintain a more consistent semantic space after compression.
The Token-Level to Fixed-Length Vector Transformation
A significant portion of the discussion dissects how Muvera (or similar techniques) transforms token-level embeddings into a fixed-length representation, highlighting similarities to clustering.
- nighthawk454 offers a detailed interpretation: "Seems to be a trend away from mean-pooling into a single embedding. But instead of dealing with an embedding per token (lots) you still want to reduce it some. This method seems to cluster token embeddings by random partitioning, mean pool for each partition, and concatenate the resulting into a fixed-length final embedding. Essentially, full multi vector comparison is challenging performance wise. Tools and performance for single vectors are much better. To compromise, cluster into k chunks and concatenate. Then you can do k-vector comparison at once with single-vector tooling and performance. Ultimately the fixed length vector comes from having a fixed number of partitions, so this is kind of just k-means style clustering of the token level embeddings."
- The same user also posits a potential improvement: "Presumably a dynamic clustering of the tokens could be even better, though that would leave you with a variable number of embeddings per document."
Retrieval Certainty and "Fuzziness"
One user raises a fundamental question about the reliability and precision of retrieval with compressed embeddings, comparing it to traditional SQL queries.
- lawlessone expresses concern about retrieval accuracy: "I'm only vaguely familiar with this. So I apologize how I phrase this. If make a basic sequel query to return all the first names in table, then i can generally expect it to return them all. If I do a similar query with these neural embeddings could i expect the same or is it more fuzzy?"
Computational Cost of FDE Calculation
The efficiency of calculating and storing the compressed representations (referred to as FDE - potentially "Fixed-Dimension Embedding") is also discussed in terms of indexing and retrieval.
- bawana questions the retrieval process: "Perhaps I misunderstood but it calculates the FDE of query and looks for a similar FDE in the dataset of the model. Doesnt this require calculating all the equivalent sized FDEs in the model?"
- moab clarifies that this can be an offline process: "Yes, but that can be done once at ingestion time. Then retrieval is done over the pre computed FDEs using MIPS." This indicates that while the initial computation is necessary, repeated calculation during retrieval is avoided.