Theoretical Limitations of Vector Embedding Models for Information Retrieval
By
fzliu
Lightly browned and well buttered. A solid pick from the rack.
Summary
This research paper examines the fundamental theoretical limitations of vector embedding models for retrieval tasks. The authors demonstrate that even state-of-the-art embedding models fail on simple queries due to inherent dimensional constraints, challenging the assumption that better training data or larger models can overcome these limitations. They connect learning theory results showing that the number of top-k document subsets returnable by embeddings is limited by embedding dimension, and create a realistic dataset called LIMIT that stress-tests models, revealing failures despite simple tasks.
Key quotes
· 5 pulledVector embeddings have been tasked with an ever-increasing set of retrieval tasks over the years, with a nascent rise in using them for reasoning, instruction-following, coding, and more.
While prior works have pointed out theoretical limitations of vector embeddings, there is a common assumption that these difficulties are exclusively due to unrealistic queries.
We demonstrate that we may encounter these theoretical limitations in realistic settings with extremely simple queries.
The number of top-k subsets of documents capable of being returned as the result of some query is limited by the dimension of the embedding.
Our work shows the limits of embedding models under the existing single vector paradigm and calls for future research to develop methods that can resolve this fundamental limitation.
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