arXiv Machine Learning By Anders Wikum, Nina Mishra, Amin Saberi, Tal Wagner

Learning Query Encoders Can Be Hard Even When Vector Retrieval Is Geometrically Easy

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The paper investigates the geometric capacity of vector retrieval systems, focusing on the maximum recall achievable with a fixed document index. It demonstrates that, on real-world benchmarks, single-vector query encoders often underperform relative to the index’s potential. The authors provide theoretical evidence that learning such encoders can be computationally hard, constructing a task where a simple neural network can achieve perfect recall while any statistical-query learner would need exponentially many queries to surpass random chance.

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