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Information Retrieval using dense low-dimensional representations recentlybecame popular and showed out-performance to traditional sparse-representationslike BM25. However, no previous work investigated how dense representationsperform with large index sizes. We show theoretically and empirically that theperformance for dense representations decreases quicker than sparserepresentations for increasing index sizes. In extreme cases, this can evenlead to a tipping point where at a certain index size sparse representationsoutperform dense representations. We show that this behavior is tightlyconnected to the number of dimensions of the representations: The lower thedimension, the higher the chance for false positives, i.e. returning irrelevantdocuments.

The Curse of Dense Low-Dimensional Information Retrieval for Large Index Sizes