Binary Hyperbolic Embeddings

Teng Long, Pascal Mettes, Nanne Van Noord

Keywords: Hyperbolic, Binary

TL;DR: We binarize hyperbolic space for fast and compact vector-based search, while matching Euclidean embeddings' performance.

Abstract: As datasets grow in size, vector-based search becomes increasingly challenging in terms of both storage and computational efficiency. Traditional solutions such as quantization techniques involve trade-offs between retrieval speed and accuracy, while hashing methods often require further optimization for binarization. In this work, we propose leveraging the compact nature of hyperbolic space for efficient search. Specifically, we introduce Binary Hyperbolic Embeddings, which transform complex hyperbolic similarity calculations into binary operations. We prove that these binary hyperbolic embeddings are retrieval-equivalent to their real-valued counterparts, ensuring minimal loss in retrieval quality. Our approach can be seamlessly integrated into FAISS to achieve improved memory efficiency and running speed while maintaining performance comparable to full-precision Euclidean embeddings. \tblue{Notably, binary hyperbolic embeddings can also be combined with product quantization}. We demonstrate significant improvements in storage efficiency, with a natural byproduct of speeding up, with scaling potential to larger datasets. A portion of the code is included in the supplementary materials, and the full implementation will be made publicly available.

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

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Submission Number: 2725