用1.58比特编码实现高效嵌入搜索，精度损失小。
Ultra-Quantisation: Efficient Embedding Search via 1.58-bit Encodings
- 将浮点向量压缩为{-1,0,1}三值编码，实现极致量化
- 1.58比特/维编码下仍保持相似性测量高相关性
- 适用于对存储与计算速度要求极高的检索场景
现代搜索任务中，神经网络生成的高维浮点嵌入向量（数百至数千维）导致存储与比较开销巨大。量化通过将浮点数替换为短整数来压缩表示并加速计算。本文将此方法推向极致：证明任意精度浮点向量可被替换为元素仅取{-1,0,1}的向量，实现1.58比特/维的编码。该方法基于高维空间中的凸多面体结构，显著降低存储与度量计算成本，同时在相似性度量上仍保持强相关性，展现出惊人的精度保留能力。
原文摘要 · Abstract (English)
Many modern search domains comprise high-dimensional vectors of floating point numbers derived from neural networks, in the form of embeddings. Typical embeddings range in size from hundreds to thousands of dimensions, making the size of the embeddings, and the speed of comparison, a significant issue. Quantisation is a class of mechanism which replaces the floating point values with a smaller representation, for example a short integer. This gives an approximation of the embedding space in return for a smaller data representation and a faster comparison function. Here we take this idea almost to its extreme: we show how vectors of arbitrary-precision floating point values can be replaced by vectors whose elements are drawn from the set {-1,0,1}. This yields very significant savings in space and metric evaluation cost, while maintaining a strong correlation for similarity measurements. This is achieved by way of a class of convex polytopes which exist in the high-dimensional space. In this article we give an outline description of these objects, and show how they can be used for the basis of such radical quantisation while maintaining a surprising degree of accuracy.
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