Refining Encoding Strategies of Vector Embeddings in Analytical Database Systems

Abstract

This paper details the modification, experimentation, and evaluation of vector embedding input streams to three lossless floating-point compression algorithms: Adaptive Lossless Floating-Point Compression (ALP), Chimp, and Gorilla. Vector embeddings are commonly used in data-driven applications, but reaching an optimal storage and performance balance is often challenging. There is an opportunity to apply lossless floating-point compression algorithms as a strategy for compressing vector embeddings when high-precision is desired. Furthermore, there are many existing lossy approaches to encoding floating-points but there is less existing work for lossless approaches. A lossless approach would be more preferred in cases such as scientific or financial precision-based application needs. Based on the way the structure of the input stream of vector embeddings is encoded, the performance of traditional floating-point compression schemes is greatly improved. The compression ratio and speed efficiency of the following input processing strategies are evaluated to determine overall improvement: row order, column order, global sort, row sort, and equal-width binning. Through experimental trials, the floating-point compression algorithms best benefit from a global sort order. Given an input stream of vector embeddings, de-structuring them and globally sorting all values to provide to a compression algorithm yields a better compression ratio than the original input stream. However, this comes with a large overhead cost of storing indices of the original positions of each value to perform reconstruction of the vector embeddings. Through equal-width bin encoding, a compromise is made between overhead and performance on datasets. With an original per value size of 32 bits per float, the strategy obtains about a total of at most 20% reduced compression size on most datasets with ALP, 16% with Chimp, and 15% with Gorilla.