EFloat: Entropy-coded Floating Point Format for Compressing Vector Embedding Models (2102.02705v3)

Abstract: In a large class of deep learning models, including vector embedding models such as word and database embeddings, we observe that floating point exponent values cluster around a few unique values, permitting entropy based data compression. Entropy coding compresses fixed-length values with variable-length codes, encoding most probable values with fewer bits. We propose the EFloat compressed floating point number format that uses a variable field boundary between the exponent and significand fields. EFloat uses entropy coding on exponent values and signs to minimize the average width of the exponent and sign fields, while preserving the original FP32 exponent range unchanged. Saved bits become part of the significand field increasing the EFloat numeric precision by 4.3 bits on average compared to other reduced-precision floating point formats. EFloat makes 8-bit and even smaller floats practical without sacrificing the exponent range of a 32-bit floating point representation. We currently use the EFloat format for saving memory capacity and bandwidth consumption of large vector embedding models such as those used for database embeddings. Using the RMS error as metric, we demonstrate that EFloat provides higher accuracy than other floating point formats with equal bit budget. The EF12 format with 12-bit budget has less end-to-end application error than the 16-bit BFloat16. EF16 with 16-bit budget has an RMS-error 17 to 35 times less than BF16 RMS-error for a diverse set of embedding models. When making similarity and dissimilarity queries, using the NDCG ranking metric, EFloat matches the result quality of prior floating point representations with larger bit budgets.