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arXiv 提交日期: 2026-04-20
📄 Abstract - A Note on TurboQuant and the Earlier DRIVE/EDEN Line of Work

This note clarifies the relationship between the recent TurboQuant work and the earlier DRIVE (NeurIPS 2021) and EDEN (ICML 2022) schemes. DRIVE is a 1-bit quantizer that EDEN extended to any $b>0$ bits per coordinate; we refer to them collectively as EDEN. First, TurboQuant$_{\text{mse}}$ is a special case of EDEN obtained by fixing EDEN's scalar scale parameter to $S=1$. EDEN supports both biased and unbiased quantization, each optimized by a different $S$ (chosen via methods described in the EDEN works). The fixed choice $S=1$ used by TurboQuant is generally suboptimal, although the optimal $S$ for biased EDEN converges to $1$ as the dimension grows; accordingly TurboQuant$_{\text{mse}}$ approaches EDEN's behavior for large $d$. Second, TurboQuant$_{\text{prod}}$ combines a biased $(b-1)$-bit EDEN step with an unbiased 1-bit QJL quantization of the residual. It is suboptimal in three ways: (1) its $(b-1)$-bit step uses the suboptimal $S=1$; (2) its 1-bit unbiased residual quantization has worse MSE than (unbiased) 1-bit EDEN; (3) chaining a biased $(b-1)$-bit step with a 1-bit unbiased residual step is inferior to unbiasedly quantizing the input directly with $b$-bit EDEN. Third, some of the analysis in the TurboQuant work mirrors that of the EDEN works: both exploit the connection between random rotations and the shifted Beta distribution, use the Lloyd-Max algorithm, and note that Randomized Hadamard Transforms can replace uniform random rotations. Experiments support these claims: biased EDEN (with optimized $S$) is more accurate than TurboQuant$_{\text{mse}}$, and unbiased EDEN is markedly more accurate than TurboQuant$_{\text{prod}}$, often by more than a bit (e.g., 2-bit EDEN beats 3-bit TurboQuant$_{\text{prod}}$). We also repeat all accuracy experiments from the TurboQuant paper, showing that EDEN outperforms it in every setup we have tried.

顶级标签: model training theory machine learning
详细标签: quantization error analysis randomized algorithms compression 或 搜索:

关于TurboQuant与早期DRIVE/EDEN系列工作的说明 / A Note on TurboQuant and the Earlier DRIVE/EDEN Line of Work


1️⃣ 一句话总结

这篇论文澄清了近期TurboQuant量化方法与早期EDEN系列工作的关系,指出TurboQuant是EDEN在特定参数下的子集或次优组合,并通过实验证明优化后的EDEN方法在精度上全面优于TurboQuant。

源自 arXiv: 2604.18555