# A Note on TurboQuant and the Earlier DRIVE/EDEN Line of Work

arXiv: https://arxiv.org/abs/2604.18555 · HTML: https://mlsanity.com/paper/2604.18555/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 12 references that are in the map.
- First posted on arXiv 20 Apr 2026.

## Builds on (most cited first, 5 of 5)

- [TurboQuant: Online Vector Quantization with Near-optimal Distortion Rate](https://mlsanity.com/paper/2504.19874/) (2025)
- [EDEN: Communication-Efficient and Robust Distributed Mean Estimation for Federated Learning](https://mlsanity.com/paper/2108.08842/) (2021)
- [DRIVE: One-bit Distributed Mean Estimation](https://mlsanity.com/paper/2105.08339/) (2021)
- [QJL: 1-Bit Quantized JL Transform for KV Cache Quantization with Zero Overhead](https://mlsanity.com/paper/2406.03482/) (2024)
- [RaBitQ: Quantizing High-Dimensional Vectors with a Theoretical Error Bound for Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2405.12497/) (2024)

## Built on by (most cited first, 8 of 8)

- [Provable Quantization with Randomized Hadamard Transform](https://mlsanity.com/paper/2605.13810/) (2026)
- [Quantizing With Randomized Hadamard Transforms: Efficient Heuristic Now Proven](https://mlsanity.com/paper/2605.06014/) (2026)
- [Entropy-Constrained Adaptive Stochastic Quantization](https://mlsanity.com/paper/2608.18147/) (2026)
- [Block-Sphere Vector Quantization](https://mlsanity.com/paper/2605.19972/) (2026)
- [A Note on Scaling in Randomly Rotated Quantization and Its Connection to the CDEF +1 Pythagorean Relation](https://mlsanity.com/paper/2609.08759/) (2026)
- [TORQUE: Optimizing What (not) to Quantize Before and After Rotation](https://mlsanity.com/paper/2609.36032/) (2026)
- [WUSH-KV: KV Cache Quantization with Data-Adaptive Transforms](https://mlsanity.com/paper/2609.38121/) (2026)
- [Fast Quantized Johnson-Lindenstrauss Transforms](https://mlsanity.com/paper/2610.16289/) (2026)

## Abstract (arXiv)

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, TurboQuantmse 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 TurboQuantmse approaches EDEN's behavior for large d. Second, TurboQuantprod 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 TurboQuantmse, and unbiased EDEN is markedly more accurate than TurboQuantprod, often by more than a bit (e.g., 2-bit EDEN beats 3-bit TurboQuantprod). We also repeat all accuracy experiments from the TurboQuant paper, showing that EDEN outperforms it in every setup we have tried.