TurboQuant's Relationship to DRIVE and EDEN Quantization Schemes Clarified
A recent update sheds light on the connection between TurboQuant and the previous quantization methods, DRIVE (NeurIPS 2021) and EDEN (ICML 2022). DRIVE serves as a 1-bit quantizer, while EDEN expands this to any b>0 bits per coordinate. TurboQuant_mse represents a specific case of EDEN, utilizing a scalar scale of S=1, which, although generally not optimal, approaches optimality in higher dimensions. On the other hand, TurboQuant_prod merges a biased (b-1)-bit EDEN step with an unbiased 1-bit QJL residual quantization. However, it falls short in three aspects: the (b-1)-bit step employs the suboptimal S=1, and the overall configuration lacks efficiency.
Key facts
- DRIVE is a 1-bit quantizer from NeurIPS 2021.
- EDEN extends DRIVE to any b>0 bits per coordinate (ICML 2022).
- TurboQuant_mse is a special case of EDEN with S=1.
- Optimal S for biased EDEN converges to 1 as dimension grows.
- TurboQuant_prod combines biased (b-1)-bit EDEN with unbiased 1-bit QJL.
- TurboQuant_prod is suboptimal due to suboptimal S=1 and inefficient combination.
- The note is from arXiv:2604.18555v1.
- The schemes are relevant to machine learning quantization.
Entities
Institutions
- NeurIPS
- ICML
- arXiv