arXiv · cs.AI · Ran Ben-Basat, William Kuszmaul, Michael Mitzenmacher, Amit Portnoy, Shay Vargaftik · 8 小时前模型评分41
两次随机 Hadamard 变换可媲美均匀随机旋转：量化预处理启发式获理论证明
Quantizing With Randomized Hadamard Transforms: Efficient Heuristic Now Proven
导读
研究证明，对任意 d 维输入向量连续施加两次随机 Hadamard 变换（RHT，Randomized Hadamard Transform）后，归一化旋转向量各坐标的边缘分布与标准高斯分布在 Kolmogorov 距离和 1-Wasserstein 距离上相差 O(d^{-1/2})。
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中 · 待人工复核
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来源级别：媒体与个人
事件类型：研究发布
证据摘录
- “We show that after composing two RHTs on any $d$-sized input vector, the marginal distribution of every fixed coordinate of the normalized rotated vector is within $O(d^{-1/2})$ of a standard Gaussian both in Kolmogorov distance and in $1$-Wasserstein distance.”
- “However, while two RHTs suffice for scalar quantization, they may be insufficient for Vector Quantization (VQ), which depends on the joint distribution across fixed-size blocks of coordinates (as opposed to only marginal distribution convergence for single coordinates).”
- “We prove that a composition of three RHTs leads to decaying coordinate covariance.”
- “Finally, because practical inputs are rarely adversarial, we propose a linear-time $O(d)$ check on the input's moments to dynamically adapt the number of RHTs used at runtime to improve performance.”
来源：arXiv · cs.AI · arxiv.org