Two randomized Hadamard transforms suffice to make coordinate marginals O(d^{-1/2})-close to Gaussian for most quantization methods, with three needed for vector quantization to match uniform random rotations asymptotically.
Since the eigenvalues of Σ lie in [1/2,3/2] , the eigenvalues of Σ−1/2 lie in hq 2 3 , √ 2 i
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Quantizing With Randomized Hadamard Transforms: Efficient Heuristic Now Proven
Two randomized Hadamard transforms suffice to make coordinate marginals O(d^{-1/2})-close to Gaussian for most quantization methods, with three needed for vector quantization to match uniform random rotations asymptotically.