Dithered quantization after a single randomized Hadamard transform yields unbiased estimates whose MSE asymptotically equals that of dense random rotations, specifically (π√3/2 + o(1))·4^{-b} for b-bit TurboQuant.
Improved analysis of the subsampled randomized
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Provable Quantization with Randomized Hadamard Transform
Dithered quantization after a single randomized Hadamard transform yields unbiased estimates whose MSE asymptotically equals that of dense random rotations, specifically (π√3/2 + o(1))·4^{-b} for b-bit TurboQuant.