The authors show that the claimed improvement by Song, Ye, Yin and Zhang to ℓ∞-accurate sketch-and-solve regression rests on an independence assumption that fails, and they exhibit an explicit counterexample. Building on work by Price, Song and Woodruff, they propose a new dense randomized transform—combining Hadamard flattening, a random permutation, and Gaussian pooling—that achieves the ℓ∞ guarantee with O(ε⁻² d log d) rows in Õ(nd + ε⁻² d⁴) time.
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