Rerandomized Subsampled Trigonometric Transforms
A Lean formalization of a two-round real Walsh subsampled randomized Hadamard embedding. For every fixed d-dimensional real subspace of a Walsh space of dimension n, independent unbiased diagonal signs and a uniform sample of M distinct rows preserve every squared Euclidean norm within factors 1-epsilon and 1+epsilon with probability at least 1-delta. The prescribed M is at most n and at most [8192(1+432/delta)+1]d/epsilon^2. Thus, at any fixed failure probability, the embedding dimension is O(d/epsilon^2), the scaling asked for in Problem 5.6 of arXiv:2602.05394v3 for its Walsh model. The…
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