Spectral-gap-aware Jacobi whitening

Integrate this into the approximate symmetric eigendecomposition used by a whitening, covariance-normalization, K-FAC-style preconditioner, or spectral-regularization layer. Given a symmetric d by d covariance or curvature proxy A, maintain an accumulated orthogonal matrix Q = I and perform only K Jacobi rotations rather than iterating to full convergence. At each step, compute candidate scores s_ij = A_ij^2/(abs(A_ii-A_jj)+epsilon), optionally mask pairs already processed in the current sweep, and select the largest score. For the selected pair, compute tau, t, c, and s using the formulas above. Update the affected rows and columns of A by A <- J transpose A J, and update Q <- Q J. After K rotations, use the diagonal of A as approximate eigenvalues and Q as approximate eigenvectors. For whitening, construct W = Q diag((diag(A)+delta)^(-1/2)) Q transpose, with delta added for positive definiteness. Use epsilon equal to 10^-6 times the mean diagonal magnitude and delta equal to 10^-5. The mathematical score and rotation are fixed by the paper; estimate A empirically from minibatch activations. Compare against magnitude pivoting based on abs(A_ij), random pivoting, and a full eigendecomposition baseline. Start with a two-layer MLP on CIFAR-10, whitening 128-dimensional hidden activations, and test K in {d, 2d, 4d} using FP16 or BF16. Measure whitening error ||W A W transpose - I||_F, downstream validation accuracy, loss descent at equal rotation count, and eigensolver wall-clock time. Success means lower whitening error or faster loss reduction than magnitude pivoting at equal K, particularly for covariance matrices with clustered eigenvalues.