Cubic-Root Gaussian Approximation under Unrestricted Covariance

What the math gives to ML

The paper gives a sharper high-dimensional Gaussian approximation for maxima of sums of independent, coordinatewise subexponential variables under completely unrestricted covariance, improving the dominant rate from roughly n^{-1/4} to n^{-1/3} up to logarithmic factors. The transferable asset is a covariance-aware approximation for correlated coordinatewise extremes that does not require a low-rank or well-conditioned covariance matrix. A practical neural-network use is to calibrate simultaneous gradient or activation clipping thresholds from a correlated Gaussian surrogate instead of noisy empirical quantiles or independence-based approximations.