Closed-form fractional radial links for elliptical Mahalanobis discriminant analysis

What the math gives to ML

The paper gives an exact decomposition of the Bayes logit for two shared-generator elliptical classes into a sum of one-dimensional functions of class-specific squared Mahalanobis radii. The transferable asset is a strong inductive bias: replace an unconstrained final classifier with a radial link that can represent heavy-tailed and non-Gaussian class geometry while retaining an interpretable likelihood-ratio form. In a neural model, this can become a differentiable Mahalanobis radial head on top of a learned embedding, with a low-dimensional fractional-power basis instead of a generic MLP or spline. The Gaussian/QDA case is recovered when the radial link is affine, providing a direct ablation and useful initialization.