Hausdorff Dimension of the Set of Extreme Points of a Random Countable Stable Zonotope

What the math gives to ML

The paper constructs a random directional field whose output is a sum of heavy-tailed vector increments gated by spherical half-spaces, and proves that its image has almost-sure Hausdorff dimension exactly $(d-1)\alpha$. The transferable asset is the explicit multiscale separation between a finite set of large jumps, which induces a hyperplane arrangement, and a small-jump residual that controls local image diameters. This suggests a finite neural feature or routing layer in which large random vectors define discrete angular cells while a truncated stable residual supplies within-cell variation, with the truncation level controlling compute, memory, and approximation error.