Sharp Convex Concentration for Symmetric Random Tensors with Subgaussian Coordinates

What the math gives to ML

The paper proves a sharp, degree-aware concentration law for convex Lipschitz functions of symmetric tensor features X^{\otimes d}, separating radial fluctuations from nearly norm-preserving directional fluctuations. The transferable asset is an explicit tail scale of L n^{(d-1)/2} with both a d^2 penalty and a logarithmic directional penalty, rather than treating the tensor slots as independent. This can calibrate robust loss or gradient clipping for polynomial and tensorized neural layers, particularly when latent coordinates are whitened and approximately independent. The key experiment is whether theorem-based thresholds reduce gradient outliers without harming accuracy compared with generic clipping.