Math: Fractional analysis

Machine-learning ideas tagged Fractional analysis in the Math taxonomy of the Math2NN corpus.

Unverified 2026

Fractional Ellipsoidal Sparse Attention

Replace dense attention weights with a compactly supported anisotropic bump derived from the obstacle solution, using one learnable ellipsoid per attention head or feature group. Tokens outside the learned ellipsoid receive exactly zero weight, while tokens inside receive smoothly decaying weights according to a fractional exponent. The learned positive-definite matrix represents orientation, scale, and correlations between feature dimensions.

Useful6/10
Difficulty6/10
Novelty5/10
Paper: Ellipsoidal Positivity Sets for Fractional Obstacle Problems with Quadratic Forcing arXiv:2609.00703