Math: Fractional analysis

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

2 ideas found

Status: Unverified Math: Fractional analysis Clear all

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

Architecture Speedup Scalability Accuracy

Paper: Ellipsoidal Positivity Sets for Fractional Obstacle Problems with Quadratic Forcing arXiv:2609.00703

Unverified 2026

Pareto-Sparse Fractional Dynamics Layer

Add a sparse, interpretable fractional-dynamics layer to a neural world model: candidate terms are evaluated through weak projections, while both their support and continuous derivative orders are selected by validation error versus model complexity. This avoids forcing the model to choose from a dense fixed dictionary containing many nearly collinear fractional orders.

Useful6/10

Difficulty6/10

Novelty6/10

Regularization Accuracy Generalization Sample efficiency

Paper: Robust data-driven discovery of fractional differential equations via weak formulations and Pareto-based subset selection arXiv:2608.12879