Math: Fractional analysis

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

2 ideas found

ML: Regularization Math: Fractional analysis Clear all

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

✗ Mechanism failed 2026

Fractional Jacobian topology loss

Train a neural field to represent a sphere-valued phase or feature map with a prescribed codimension-two defect set. Add a fractional Sobolev energy to suppress high-frequency oscillations, but enforce topology through a discrete Jacobian or winding-current loss so that smoothing cannot remove holes, filaments, or vortex defects.

Useful6/10

Difficulty5/10

Novelty7/10

Geometry Accuracy Stability Generalization

Paper: Another look at a notion of fractional mass in codimension two arXiv:2607.00810