Math: Regularization

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

2 ideas found

Solves: Accuracy Math: Regularization Clear all

△ Mechanism confirmed, baseline not beaten 2026

CVaR-tail active residual correction

Train a cheap neural surrogate globally, then use an ensemble or bootstrap covariance to identify inputs near the estimated upper-tail boundary and inputs where high-fidelity correction is uncertain. Fit a Tikhonov-regularized residual model on the acquired expensive labels and use the corrected predictor for CVaR estimation or risk-constrained optimization. The acquisition policy deliberately ignores easy central-region samples unless they influence the tail threshold.

Useful7/10

Difficulty5/10

Novelty6/10

Sampling Sample efficiency Accuracy Scalability

Paper: Risk-averse design optimization with CVaR constraints via multifidelity tail-region correction arXiv:2608.29222

Unverified 2026

Elliptic Low-Oscillation Feature Layer

Construct a spatially varying diffusion layer whose coefficient matrix is explicitly uniformly elliptic and whose local mean oscillation is penalized. Use it inside an implicit residual block, so the learned operator remains a controlled perturbation of a constant-coefficient elliptic operator rather than becoming an unstable collection of unrelated local filters.

Useful5/10

Difficulty6/10

Novelty8/10

Architecture Stability Accuracy Generalization

Paper: Regularity for Elliptic Equations with Coefficients of Small Mean Oscillation arXiv:2608.10813