Math: Analysis

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

2 ideas found

Unverified 2026

RLCT-Certified Singular Attention

Use an anisotropic singular relative-position kernel in attention or graph message passing, with its exponent constrained by the paper's local integrability threshold. The module can represent sharper directional interactions than an RBF while providing an explicit certificate that its spatial gradient belongs to a chosen L^p space.

Useful6/10

Difficulty5/10

Novelty9/10

Architecture Stability Accuracy Sample efficiency

Paper: Geometric Criteria for Morrey Admissibility via the Real Log-Canonical Threshold arXiv:2607.14991

Unverified 2026

Bessel Totally-Positive Attention

Replace ordinary dot-product attention logits with a strictly totally positive kernel evaluated on positive, ordered scalar coordinates attached to queries and keys. Use the modified-Bessel kernel K(x,s)=I_s(x), whose every ordered minor is positive, then row-normalize it as an attention matrix. This creates an attention operator with a mathematically enforced anti-oscillatory structure rather than merely positive entries.

Useful5/10

Difficulty6/10

Novelty8/10

Architecture Stability Accuracy Generalization

Paper: Strict Total Positivity from Spectral Darboux and Toeplitz Smoothing Mechanisms arXiv:2607.02778