Math: Symplectic

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

2 ideas found

ML: Attention Math: Symplectic Clear all

Unverified 2026

Polygon-Closure Attention

Represent each token value in an attention head as a bounded three-dimensional Lie-algebra vector and impose a weighted polygon-closure condition on the aggregate value vectors. The module is invariant to a common \(SU(2)\simeq SO(3)\) rotation of all token vectors, preventing the head from spending capacity on an arbitrary global orientation. A soft closure penalty gives a drop-in experiment, while projection onto the zero-sum manifold provides a harder constrained variant.

Useful6/10

Difficulty5/10

Novelty7/10

Geometry Stability Generalization Accuracy

Paper: Mori theory and symplectic reduction for polygons and quivers arXiv:2608.20930

Unverified 2026

Horizontal Symmetry Quotient Layer

Replace explicit quotient construction by a differentiable projection that removes learned group-orbit directions from both source and target features. The paper's reduction argument shows that a closed level constraint makes the restricted form horizontal, so the network can operate on invariant coordinates while retaining a measurable residual for symmetry leakage.

Useful6/10

Difficulty6/10

Novelty5/10

Architecture Scalability Stability Generalization

Paper: Reduction of relative multisymplectic manifolds arXiv:2607.12350