Math: Lie groups

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

2 ideas found

ML: Optimizer Math: Lie groups Clear all

Unverified 2026

Projective Jacobian Compensation

Add a low-rank control perturbation to each optimizer block so that the next-step parameter dynamics compensate for growth of selected normalized perturbation directions. The control is computed by least squares from Jacobian-vector products, with a trust-region penalty limiting its stochastic cost; unlike isotropic weight decay, it targets directional instability while preserving directions that are already contracting.

Useful5/10

Difficulty6/10

Novelty7/10

Dynamics Stability Generalization Optimizer

Paper: Unique Ergodicity for the Projective Process of the 2D Navier--Stokes Equation with Nondegenerate Noise arXiv:2608.18075

Unverified 2026

Casimir-Preserving Matrix Optimizer

Introduce an auxiliary matrix-valued optimizer state whose update is a Lie–Poisson flow discretized by similarity transforms rather than additive Euler steps. Because similarity transforms preserve $\operatorname{tr}(Z^k)$ and the full eigenvalue multiset, long training runs avoid spectral drift in the optimizer state; the state can then generate a preconditioned update for ordinary neural-network parameters.

Useful5/10

Difficulty6/10

Novelty7/10

Dynamics Stability Generalization Optimizer

Paper: Vakonomic Fluids arXiv:2607.18312