Math: Symmetry

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

2 ideas found

Status: Beats tuned baseline Math: Symmetry Clear all

✓✓ Beats tuned baseline 2026

Commutant-gated spectral loss

Replace per-eigenvector spectral supervision on symmetry-forced multiplets by a projector-trace target determined from the operator family's commutant. Use individual eigenvalue or eigenvector targets only outside detected forced blocks, avoiding arbitrary basis choices and exploding gradients at protected crossings.

Useful8/10

Difficulty5/10

Novelty8/10

Regularization Stability Accuracy Generalization

Paper: A commutant gate for spectral fitting through symmetry forced degeneracy arXiv:2608.04903

✓✓ Beats tuned baseline 2026

Reciprocal-Lattice Gauge-Covariant Bloch Network

Build a Bloch-conditioned neural model whose periodic-factor representation transforms covariantly when the supplied Bloch wavenumber is shifted by a reciprocal lattice vector. Either canonicalize q to the first Brillouin zone or augment training with mathematically paired examples whose outputs differ by the exact phase gauge. This prevents the network from learning inconsistent predictions for physically identical Bloch modes.

Useful7/10

Difficulty4/10

Novelty8/10

Architecture Accuracy Stability Generalization

Paper: Full-field and Bloch-periodic-factor discretizations: Accuracy and phantom modes arXiv:2608.14348