Math: Symmetry

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

2 ideas found

ML: Regularization Math: Symmetry Clear all

✓✓ 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

Unverified 2026

Full-Field Phase-Boundary PINN

For neural eigenmode solvers on periodic domains, train the full field directly and impose Bloch phase coupling only at opposite cell boundaries, rather than differentiating a periodic factor with respect to q through a quadratic volume operator. The boundary formulation preserves reciprocal-lattice equivalence exactly through z=exp(iqa), reducing spurious eigenmodes caused by inconsistent q-dependent discretization.

Useful6/10

Difficulty5/10

Novelty9/10

Regularization Stability Accuracy Generalization

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