GlobalCY I: A JAX Framework for Globally Defined and Symmetry-Aware Neural Kahler Potentials

arXiv:2604.11404v1 Announce Type: cross Abstract: We present GlobalCY, a JAX-based framework for globally defined and symmetry-aware neural Kahler-potential models on projective hypersurface Calabi--Yau geometries. The central problem is that local-input neural Kahler-potential models can train successfully while still failing the geometry-sensitive diagnostics that matter in hard quartic regimes, especially near singular and near-singular members of the Cefalu family. To study this, we compare three model families -- a local-input baseline, a globally defined invariant model, and a symmetry-aware global model -- on the hard Cefalu cases lambda=0.75 and lambda=1.0 using a fixed multi-seed protocol and a geometry-aware diagnostic suite. In this benchmark, the globally defined invariant model is the strongest overall family, outperforming the local baseline on the two clearest geometric comparison metrics, negative-eigenvalue frequency and projective-invariance drift, in both cases. The gains are strongest at lambda=0.75, while lambda=1.0 remains more difficult. The current symmetry-aware model improves projective-invariance drift relative to the local baseline, but does not yet surpass the plain global invariant model. These results show that global invariant structure is a meaningful architectural constraint for learned Kahler-potential modeling in hard quartic Calabi--Yau settings.

Source: arXiv cs.LG | 2026-04-14