Geometric priors for single-patch neural Calabi--Yau metrics on the quintic: a conservative fixed-ψ Ablation study
Abstract
We investigate how geometric priors shape neural approximations of the complex Monge--Amp`ere equation on the quintic Calabi--Yau threefold. This fixed-ψ diagnostic compares four single-patch ans"atze: a coordinate SIREN potential model, a direct-metric Cholesky baseline, an algebraic section ansatz, and a section-plus-neural hybrid. In a 96-run learning-rate and frequency archive, section-based models reach validation σ=4.14--4.16%, whereas SIREN and Cholesky remain at 41.29% and 44.27%. Multi-seed controls use a shared affine-η evaluator and five fresh validation clouds. Stable section settings give $3.84−−4.77%$, compared with $28.46−−30.59%$ for Cholesky and $34.73−−38.13%$ for SIREN. Hybrid projective features do not improve best-case accuracy, but they stabilise the stressed regime. They limit σ to $4.26−−4.41%$, versus $4.45−−205.45%$ for raw coordinates. Within this protocol, section-based geometric structure is the main driver of accuracy; coordinate-only models plateau at substantially higher error, and raw hybrid flexibility can amplify instability. We provide a projective-scaling derivation, document protocol asymmetries, and identify projectively consistent hybrid corrections as the next step.
Versions
Related
- Isometry Groups of Right Invariant Metrics in Geometric Quantum Complexity
- On Waring-Goldbach problem for two squares, three biquadratics, one quintic and one septic
- Character variety of the five-punctured sphere and the determinantal quintic hypersurface
- A smooth quintic surface with 85 lines and Picard number 43
- Soliton Dynamics for the Cubic-Quintic Nonlinear Schrödinger Equation with a Potential
BibTeX
@misc{eng2026geometric,
title = {{Geometric priors for single-patch neural Calabi--Yau metrics on the quintic: a conservative fixed-$ψ$ Ablation study}},
author = {D Yang Eng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35920},
eprint = {2610.35920},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35920},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Geometric priors for single-patch neural Calabi--Yau metrics on the quintic: a conservative fixed-ψ Ablation study
AU - D Yang Eng
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.35920
UR - https://arxiv.org/abs/2610.35920
AB - We investigate how geometric priors shape neural approximations of the complex Monge--Amp`ere equation on the quintic Calabi--Yau threefold. This fixed-ψ diagnostic compares four single-patch ans"atze: a coordinate SIREN potential model, a direct-metric Cholesky baseline, an algebraic section ansatz, and a section-plus-neural hybrid. In a 96-run learning-rate and frequency archive, section-based models reach validation σ=4.14--4.16%, whereas SIREN and Cholesky remain at 41.29% and 44.27%. Multi-seed controls use a shared affine-η evaluator and five fresh validation clouds. Stable section settings give $3.84−−4.77%$, compared with $28.46−−30.59%$ for Cholesky and $34.73−−38.13%$ for SIREN. Hybrid projective features do not improve best-case accuracy, but they stabilise the stressed regime. They limit σ to $4.26−−4.41%$, versus $4.45−−205.45%$ for raw coordinates. Within this protocol, section-based geometric structure is the main driver of accuracy; coordinate-only models plateau at substantially higher error, and raw hybrid flexibility can amplify instability. We provide a projective-scaling derivation, document protocol asymmetries, and identify projectively consistent hybrid corrections as the next step.
ER -