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We formalise cases in which the flat metric has more symmetries than the underlying manifold, and prove that these symmetries imply that the flat metric admits a surprisingly compact representation for certain choices of complex structure moduli. We show that such symmetries uniquely determine the flat metric on certain loci on the Fermat manifold, for which we present an analytic form. We also incorporate our theoretical results into neural networks to reduce Ricci curvature for multiple CY manifolds compared to previous machine learning approaches. We conclude with distilling the ML models to obtain closed form expressions for K\u00e4hler metrics with near-zero scalar curvature, discovering them directly from numerical data.<\/jats:p>","DOI":"10.1088\/2632-2153\/adf68c","type":"journal-article","created":{"date-parts":[[2025,7,31]],"date-time":"2025-07-31T22:52:53Z","timestamp":1754002373000},"page":"035029","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Symbolic approximations to Ricci-flat metrics via extrinsic symmetries of Calabi\u2013Yau hypersurfaces"],"prefix":"10.1088","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-7300-7104","authenticated-orcid":true,"given":"Viktor","family":"Mirjani\u0107","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7920-0897","authenticated-orcid":false,"given":"Challenger","family":"Mishra","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2025,8,8]]},"reference":[{"key":"mlstadf68cbib1","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1002\/cpa.3160310304","article-title":"On the Ricci curvature of a compact K\u00e4hler Manifold and the complex Monge\u2013Amp\u00e9re equation, I","volume":"31","author":"Yau","year":"1978","journal-title":"Commun. 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