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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | https://arxiv.org/abs/2602.07834 |
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| _version_ | 1866912888170479616 |
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| author | Eng, D Yang |
| author_facet | Eng, D Yang |
| contents | Calabi--Yau manifolds are essential for string theory but require computing intractable metrics. Here we show that symbolic regression can distill neural approximations into simple, interpretable formulas. Our five-term expression matches neural accuracy ($R^2 = 0.9994$) with 3,000-fold fewer parameters. Multi-seed validation confirms that geometric constraints select essential features, specifically power sums and symmetric polynomials, while permitting structural diversity. The functional form can be maintained across the studied moduli range ($ψ\in [0, 0.8]$) with coefficients varying smoothly; we interpret these trends as empirical hypotheses within the accuracy regime of the locally-trained teachers ($σ\approx 8-9\%$ at $ψ\neq 0$). The formula reproduces physical observables -- volume integrals and Yukawa couplings -- validating that symbolic distillation recovers compact, interpretable models for quantities previously accessible only to black-box networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07834 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Interpretable Analytic Calabi-Yau Metrics via Symbolic Distillation Eng, D Yang Machine Learning Differential Geometry Calabi--Yau manifolds are essential for string theory but require computing intractable metrics. Here we show that symbolic regression can distill neural approximations into simple, interpretable formulas. Our five-term expression matches neural accuracy ($R^2 = 0.9994$) with 3,000-fold fewer parameters. Multi-seed validation confirms that geometric constraints select essential features, specifically power sums and symmetric polynomials, while permitting structural diversity. The functional form can be maintained across the studied moduli range ($ψ\in [0, 0.8]$) with coefficients varying smoothly; we interpret these trends as empirical hypotheses within the accuracy regime of the locally-trained teachers ($σ\approx 8-9\%$ at $ψ\neq 0$). The formula reproduces physical observables -- volume integrals and Yukawa couplings -- validating that symbolic distillation recovers compact, interpretable models for quantities previously accessible only to black-box networks. |
| title | Interpretable Analytic Calabi-Yau Metrics via Symbolic Distillation |
| topic | Machine Learning Differential Geometry |
| url | https://arxiv.org/abs/2602.07834 |