# Interpretable Analytic Calabi-Yau Metrics via Symbolic Distillation

arXiv: https://arxiv.org/abs/2602.07834 · HTML: https://mlsanity.com/paper/2602.07834/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 45 references that are in the map.
- First posted on arXiv 8 Feb 2026.

## Builds on (most cited first, 13 of 13)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Neural Network Approximations for Calabi-Yau Metrics](https://mlsanity.com/paper/2012.15821/) (2020)
- [Learning Size and Shape of Calabi-Yau Spaces](https://mlsanity.com/paper/2111.01436/) (2021)
- [Fast, accurate, and transferable many-body interatomic potentials by symbolic regression](https://mlsanity.com/paper/1904.01095/) (2019)
- [Machine learning Calabi-Yau metrics](https://mlsanity.com/paper/1910.08605/) (2019)
- [Distill n' Explain: explaining graph neural networks using simple surrogates](https://mlsanity.com/paper/2303.10139/) (2023)
- [Machine Learned Calabi-Yau Metrics and Curvature](https://mlsanity.com/paper/2211.09801/) (2022)
- [Discovering physical laws with parallel symbolic enumeration](https://mlsanity.com/paper/2407.04405/) (2024)
- [Calabi-Yau metrics through Grassmannian learning and Donaldson's algorithm](https://mlsanity.com/paper/2410.11284/) (2024)
- [Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces](https://mlsanity.com/paper/2412.19778/) (2024)
- [Approximate Ricci-flat Metrics for Calabi-Yau Manifolds](https://mlsanity.com/paper/2506.15766/) (2025)

## Built on by (most cited first, 1 of 1)

- [GlobalCY I: A JAX Framework for Globally Defined and Symmetry-Aware Neural K"ahler Potentials](https://mlsanity.com/paper/2604.11404/) (2026)

## Abstract (arXiv)

The pointwise determinant ratio [ R_psi(z)equiv log!left(fracdet gRF(z;psi)det gFS(z)right) ] measures how the Ricci-flat metric on the Dwork quintic departs from the Fubini--Study baseline. We ask whether this scalar observable can be described compactly in terms of a small number of projective invariants, and whether the same scaffold remains usable across complex-structure moduli. Using Donaldson's k=10 balanced metric as an algebraic teacher and symbolic regression on sampled points, we find that, within the restricted moduli-only feature class studied here, two low-order symmetric features, the power sum p2=sumi |zi|4 and the cubic elementary symmetric polynomial σ3=e3, already capture most of the teacher variation. A degree-3 polynomial in (p2,σ3) achieves held-out test R2=0.946, while adding the remaining low-order symmetric generators changes this by less than 10-3. Within the same two-feature space, symbolic regression identifies a five-term rational-polynomial expression that matches the k=10 teacher with R2=0.9994. Refitting the same functional scaffold across psi∈[0,0.8] keeps the mean determinant-ratio proxy langle R_psirangle within 0.01% of the local teachers on the sampled point clouds and yields smoothly varying fitted coefficients over the studied range. The holomorphic Yukawa coupling kappa111=5 is reproduced as a normalization check only. Taken together, these results provide a compact symbolic description of one metric-derived scalar observable on the Dwork family, while remaining bounded by the finite-k teacher used for distillation rather than establishing a closed-form Ricci-flat metric.