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.

翻译：Calabi-Yau流形在弦理论中至关重要，但其度量的计算往往难以处理。本文证明，符号回归可将神经网络的近似结果提炼为简洁、可解释的解析公式。我们提出的五项表达式在参数量减少3000倍的情况下，仍保持了神经网络的精度（$R^2 = 0.9994$）。多种子验证表明，几何约束会筛选出关键特征——特别是幂和与对称多项式——同时允许结构多样性。该函数形式在所研究的模空间范围内（$ψ\in [0, 0.8]$）得以保持，其系数平滑变化；我们将这些变化趋势解释为局部训练教师网络精度范围内（$ψ\neq 0$时$σ\approx 8-9\%$）的经验假设。该公式成功复现了物理可观测量——体积积分与Yukawa耦合——从而验证了符号蒸馏能够为以往仅能通过黑箱神经网络计算的物理量，重建出紧凑且可解释的模型。