Interpretable Neural Marked Statistics for Cosmological Inference
可解释的神经标记统计用于宇宙学推断
Federico Semenzato, Benjamin D. Wandelt, Michele Liguori, Alvise Raccanelli
AI总结 提出一种神经标记方案,通过可解释的物理变换从形态学层面提取宇宙学信息,在对比学习目标下优化标记统计,显著提高对σ₈和Ωₘ的约束精度。
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- 11 pages, 6 figures. Accepted to the Workshop on AI for Physics (ICML 2026)
恢复超出功率谱的宇宙学信息是即将进行的宇宙学调查的核心目标,因为物质密度中的晚期非高斯信号无法仅通过两点统计获得。标记统计通过使用非线性函数对场进行重新加权,将部分信息折叠回两点水平。我们提出了一种神经标记方案,通过一组可解释的、物理驱动的变换来推广这一过程,这些变换直接允许在形态学层面解释宇宙学信息的增益。我们采用对比学习目标将可学习的标记摘要与底层宇宙学参数对齐。在$k_{\max}=0.2\\,h\mathrm{Mpc}^{-1}$处,与经典标记相比,我们的神经标记将$\sigma_8$的边缘化约束提高了$2.9\times$,将$\Omega_m$提高了$1.8\times$,在Fisher信息层面打破了$\Omega_m-\sigma_8$简并。它进一步将参数MSE在整个宇宙学参数先验上比最佳经典标记降低了$1.45\times$。学习到的潜在几何与参数空间中的$\Omega_m$和$\sigma_8$方向对齐,表明对比目标恢复了宇宙学信息的主导轴。我们的方法为更强大、可解释的宇宙学推断摘要统计打开了大门。
Recovering cosmological information beyond the power spectrum is a central goal for upcoming cosmological surveys, since late-time non-Gaussian signal in the matter density cannot be accessed through two-point statistics alone. Marked statistics fold part of this information back into the two-point level by reweighting the field with non-linear functions. We propose a neural marking scheme to generalize this process through a set of interpretable, physically motivated transformations that directly allow to interpret the gain in cosmological information at the morphological level. We employ a contrastive learning objective to align learnable marked summaries with the underlying cosmological parameters. At $k_{\max}=0.2\,h\mathrm{Mpc}^{-1}$, our neural mark tightens the marginalized constraint on $\sigma_8$ by $2.9\times$ and on $\Omega_m$ by $1.8\times$ compared to classical marks, breaking the $\Omega_m-\sigma_8$ degeneracy at the Fisher information level. It further reduces the parameter MSE across our cosmological parameter prior by $1.45\times$ over the best classical mark. The learned latent geometry aligns with the $\Omega_m$ and $\sigma_8$ directions in parameter space, indicating that the contrastive objective recovers the dominant axes of cosmological information. Our approach opens the door to more powerful, interpretable summary statistics for cosmological inference.