用可解释的神经标记法,显著提升宇宙学参数估计精度。
Interpretable Neural Marked Statistics for Cosmological Inference

- 设计可解释的神经标记函数,融合物理先验知识
- 对σ₈约束提升2.9倍,打破Ωₘ-σ₈退化关系
- 适合需要高精度、可解释性统计量的研究者
超越功率谱的宇宙学信息提取是下一代巡天的核心目标,因为晚期非高斯信号无法仅通过两点统计量获取。标记统计量通过非线性函数加权场,将部分信息重构至两点水平。本文提出一种神经标记方法,基于可解释的物理动机变换,直接在形态层面解析信息增益。采用对比学习目标,使可学习的标记摘要与宇宙学参数对齐。在k_max=0.2 h Mpc⁻¹时,相比经典标记,该方法使σ₈的边际约束收紧2.9倍,Ωₘ约束收紧1.8倍,突破费舍尔信息层面的Ωₘ-σ₈退化。同时,在整个参数先验范围内,参数均方误差降低1.45倍。学习到的隐空间几何与参数空间中Ωₘ和σ₈方向一致,表明对比目标成功捕获了主要信息轴。本方法为宇宙学推断提供了更强大且可解释的统计摘要。
原文摘要 · Abstract (English)
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 $σ_8$ by $2.9\times$ and on $Ω_m$ by $1.8\times$ compared to classical marks, breaking the $Ω_m-σ_8$ 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 $Ω_m$ and $σ_8$ 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.
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