Interpretable Neural Marked Statistics for Cosmological Inference

• URL: http://arxiv.org/abs/2606.11295v1
• Date: Tue, 09 Jun 2026 18:00:01 GMT
• Title: Interpretable Neural Marked Statistics for Cosmological Inference
• Abstract summary: Marked statistics fold part of this information back into the two-point level by reweighting the field with non-linear functions.<n>We propose a neural marking scheme to generalize this process through a set of interpretable, physically motivated transformations.<n>Our approach opens the door to more powerful, interpretable summary statistics for cosmological inference.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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