Interpretable Equivariant Marks for Contrastive Cosmological Inference

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. Our neural mark tightens the marginalized $\sigma_8$ constraint by $2.6\times$ and $\Omega_m$ by $1.7\times$ compared to th best classical mark, breaking the $\Omega_m-\sigma_8$ degeneracy at the Fisher information level, and reducing the held-out parameter MSE by up to $2.5\times$ over the best classical mark on $\sigma_8$. 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.