Interpretable Neural Marked Statistics for 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. At kmax=0.2,hMpc-1, our neural mark tightens the marginalized constraint on σ8 by 2.9× and on Omegam by 1.8× compared to classical marks, breaking the Omegam-σ8 degeneracy at the Fisher information level. It further reduces the parameter MSE across our cosmological parameter prior by 1.45× over the best classical mark. The learned latent geometry aligns with the Omegam and σ8 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.