We present forecasts for constraints on the matter density (${\mathrm{\Omega }}_m$) and the amplitude of matter density fluctuations at $8{\mathrm{h}}^{-1}\mathrm{Mpc}$ (${\sigma }_8$) from cosmic microwave background lensing convergence (${\kappa }_{\mathrm{CMB}}$) maps and galaxy weak lensing convergence (${\kappa }_{\mathrm{WL}}$) maps. For ${\kappa }_{\mathrm{CMB}}$ auto statistics, we compare the angular power spectra ($C_{\ell }$’s) to the wavelet scattering transform (WST) coefficients. For ${\kappa }_{\mathrm{CMB}}\times {\kappa }_{\mathrm{WL}}$ statistics, we compare the cross angular power spectra to wavelet phase harmonics (WPH). This work also serves as the first application of WST and WPH to these probes. For ${\kappa }_{\mathrm{CMB}}$, we find that WST and $C_{\ell }$’s yield similar constraints in forecasts for all surveys considered in this work. When ${\kappa }_{\mathrm{CMB}}$ is crossed with ${\kappa }_{\mathrm{WL}}$ projected from Euclid Data Release 2, we find that WPH outperforms cross-$C_{\ell }$’s by factors between 2.2 and 3.4 for individual parameter constraints. To compare these different summary statistics, we develop a novel learned binning approach. This method compresses summary statistics while maintaining interpretability. We find this leads to improved constraints compared to more naive binning schemes for our wavelet-based statistics, but not for $C_{\ell }$’s. By learning the binning and measuring constraints on distinct datasets, our method is robust to overfitting by construction.

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• Cosmic microwave background
• Cosmological parameters
• Gravitational lenses
• Astrophysical & cosmological simulations