3D ScatterNet: Inference from 21~cm Light-cones

The Square Kilometre Array (SKA) will have the sensitivity to take the 3D light-cones of the 21~cm signal from the epoch of reionization. This signal, however, is highly non-Gaussian and can not be fully interpreted by the traditional power spectrum. In this work, we introduce the {\tt 3D ScatterNet} that combines the normalizing flows with solid harmonic wavelet scattering transform, a 3D CNN featurizer with inductive bias, to perform implicit likelihood inference (ILI) from 21~cm light-cones. We show that {\tt 3D ScatterNet} outperforms the ILI with 3D CNN in the literature. It also reaches better performance than ILI with the power spectrum for varied light-cone effects and varied signal contaminations.