Title: Benchmarks and Explanations for Deep Learning Estimates of X-ray Galaxy Cluster Masses

Abstract: We evaluate the effectiveness of deep learning (DL) models for reconstructing the masses of galaxy clusters using X-ray photometry data from next-generation surveys. We establish these constraints using a catalogue of realistic mock eROSITA X-ray observations which use hydrodynamical simulations to model realistic cluster morphology, background emission, telescope response, and AGN sources. Using bolometric X-ray photon maps as input, DL models achieve a predictive mass scatter of $\sigma_{\ln M_\mathrm{500c}} = 17.8\%$, a factor of two improvements on scalar observables such as richness $N_\mathrm{gal}$, 1D velocity dispersion $\sigma_\mathrm{v,1D}$, and photon count $N_\mathrm{phot}$ as well as a $32\%$ improvement upon idealised, volume-integrated measurements of the bolometric X-ray luminosity $L_X$. We then show that extending this model to handle multichannel X-ray photon maps, separated in low, medium, and high energy bands, further reduces the mass scatter to $16.2\%$. We also tested a multimodal DL model incorporating both dynamical and X-ray cluster probes and achieved marginal gains at a mass scatter of $15.9\%$. Finally, we conduct a quantitative interpretability study of our DL models and find that they greatly down-weight the importance of pixels in the centres of clusters and at the location of AGN sources, validating previous claims of DL modelling improvements and suggesting practical and theoretical benefits for using DL in X-ray mass inference.