Crystal-graph attention networks have emerged recently as remarkable tools for the prediction of thermodynamic stability and materials properties from unrelaxed crystal structures. Previous networks trained on two million materials exhibited, however, strong biases originating from underrepresented chemical elements and structural prototypes in the available data. We tackled this issue computing additional data to provide better balance across both chemical and crystal-symmetry space. Crystal-graph networks trained with this new data show unprecedented generalization accuracy, and allow for reliable, accelerated exploration of the whole space of inorganic compounds. We applied this universal network to performed machine-learning assisted high-throughput materials searches including 2500 binary and ternary prototypes and spanning about 1 billion compounds. After validation using density-functional theory, we uncover in total 19512 additional materials on the convex hull of thermodynamic stability and around 150000 compounds with a distance of less than 50 meV/atom from the hull. Here we include the DCGAT-1, DCGAT-2, and DCGAT-3 datasets used in this work.