Ideally, HTVS approaches explore all possible compounds in chemical space, which are generated by several methods such as elemental substitution and generative models . Thus, one should develop ML models to directly predict ground state energies using unrelaxed initial structures, i.e., initial structure to relaxed energy (IS2RE) task . Graph neural networks (GNN), e.g., crystal graph convolutional neural network (CGCNN) , are one of the most accurate and widely used approaches in the field, which describe local atomic environments of each atom in crystals as ML inputs . They achieved very high accuracy for predicting crystal properties and can also be utilized to perform IS2RE task indirectly through numerical optimization algorithms, such as Broyden-Fletcher-Goldfarb-Shanno (BFGS) or Bayesian optimization (BO) . However, these are not suitable for practical HTVS since interatomic distances between neighboring atoms in relaxed structures are used to prepare input representations. Further, indirect IS2RE requires nearly 200 iterations of energy and force predictions for numerical geometry optimizations , and the predicted formation energy significantly depends on "pseudo" optimized structures, making IS2RE inefficient. . Direct IS2RE is also available with properly developed input representations such as direction, which is moderately sensitive to structures . Meanwhile, a model which uses stoichiometry-based inputs achieved reasonable prediction accuracy, but it was not able to distinguish polymorphs of materials. To accelerate materials discovery, it is thus necessary to develop accurate ML models for direct IS2RE with appropriate representations, neither too structure-sensitive nor too insensitive .