The histopathological phenotype of tumors reflects the underlying genetic makeup. Deep learning can predict genetic alterations from pathology slides, but it is unclear how well these predictions generalize to external datasets. We performed a systematic study on Deep-Learning-based prediction of genetic alterations from histology, using two large datasets of multiple tumor types. We show that an analysis pipeline that integrates self-supervised feature extraction and attention-based multiple instance learning achieves a robust predictability and generalizability.