Machine learning in atomistic materials science has grown to become a powerful tool, with most approaches focusing on atomic geometry, typically decomposed into local atomic environments. This approach, while well-suited for machine-learned interatomic potentials, is conceptually at odds with learning complex intrinsic properties of materials, often driven by spectral properties commonly represented in reciprocal space (e.g., band gaps or mobilities) which cannot be readily partitioned in real space. For such applications, methods that represent the electronic rather than the atomic structure could be more promising. In this work, we present a general framework focused on electronic-structure descriptors that take advantage of the natural symmetries and inherent interpretability of physical models. We apply this framework first to material similarity and then to accelerated screening, where a model trained on 217 materials correctly labels 75% of entries in the Materials Cloud 3D database, which meet common screening criteria for promising transparent-conducting materials.