While synthetic biology has revolutionized our approaches to medicine, agriculture, and energy, the design of completely novel biological circuit components beyond naturally-derived templates remains challenging due to poorly understood design rules. Toehold switches, which are programmable nucleic acid sensors, face an analogous design bottleneck; our limited understanding of how sequence impacts functionality often necessitates expensive, time-consuming screens to identify effective switches. Here, we introduce Sequence-based Toehold Optimization and Redesign Model (STORM) and Nucleic-Acid Speech (NuSpeak), two orthogonal and synergistic deep learning architectures to characterize and optimize toeholds. Applying techniques from computer vision and natural language processing, we 'un-box' our models using convolutional filters, attention maps, and in silico mutagenesis. Through transfer-learning, we redesign sub-optimal toehold sensors, even with sparse training data, experimentally validating their improved performance. This work provides sequence-to-function deep learning frameworks for toehold selection and design, augmenting our ability to construct potent biological circuit components and precision diagnostics.