Enormous efforts are expended creating high-fidelity simulations of accelerator beamlines. While these simulations provide an initial starting point for operators, there exists a gap between the ideal simulated entity and the real-world implementation. Bridging that gap requires a brute force and time consuming task known as beam tuning. This project develops a data-driven approach to beam tuning in the CEBAF injector, which leverages deep learning over structured data (graphs). Specifically, we use graphs to represent the injector beamline at any arbitrary date and time and invoke a graph neural network to extract a low-dimensional representation that can be visualized in two-dimensions. By analyzing historical operational data from the CEBAF archiver, good and bad regions of parameter space can be mapped out. Initial results demonstrate the validity of the concept. We then suggest how this framework can serve as a real-time tool to aid beam tuning – which represents the dominant source of machine downtime – as well as address issues of reproducibility and stability in the machine.