Recent backscatter communication techniques enable ultra low power wireless devices that operate without batteries while interoperating directly with unmodified commodity wireless devices. Commodity devices cooperate in providing the unmodulated carrier that the battery-free nodes need to communicate while collecting energy from their environment to perform sensing, computation, and communication tasks. The optimal provision of the unmodulated carrier limits the size of the network because it is an NP-hard combinatorial optimization problem. Consequently, previous works either ignore carrier optimization altogether or resort to suboptimal heuristics, wasting valuable energy and spectral resources. We present DeepGANTT, a deep learning scheduler for battery-free devices interoperating with wireless commodity ones. DeepGANTT leverages graph neural networks to overcome variable input and output size challenges inherent to this problem. We train our deep learning scheduler with optimal schedules of relatively small size obtained from a constraint optimization solver. DeepGANTT not only outperforms a carefully crafted heuristic solution but also performs within ~3% of the optimal scheduler on trained problem sizes. Finally, DeepGANTT generalizes to problems more than four times larger than the maximum used for training, therefore breaking the scalability limitations of the optimal scheduler and paving the way for more efficient backscatter networks.