Our main algorithmic contribution lies in identifying and addressing the shortcomings of classical graph neural networks that are unable to harness the multi-fidelity observations produced by screening funnels. More specifically, we have proposed two main transfer learning schemes that enable effective knowledge transfer between fidelities: transfer by embeddings or predictions generated by models trained on lowfidelity data, and (supervised) pre-training on low-fidelity and fine-tuning on high-fidelity. All approaches are independent of the convolution operator used for feature extraction within graph neural networks. While learning molecular properties with architectures involving standard readouts is competitive on a range of tasks, particularly quantum properties that are extensive and not localised, this is generally not the case with large-scale and noisy drug discovery datasets. For those tasks, graph neural networks with adaptive readouts excel and unlock the transfer learning capability of supervised pre-training and fine-tuning, which is notoriously challenging for GNNs in general and molecular data in particular .