We investigate the effectiveness of trace-based supervision methods for training existing neural abstract machines. To define the class of neural machines amenable to trace-based supervision, we introduce the concept of a differential neural computational machine (dNCM) and show that several existing architectures (NTMs, NRAMs) can be described as dNCMs. We performed a detailed experimental evaluation with NTM and NRAM machines, showing that additional supervision on the interpretable portions of these architectures leads to better convergence and generalization capabilities of the learning phase than standard training, in both noise-free and noisy scenarios.