Crossbar arrays of non-volatile memory (NVM) devices represent one possible path for implementing highly energy-efficient neuromorphic computing systems. For Deep Neural Networks (DNN), where information can be encoded as analog voltage and current levels, such arrays can represent matrices of synaptic weights, implementing the matrix-vector multiplication needed for algorithms such as backpropagation in a massively-parallel fashion. Previous research demonstrated a large-scale hardware-software implementation based on phase-change memories and analyzed the potential speed and power advantages over GPU-based training. In this proceeding we will discuss extensions of this work leveraging a different class of memory elements. Using the concept of jump-tables we simulate the impact of real conductance response of non-filamentary resistive devices based on Pr0.3Ca0.7 Mn O3 (PCMO). With the same approach as of , we simulate a three-layer neural network with training accuracy >90% on the MNIST dataset. The higher ON/OFF conductance ratio of improved Al[Mo/PCMO devices together with new programming strategies can lead to further accuracy improvement. Finally, we show that the bidirectional programming of Al[Mo/PCMO can be used to implement high-density neuromorphic systems with a single conductance per synapse, at only a slight degradation to accuracy.