A neural system comprises multiple neurons interconnected via synapse devices. Each neuron integrates input signals arriving on its dendrite, generates a spike in response to the integrated input signals exceeding a threshold, and sends the spike to the interconnected neurons via its axon. The system further includes multiple noruens, each noruen is interconnected via the interconnect network with those neurons that the noruen's corresponding neuron sends its axon to. Each noruen integrates input spikes from connected spiking neurons and generates a spike in response to the integrated input spikes exceeding a threshold. There can be one noruen for every corresponding neuron. For a first neuron connected via its axon via a synapse to dendrite of a second neuron, a noruen corresponding to the second neuron is connected via its axon through the same synapse to dendrite of the noruen corresponding to the first neuron.