1. A neural network, comprising: multiple neurons interconnected via an interconnect network comprising a plurality of synapse devices, wherein each neuron integrates input signals arriving on its dendrite, generates a spike signal in response to the integrated input signals exceeding a threshold, and sends the spike signal to the interconnected neurons via its axon; and multiple noruens corresponding one-to-one to said neurons, each noruen comprising a symmetric dual of a neuron, wherein each noruen is interconnected via the interconnect network with those neurons that a corresponding neuron of said noruen communicates with via an axon of said corresponding neuron; wherein each noruen integrates input spike signals from connected spiking neurons and generates a spiking signal in response to the integrated input spike signals exceeding a threshold.