1. A neural network circuit, comprising: multiple symmetric core circuits, wherein each symmetric core circuit comprises: a first core module and a second core module, wherein each core module comprises: a plurality of electronic neurons; a plurality of electronic axons; and an interconnection network comprising multiple electronic synapses interconnecting the axons to the neurons, wherein each synapse interconnects an axon to a neuron; and at least one adaptive lookup table, wherein each lookup table corresponds to a core module of said symmetric core circuit, and wherein each lookup table is used to determine target axons for neuronal firing events generated by neurons in a corresponding core module; wherein the first core module and the second core module are logically overlayed overlaid on one another such that neurons in the first core module are proximal to axons in the second core module, and axons in the first core module are proximal to neurons in the second core module; and wherein each neuron in each core module receives axonal firing events via interconnected axons and generates a neuronal firing event according to a neuronal activation function.