1. A method, comprising: propagating a first set and a second set of axonal firing events through a symmetric core circuit in a first direction and a second direction, respectively, wherein the second direction is opposite of the first direction, the symmetric core circuit comprises a first core module and a second core module overlaid on one another and oriented differently relative to each other such that axonal firing events propagate through the first core module in the first direction and axonal firing events propagate through the second core module in the second direction, and each core module comprises an interconnection network for interconnecting multiple electronic neurons with multiple electronic axons; for at least one neuron, receiving an axonal firing event via an interconnected axon; and for at least one neuron, generating a neuronal firing event according to a neuronal activation function; wherein each core module of the symmetric core circuit has a corresponding adaptive lookup table, the corresponding adaptive lookup table used to determine target axons for neuronal firing events generated by neurons in the core module; and wherein a first neuron of the first core module is overlaid on and within proximity of a first axon of the second core module, thereby enabling the first neuron to share its neuronal activations with the first axon, and further enabling the first axon to share its axonal activations with the first neuron.