Abstract: A graph includes nodes connected with one or more edges. Each node in the graph may be encoded in a neuron in a neural network. The neural network may include neurons arranged in a spiking neuromorphic architecture. To find the shortest path between a first node and a second node in the graph, a spike may propagate from a first neuron encoding the first node to a second neuron encoding the second node. Another spike may propagate from the second neuron to the first neuron. Each neuron spiking in a propagation may store a value that indicates the depth of the neuron in a propagation path. A spiking neuron may generate two values in the two propagations, respectively. A spiking neuron having two equal values may be identified. The shortest path includes one or more edges that connect the nodes encoded in the identified spiking neurons.

Abstract: A neural network, which can solve conic optimization problems may include a first layer, a second layer, and a third layer. The first layer includes first neurons encoding constraint coefficients of the conic optimization problem. The second layer includes second neurons encoding decision variables of the conic optimization problem. The third layer includes an integrator neuron. Data may be sent from a first neuron to a second neuron or from the second neuron to the first neuron. A neuron, after receiving data from another neuron, may update its internal state parameter based on the data and the weight of the connection between the two neurons. The communication may be triggered by the internal state parameter of the neuron sending the data meets a criterion. After the internal state parameter of the integrator neuron meets a criterion, the integrator neuron may output a solution to the conic optimization problem.