Abstract: Nodes in a graph may be encoded in neurons of a neural network. Forward and backward spiking phases may be conducted to find shortest path. During the forward spiking phase, each neuron may update its state after determining that a spike it has received from a spiking neuron in the last time step has a value smaller than its current state value. The spike may include an edge weight and a state of the spiking neuron. During the backward spiking phase, each neuron may update its other state based on a spike from a neighboring neuron in a time step and an index of the current time step. The neuron may send its identifier (ID) to a host based on its states. The host may identify the shortest path from the source node to the target node based on neuron IDs it receives.

Abstract: A neuromorphic network may solve combinatorial optimization problems. The neuromorphic network may include variable neurons, a solution monitoring neuron, and one or more readout neurons. The variable neurons may each represent one binary variable in a combinatorial optimization problem. An internal state of a variable neuron may change as the variable flips. The internal state may be stored in a memory of the variable neuron. The variable neuron may spike when its internal state changes. One or more other variable neurons receiving the spike may determine whether to change their internal states based on the spike. The variable neurons may send their internal states to the solution monitoring neuron to compute a cost of the QUBO problem and determine whether a solution is found. A readout neuron may receive variable assignments resulting in the solution from at least some variable neurons and integrate the variable assignments into one message.

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.