A spiking neural network (SNN) is defined that includes artificial neurons interconnected by artificial synapses, the SNN defined to correspond to one or more numerical matrices in an equation such that weight values of the synapses correspond to values in the numerical matrices. An input vector is provided to the SNN to correspond to a numerical vector in the equation. A steady state spiking rate is determined for at least a portion of the neurons in the SNN and an approximate result of a matrix inverse problem corresponding to the equation is determined based on values of the steady state spiking rates.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. At least one machine accessible storage medium having instructions stored thereon, wherein the instructions when executed on a machine, cause the machine to: define, using one or more routing tables, a particular spiking neural network (SNN) comprising a plurality of artificial neurons interconnected by a plurality of artificial synapses, wherein the particular SNN is defined to correspond to one or more numerical matrices in an equation, each of the plurality of artificial synapses comprises a respective weight value, and the weight values of the plurality of artificial synapses correspond to values in the one or more numerical matrices; provide, to the particular SNN, a plurality of inputs, wherein the plurality of inputs are selected to correspond to a numerical vector in the equation; determine a spiking rate for at least a portion of the plurality of artificial neurons based on the plurality of inputs; determine a steady state condition for the particular SNN; and determine an approximate result for the equation based on the spiking rate values determined for at least the portion of the plurality of artificial neurons in the steady state condition, wherein the equation comprises multiplication of an inverse of at least one of the numerical matrices. 2. The storage medium of claim 1, wherein the number of neurons in the plurality of neurons is based on dimensions of a particular one of the numerical matrices, and the number of inputs corresponds to a dimension of the numerical vector. 3. The storage medium of claim 1, wherein the particular SNN is implemented using a neuromorphic computing device comprising a network of neuromorphic cores. 4. The storage medium of claim 3, wherein the network of neuromorphic cores comprises: a plurality of neuromorphic cores, wherein each neuromorphic core in the plurality of neuromorphic cores comprises a respective processing resource and logic to implement one or more artificial neurons; one or more routers to route spiking messages between artificial neurons implemented using the plurality of neuromorphic cores; and memory comprising data to define interconnections of the plurality of artificial neurons in the particular SNN. 5. The storage medium of claim 4, wherein the data comprises: the one or more routing tables to define connections between the plurality of artificial neurons corresponding to the plurality of artificial synapses; and the weight values assigned to each of the plurality of artificial synapses. 6. The storage medium of claim 4, wherein each neuromorphic core is to implement two or more of the plurality of artificial neurons. 7. The storage medium of claim 6, wherein the neuromorphic cores time multiplex access to the processing resources of the respective neuromorphic core to concurrently implement the two or more artificial neurons. 8. The storage medium of claim 3, wherein the neuromorphic computing device comprises an interface to accept programming inputs to configure the network of neuromorphic cores to implement any one of a plurality of different spiking neural networks including the particular SNN. 9. The storage medium of claim 1, wherein defining the particular SNN comprises generating the plurality of neurons, defining the one or more routing tables, setting the weight values of the plurality of artificial synapses, and setting values of parameters for the plurality of neurons. 10. The storage medium of claim 9, wherein the parameters comprise one or more of a firing potential threshold, a synaptic decay time constant, a membrane potential decay time constant, and a bias current. 11. The storage medium of claim 1, wherein the numerical matrix comprises a sparse matrix. 12. The storage medium of claim 1, wherein the particular SNN comprises a first set of the plurality of neurons, and each of the first set of neurons is recurrently connected with other neurons in the first set using a first set of the plurality of synapses. 13. The storage medium of claim 12, wherein the equation comprises a2=WI1, where W comprises the one or more matrices, l comprises the input vector, and a comprises a vector corresponding to the spiking rate values determined for at least the portion of the plurality of artificial neurons in the steady state condition. 14. The storage medium of claim 12, wherein the first set of the plurality of neurons comprises a first subset of the plurality of neurons, the first set of the plurality of synapses comprises a first subset of the plurality of synapses, the particular SNN comprises a second subset of the plurality of neurons, the neurons in the second subset of neurons are feedforward connected to the neurons in the first subset through a second subset of the plurality of synapses, and the neurons in the second subset is recurrently connected with other neurons in the second subset using a third subset of the plurality of synapses. 15. The storage medium of claim 14, wherein the equation comprises r=C−1BA−1y, where A comprises a first one of the one or more matrices, B comprises a second one of the one or more matrices, C comprises a third one of the one or more matrices, y comprises the input vector, r comprises a vector corresponding to the spiking rate values determined for neurons in the second subset of neurons in the steady state condition, weight values of synapses in the first subset of synapses correspond to values of matrix A, weight values of synapses in the second subset of synapses correspond to values of matrix B, and weight values of synapses in the third subset of synapses correspond to values of matrix C. 16. The storage medium of claim 12, wherein the first set of the plurality of neurons comprises a first subset of the plurality of neurons, the first set of the plurality of synapses comprises a first subset of the plurality of synapses, the particular SNN comprises a second subset of the plurality of neurons, each of the neurons in the second subset of neurons is feedforward connected to each of the neurons in the first subset through a second subset of the plurality of synapses, and each of the neurons in the second subset is recurrently connected with other neurons in the second subset using a third subset of the plurality of synapses. 17. The storage medium of claim 14, wherein the equation comprises r=C−1BA−1y, where A comprises a first one of the one or more matrices, B comprises a second one of the one or more matrices, C comprises a third one of the one or more matrices, y comprises the input vector, r comprises a vector corresponding to the spiking rate values determined for neurons in the second subset of neurons in the steady state condition, weight values of synapses in the first subset of synapses correspond to values of matrix A, weight values of synapses in the second subset of synapses correspond to values of matrix B, and weight values of synapses in the third subset of synapses correspond to values of matrix C. 18. A method comprising: receiving one or more inputs to define a particular spiking neural network (SNN), wherein definition of the particular SNN comprises definition of a number of digital artificial neurons to be implemented by a neuromorphic computing device, definition of a routing table to define a plurality of artificial synapses corresponding to interconnections of the number of neurons in the particular SNN, and definition of weight values for each of the plurality of synapses, wherein the weight values of the plurality of synapses correspond to values in the one or more numerical matrices; generating the particular SNN on the neuromorphic computing device based on the one or more inputs; receiving an input to the particular SNN comprising a vector, wherein the vector corresponds to a numerical vector in the equation; running the particular SNN based on the input; determining a steady state condition of the particular SNN; determining spiking rate values for at least a portion of the plurality of artificial neurons based on the plurality of inputs; and determining an approximate result for the equation based on the spiking rate values of the portion of the plurality of artificial neurons in the steady state condition, wherein the equation comprises multiplication of the particular vector with an inverse of at least one of the numerical matrices. 19. A system comprising: a neuromorphic computing device comprising: one or more routers; a plurality of neuromorphic cores interconnected by the one or more routers, wherein each neuromorphic core in the plurality comprises: a processor; a memory to store one or more routing tables; and logic to implement one or more artificial neurons to be hosted by the neuromorphic core, wherein each of the artificial neurons comprises a respective dendrite process and a respective soma process to be executed using the processor, and state information for each of the artificial neurons is to be stored in the memory, wherein the one or more routing tables define synapses to interconnect the artificial neurons to define a particular spiking neural network (SNN) comprising the artificial neurons, the particular SNN is defined to correspond to a particular equation comprising inversion of a particular one of one or more numerical matrices and multiplication of a particular vector with the one or more matrices, each of the plurality of artificial synapses has a respective weight value based on values in the one or more numerical matrices; an input source to provide an input with values corresponding to values in the particular vector to the particular SNN; and a spike rate calculator to determine, in a steady state of the particular SNN, spiking rates of a particular portion of the artificial neurons to represent an approximate solution to the equation. 20. The system of claim 19, further comprising another device comprising: a processor; a memory; solver logic to perform a particular iterative solver algorithm, wherein the solver logic is further to: receive the approximate solution; perform the particular iterative solver algorithm using the approximate solution in an initial iteration of the particular iterative solver algorithm; determine a solution to the equation.