A spiking neural network (SNN) is implemented on a neuromorphic computers and includes a plurality of neurons, a first set of the plurality of synapses defining feed-forward connections from a first subset of the neurons to a second subset of the neurons, a second subset of the plurality of synapses to define recurrent connections between the second subset of neurons, and a third subset of the plurality of synapses to define feedback connections from the second subset of neurons to the first subset of neurons. A set of input vectors are provided to iteratively modify weight values of the plurality of synapses. Each iteration involves selectively enabling and disabling the third subset of synapses with a different one of the input vectors applied to the SNN. The weight values are iteratively adjusted to derive a solution to an equation comprising an unknown matrix variable and an unknown vector variable.
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 a spiking neural network (SNN), wherein the SNN is to comprise: a plurality of neurons, a first set of the plurality of synapses to define feed-forward connections from a first subset of the plurality of neurons to a second subset of the plurality of neurons, a second subset of the plurality of synapses to define recurrent connections between the second subset of neurons, and a third subset of the plurality of synapses to define feedback connections from the second subset of neurons to the first subset of neurons; provide a plurality of input vectors to the SNN to iteratively modify weight values of the plurality of synapses, wherein iteratively modifying the plurality of synapses is to comprise, in each iteration: providing one of the plurality of input vectors to the SNN with the third subset of synapses disabled; determining first steady state spiking rates of at least the second subset of neurons with the respective input vector provided and the third subset of synapses disabled; determining second spiking rates of at least the second subset of neurons with the third subset of synapses enabled and based on the respective input vector; modifying weight values of the plurality of synapses based on a difference between the first spiking rates and the second spiking rates; determine a convergence of weight values of the plurality of synapses to a particular set of weight values, wherein the particular set of weight values are to correspond to an unknown matrix in an equation. 2. The storage medium of claim 1, wherein first steady state spiking rates and second steady state spiking rates are to be determined for both the first and second subsets of neurons. 3. The storage medium of claim 1, wherein the weight values are to be modified according to equations: F←F+η3(b1−b2)a2T D←D+η2(b1−b2)a2T, and G←G+η1(a2−a1)a2T, where G comprises a matrix of weight values for the second subset of synapses, D comprises a matrix of weight values for the first subset of synapses, a1 comprises first steady state spiking rates of the second subset of neurons, a2 comprises second steady state spiking rates of the second subset of neurons, b1 comprises first steady state spiking rates of the first subset of neurons, b2 comprises second steady state spiking rates of the first subset of neurons, η1 comprises a first learning rate, and η2 comprises a second learning rate. 4. The storage medium of claim 1, wherein a modified version of the respective input vector is to be provided to the SNN when the third subset of synapses are enabled and the second steady state spiking rates are determined with the modified version of the respective input vector provided to the SNN. 5. The storage medium of claim 4, wherein the respective input vector comprises xi and the modified version of the respective input vector is to be according to (1−γ) xi, where γ is a variance coefficient. 6. The storage medium of claim 1, wherein the SNN is to be defined for a neuromorphic computing device to implement the SNN. 7. The storage medium of claim 6, wherein defining the SNN comprises providing definition data to the neuromorphic computing device to cause the neuromorphic computing device to implement the SNN. 8. The storage medium of claim 7, wherein the plurality of synapses are to be defined within the neuromorphic computing device in one or more routing tables of the neuromorphic computing device. 9. The storage medium of claim 7, wherein the neuromorphic computing device comprises a plurality of neuromorphic processing cores interconnected by one or more routers of the neuromorphic computing device. 10. The storage medium of claim 1, wherein the instructions, when executed, further cause the machine to determine final steady state spiking rates for at least the second subset of neurons corresponding to the particular set of weight values. 11. The storage medium of claim 10, wherein the final steady state spiking rates are to correspond to values of an unknown vector in the equation. 12. The storage medium of claim 11, wherein the number of neurons in the SNN is based on dimensions of the unknown matrix and a dimension of the unknown vector. 13. The storage medium of claim 1, wherein random weight values are to be applied to the plurality of synapses as initial weight values for the plurality of synapses. 14. The storage medium of claim 1, wherein the second subset of neurons are to correspond to a plurality of clusters and the unknown matrix is to correspond to unknown features of the plurality of clusters. 15. A method comprising: defining a spiking neural network (SNN) comprising a plurality of artificial neurons interconnected by a plurality of artificial synapses, wherein the SNN is to comprise: a first subset of the plurality of synapses to define feedforward connections from a first subset of the plurality of neurons to a second subset of the plurality of neurons, a second subset of the plurality of synapses to define recurrent connections between the second subset of neurons, and a third subset of the plurality of synapses to define feedback connections from the second subset of neurons to the first subset of neurons; disabling the third subset of synapses; providing a first input vector as an input to the SNN with the third subset of synapses disabled; determining a first steady state condition for the SNN when the first input vector is provided as the input to the SNN and the third subset of synapses is disabled; determining first spiking rates of at least a subset of the plurality of neurons associated with the first steady state condition; enabling the third subset of synapses; providing a modified version of the first input vector as an input to the SNN with the third subset of synapses enabled; determining a second steady state condition for the SNN when the modified version of the first input vector is provided as the input to the SNN and the third subset of synapses is enabled; determining second spiking rates of the first subset of neurons and the second subset of neurons, wherein the second spiking rates are associated with the second steady state condition; and modifying weights of the plurality of synapses based on a difference between the first spiking rates and the second spiking rates. 16. 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 is to implement one or more artificial neurons in a particular spiking neural network and comprises: a processor; a memory to store one or more routing tables; a respective dendrite process to be executed using the processor; and a respective soma process to be executed using the processor, wherein the one or more routing tables define a plurality of artificial synapses to interconnect the artificial neurons to define a particular spiking neural network (SNN), and the particular SNN is to comprise: a first layer of artificial neurons, a second layer of artificial neurons, a first subset of the plurality of synapses to define feedforward connections from neurons in the first layer neurons to neurons in the second layer, a second subset of the plurality of synapses to define recurrent connections between neurons in the second layer, and a third subset of the plurality of synapses to define feedback connections from neurons in the second layer to neurons in the first layer; and logic to: provide a set of input vectors to the particular SNN; selectively enable and disable the third subset of synapses; iteratively adjust weight values for at least the first subset of synapses based on the set of input vectors to derive a solution to an equation comprising an unknown matrix variable and an unknown vector variable. 17. The system of claim 16, wherein the logic is to be executed on a machine separate from the neuromorphic computing device. 18. The system of claim 16, wherein at least a portion of the logic is resident on the neuromorphic computing device. 19. The system of claim 16, wherein the plurality of neuromorphic cores are configurable to implement any one of a plurality of different spiking neural networks. 20. The system of claim 19, wherein the logic is further to provide one or more inputs to cause the neuromorphic computing device to implement a particular one of the plurality of different spiking neural networks.