A method of training a neural network with back propagation includes generating error events representing a gradient of a cost function for the neural network. The error events may be generated based on a forward pass through the neural network resulting from input events, weights of the neural network and events from a target signal. The method further includes updating the weights of the neural network based on the error events.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method of training a neural network with back propagation, comprising: generating error events representing a gradient of a cost function for the neural network based on a forward pass through the neural network resulting from input events, weights of the neural network and events from a target signal; and updating the weights of the neural network based on the error events. 2. The method of claim 1, in which the weights of the neural network are updated based on a single error event. 3. The method of claim 1, in which the input events comprise signed spikes. 4. The method of claim 1, in which the input events includes only positive spikes. 5. The method of claim 1, further comprising: receiving an input vector; and generating the input events corresponding to the input vector. 6. The method of claim 1, further comprising generating output events via the forward pass through the neural network, the output events generated at timings based on an occurrence of a predefined event. 7. The method of claim 1, in which the error events are generated based on a computed error and a mean squared error cost. 8. An apparatus for training a neural network with back propagation, comprising: a memory; and at least one processor coupled to the memory, the at least one processor configured: to generate error events representing a gradient of a cost function for the neural network based on a forward pass through the neural network resulting from input events, weights of the neural network and events from a target signal; and to update the weights of the neural network based on the error events. 9. The apparatus of claim 8, in which the at least one processor is further configured to update the weights of the neural network based on a single error event. 10. The apparatus of claim 8, in which the input events comprise signed spikes. 11. The apparatus of claim 8, in which the input events includes only positive spikes. 12. The apparatus of claim 8, in which the at least one processor is further configured: to receive an input vector; and to generate the input events corresponding to the input vector. 13. The apparatus of claim 8, in which the at least one processor is further configured to process the input events via the forward pass through the neural network to generate output events at timings based on an occurrence of a predefined event. 14. The apparatus of claim 8, in which the at least one processor is further configured to generate the error events based on a computed error and a mean squared error cost. 15. An apparatus for training a neural network with back propagation, comprising: means for generating error events representing a gradient of a cost function for the neural network based on a forward pass through the neural network resulting from input events, weights of the neural network and events from a target signal; and means for updating the weights of the neural network based on the error events. 16. The apparatus of claim 15, in which the weights of the neural network are updated based on a single error event. 17. The apparatus of claim 15, in which the input events comprise signed spikes. 18. The apparatus of claim 15, in which the input events includes only positive spikes. 19. The apparatus of claim 15, further comprising: means for receiving an input vector; and means for generating the input events corresponding to the input vector. 20. The apparatus of claim 15, further comprising means for generating output events via the forward pass through the neural network at timings based on an occurrence of a predefined event. 21. The apparatus of claim 15, in which the error events are generated based on a computed error and a mean squared error cost. 22. A non-transitory computer-readable medium having encoded thereon program code for training a neural network with back propagation, the program code being executed by a processor and comprising: program code to generate error events representing a gradient of a cost function for the neural network based on a forward pass through the neural network resulting from input events, weights of the neural network and events from a target signal; and program code to update the weights of the neural network based on the error events. 23. The non-transitory computer-readable medium of claim 22, further comprising program code to update the weights of the neural network based on a single error event. 24. The non-transitory computer-readable medium of claim 22, in which the input events comprise signed spikes. 25. The non-transitory computer-readable medium of claim 22, in which the input events includes only positive spikes. 26. The non-transitory computer-readable medium of claim 22, further comprising: program code to receive an input vector; and program code to generate the input events corresponding to the input vector. 27. The non-transitory computer-readable medium of claim 22, in which the forward pass through the neural network generates an output event at timings based on an occurrence of a predefined event. 28. The non-transitory computer-readable medium of claim 22, in which the error events are generated based on a computed error and a mean squared error cost.