System and method for parameter multiplexed gradient descent

A multiplexed gradient descent method for training a neural network implemented in a neuromorphic hardware, the method comprising:

• receiving a first plurality of input signal from an input layer comprising a first plurality of neurons;
• modulating at least one of a first plurality of neuromorphic hardware signals generated by at least one of a first plurality of hardware elements in at least one of a plurality of synaptic circuits, wherein the at least one of the first plurality of neuromorphic hardware signals is modulated to a predetermined value set by a first plurality of neuromorphic hardware parameters;
• applying a first perturbation to each of the first plurality of the neuromorphic hardware parameters, wherein the applying the perturbation modifies the first plurality of the neuromorphic hardware parameters to a second plurality of neuromorphic hardware parameters;
• generating at a second plurality of neurons a second plurality of neuromorphic hardware signals from the modulated first plurality of the neuromorphic hardware signals, wherein each of the second plurality of the neuromorphic hardware signals is a nonlinear function of the at least one of the modulated first plurality of the neuromorphic hardware signals;
• generating at a third plurality of neurons a plurality of output signals from the second plurality of the neuromorphic hardware signals, wherein the plurality of the output signals represent a prediction of the neural network in the neuromorphic hardware;
• comparing at a cost element the plurality of the output signals with a target output to generate a plurality of costs, wherein comparing the plurality of the output signals with the target output comprises applying a plurality of cost functions to the plurality of the output signals and the target output, wherein each of the plurality of the cost function is a measure of correspondence between at least one of the plurality of the output signals and the target output;
• extracting a plurality of modulated cost functions, wherein extracting the plurality of the modulated cost functions comprises determining a plurality of modulations in the plurality of the costs;
• transmitting the plurality of the modulated cost functions to the second plurality of the neuromorphic hardware parameters;
• receiving in at least one of the plurality of the synaptic circuits at least one of the plurality of the transmitted modulated cost functions;
• extracting in at least one of the plurality of the synaptic circuits a partial cost gradient from the at least one of the plurality of the received modulated cost functions;
• determining in at least one of the plurality of the synaptic circuits a parameter change for the at least one of the second plurality of the neuromorphic hardware parameters from the extracted partial cost gradient;
• updating in at least one of the plurality of the synaptic circuits the at least one of the second plurality of the neuromorphic hardware parameters with the parameter change to generate a third plurality of neuromorphic hardware parameters;
• updating the first perturbation to a second perturbation after a first predetermined time period;
• repeating the extracting the partial cost gradient from the at least one of the plurality of the received modulated cost functions for a second predetermined time period;
• and
• receiving a second plurality of input signals and a second target output to the neuromorphic hardware after a third predetermined time period.

A multiplexed gradient descent method for training a neural network implemented in a neuromorphic hardware, the method comprising:

• receiving a first plurality of input signal from an input layer comprising a first plurality of neurons;
• modulating at least one of a first plurality of neuromorphic hardware signals generated by at least one of a first plurality of hardware elements in at least one of a plurality of synaptic circuits, wherein the at least one of the first plurality of the neuromorphic hardware signals is modulated to a predetermined value set by a first plurality of neuromorphic hardware parameters;
• generating at a second plurality of neurons a second plurality of neuromorphic hardware signals from the modulated first plurality of the neuromorphic hardware signals, wherein each of the second plurality of the neuromorphic hardware signals is a nonlinear function of the at least one of the modulated first plurality of the neuromorphic hardware signals;
• generating at a third plurality of neurons a plurality of output signals from the second plurality of the neuromorphic hardware signals, wherein the plurality of the output signals represent a prediction of the neural network in the neuromorphic hardware;
• comparing at a cost element the plurality of the output signals with a target output to generate a plurality of costs, wherein comparing the plurality of the output signals with the target output comprises applying a plurality of cost functions to the plurality of the output signals and the target output, wherein each of the plurality of the cost functions is a measure of correspondence between at least one of plurality of the output signals and the target output;
• extracting a plurality of modulated cost functions, wherein extracting the plurality of modulated cost functions comprises determining a plurality of modulations in the plurality of the costs;
• transmitting the plurality of the modulated cost functions to the first plurality of the neuromorphic hardware parameters;
• optimizing in at least one of the plurality of the synaptic circuits at least one of the plurality of the transmitted modulated cost functions to determine a parameter change for the at least one of the first plurality of the neuromorphic hardware parameters;
• and
• updating the at least one of the first plurality of the neuromorphic hardware parameters with the parameter change to generate a second plurality of neuromorphic hardware parameters.