Figure 2.

Training of a 3-layered artificial neural network with 500 neurons in the hidden layer by the stochastic photonic updates. (a) The network is trained for an MNIST hand-written recognition task. For each training trial, the network receives sets of handwritten digits as input and their corresponding digit classes as the target output. (b) The network computes the feedforward weights and updates them with stochastic photonic feedback. The parameter q is the probability of transmitting one photon per neuron, and as it gets larger (closer to 1), the network sends more backward photons and behaves closer to the conventional backpropagation algorithm. (c) As the trial number grows, the error rate (that is the moving average of the past 100 trial errors, see Eq. (11) converges to a small value and the training completes. This convergence happens even for small values of q but after greater numbers of trials. Here, the learning rate, $ϵ=0.01$, has been kept small for the stability of the network. (d) The test error, which measures the distance between the target and the output of the trained model, is averaged over 10 repetitions of the test experiment for each different values of q and $ϵ$ (see “Methods” for details).