Fig. 3: Training a convolutional neural network.

a Detailed view of the convolutional neural network trained on the D-Wave Ising machine. The inputs are 3 × 3 pixel images. The convolution layer applies four different sets of 2 × 2 weight filters to the input images, generating four 2 × 2 feature maps. Each feature map is then condensed to a single value through an average pooling operation. After flattening, a fully connected classifier provides the output of the network, a vector of dimension 4. b Schematic of the convolutional neural network’s implementation on the Chimera architecture of a D-Wave Ising machine. The four peripheral crossbar arrays perform the convolution operation in parallel. Each array receives a distinct patch of pixels from the input data, yet all share identical couplings, ensuring uniform filter application across different patches. The blue spins on the four crossbar arrays individually represent the values x₁, x₂, x₃, x₄ of the feature map highlighted in a, obtained by convolving the input with the filter encoded in the couplings depicted in light blue circles. The output of the convolutional operation is then down-sampled via the averaged pooling coupling ( \(J=\frac{1}{4}\)) and linked through identity couplings ( J = 1). The dotted blue chain represents the output of the averaged pooling operation applied to the feature map depicted with the blue spins. Finally, the results of the averaged pooling operation are fed into the fully connected classifier, which predicts the input’s class. Here we have four output neurons as we use two output neurons to encode a class. The convolutional neural network is mapped as-is on the chip, eliminating the need for an embedding step. c The training dataset consisting in the 2 patterns used for training the CNN implemented on the D-Wave Ising machine. d Training curve (mean squared error) related to training the CNN on the D-Wave Ising machine. e Training curve (accuracy (%) related to training the CNN on the D-Wave Ising machine.