Fig. 6. Handwriting recognition with a complex-valued multilayer perceptron.

a The network consists of an input layer Wⁱⁿ, a hidden layer W and an output layer W^out. All 10 digits are included in our experiment. The input image sized as 28 × 28 is stretched into a 784 × 1 vector. The output layer maps the four hidden outputs to 10 classes. b The performance comparison of complex-valued and real-valued network implemented on the same chip. The blue and orange curves represent the accuracy and the cost of training, respectively. The solid line represents the complex-valued algorithm while the dashed line represents the real-valued algorithm. The training accuracy of complex-valued and real-valued models are 93.1% and 84.3%, respectively. In addition, a faster convergence is observed in complex model. c The confusion matrix by the chip-implemented complex model, when evaluating on testing set. Each column of the matrix represents the instances in a predicted label while each row represents the instances in a true label. The diagonal elements represent the number of instances that are correctly predicted. The chip testing accuracy is 90.5%. d The confusion matrix by the real model, showing a testing accuracy of 82.0%. e Sceneries are investigated, where complex-valued weights are implemented on chip, but input encoding and output detection are either complex-valued or real-valued. Their training curves are shown. Notably, even when we restrict both the encoding and detection to be real-valued, the complex-valued model exhibits a superior performance (87.7%) over its real-valued counterpart (84.3%).