Realization of deep learning with coherent optical field has attracted remarkably attentions presently, which benefits on the fact that optical matrix manipulation can be executed at speed of light with inherent parallel computation as well as low latency. Photonic neural network has a significant potential for prediction-oriented tasks. Yet, real-value Backpropagation behaves somewhat intractably for coherent photonic intelligent training. We develop a compatible learning protocol in complex space, of which nonlinear activation could be selected efficiently depending on the unveiled compatible condition. Compatibility indicates that matrix representation in complex space covers its real counterpart, which could enable a single channel mingled training in real and complex space as a unified model. The phase logical XOR gate with Mach-Zehnder interferometers and diffractive neural network with optical modulation mechanism, implementing intelligent weight learned from compatible learning, are presented to prove the availability. Compatible learning opens an envisaged window for deep photonic neural network.
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