Unitary Learning for Deep Diffractive Neural Network

Realization of deep learning with coherent diffraction has achieved remarkable development nowadays, which benefits on the fact that matrix multiplication can be optically executed in parallel as well as with little power consumption. Coherent optical field propagated in the form of complex-value entity can be manipulated into a task-oriented output with statistical inference. In this paper, we present a unitary learning protocol on deep diffractive neural network, meeting the physical unitary prior in coherent diffraction. Unitary learning is a backpropagation serving to unitary weights update through the gradient translation between Euclidean and Riemannian space. The temporal-space evolution characteristic in unitary learning is formulated and elucidated. Particularly a compatible condition on how to select the nonlinear activations in complex space is unveiled, encapsulating the fundamental sigmoid, tanh and quasi-ReLu in complex space. As a preliminary application, deep diffractive neural network with unitary learning is tentatively implemented on the 2D classification and verification tasks.