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Register a new userUnitary Learning for Deep Diffractive Neural Network
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Yong-Liang Xiao
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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.
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Unitary learning is a backpropagation that serves to unitary weights update in deep complex-valued neural network with full connections, meeting a physical unitary prior in diffractive deep neural network ([DN]2). However, the square matrix property of unitary weights induces that the function signal has a limited dimension that could not generalize well. To address the overfitting problem that comes from the small samples loaded to [DN]2, an optical phase dropout trick is implemented. Phase dropout in unitary space that is evolved from a complex dropout and has a statistical inference is formulated for the first time. A synthetic mask recreated from random point apertures with random phase-shifting and its smothered modulation tailors the redundant links through incompletely sampling the input optical field at each diffractive layer. The physical features about the synthetic mask using different nonlinear activations are elucidated in detail. The equivalence between digital and diffractive model determines compound modulations that could successfully circumvent the nonlinear activations physically implemented in [DN]2. The numerical experiments verify the superiority of optical phase dropout in [DN]2 to enhance accuracy in 2D classification and recognition tasks-oriented.
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