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.

中文翻译：

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深度衍射神经网络的幺正学习

如今，相干衍射深度学习的实现取得了显着的发展，这得益于矩阵乘法可以在光学上并行执行并且功耗很小。以复值实体形式传播的相干光场可以通过统计推断处理成面向任务的输出。在本文中，我们提出了一种深度衍射神经网络的幺正学习协议，满足相干衍射中的物理幺正先验。酉学习是一种反向传播，通过欧几里得空间和黎曼空间之间的梯度转换来更新酉权重。制定并阐明了幺正学习中的时空演化特征。特别是揭示了如何选择复杂空间中的非线性激活的兼容条件，封装了复杂空间中的基本 sigmoid、tanh 和 quasi-ReLu。作为初步应用，在二维分类和验证任务上初步实现了具有幺正学习的深度衍射神经网络。