Abstract 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 with high band-with and low latency. Coherent optical field in the form of complex-valued entity can be manipulated into a task-oriented output. In this paper, a modulation mechanism is established by implementing the equivalence between a digital deep unitary neural network and optical coherent diffraction. We present a unitary learning avenue on diffractive deep neural network, meeting the physical unitary prior in coherent diffraction. The Unitary learning is a Backpropagation serving to unitary weights update through the gradient translation from Euclidean to Riemannian space. The temporal-space evolution characteristics in unitary learning are formulated and elucidated. And a compatible condition on how to select the nonlinear activation in complex space is unveiled, encapsulating the fundamental sigmoid, tanh and quasi-ReLu in complex space available in a single channel training. The performance of phase-ReLu is particularly emphasized. As a preliminary application, diffractive deep neural network with unitary learning is tentatively implemented on the 2D classification and verification tasks.

中文翻译：

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衍射深度神经网络的幺正学习

摘要 目前，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高带宽和低延迟的情况下并行光学执行。复值实体形式的相干光场可以被操纵成面向任务的输出。在本文中，通过实现数字深度酉神经网络和光学相干衍射之间的等价性，建立了一种调制机制。我们在衍射深度神经网络上提出了单一学习途径，满足相干衍射中的物理单一先验。酉学习是一种反向传播，通过从欧几里得空间到黎曼空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。并揭示了如何在复杂空间中选择非线性激活的兼容条件，将基本的 sigmoid、tanh 和 quasi-ReLu 封装在单通道训练中可用的复杂空间中。特别强调了 phase-ReLu 的性能。作为初步应用，具有幺正学习的衍射深度神经网络初步应用于二维分类和验证任务。