Partially coherent high-order optical neural networks via pseudo-nonlinear encoding

<title>Abstract</title> <p>Diffractive optical neural networks (DONNs) provide a promising route towards high-speed and energy-efficient computing. However, the absence of a general framework for nonlinear activation remains a fundamental limitation. Here we propose a high-order optical neural network (HONN) framework under partially coherent illumination, which enables effective nonlinearity through a unified system-level description. In this framework, the nonlinear response arises from the interplay of coherence-dependent detection and input-dependent pseudo-nonlinearity to a controllable order. We experimentally demonstrate this model in visible spectrum on Digit MNIST and Fashion MNIST, and results show that HONN can successfully capture the performance evolution across varying coherence conditions and nonlinear orders. Further validations on RAF and MedMNIST verify that our HONN surpasses conventional DONNs with competing performance to traditional electrical neural networks with &lt;10% of their computational complexity only. Furthermore, our model possesses superior coherent robustness, laying a solid foundation for practical real-world deployment. These results establish a general framework for high-order optical inference beyond traditional diffractive models and provide a practical route towards optical computing in machine vision, computational imaging and sensing.</p>