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Application-specific optical processors have been considered disruptive technologies for modern computing that can fundamentally accelerate the development of artificial intelligence (AI) by offering substantially improved computing performance. Recent advancements in optical neural network architectures for neural information processing have been applied to perform various machine learning tasks. However, the existing architectures have limited complexity and performance; and each of them requires its own dedicated design that cannot be reconfigured to switch between different neural network models for different applications after deployment. Here, we propose an optoelectronic reconfigurable computing paradigm by constructing a diffractive processing unit (DPU) that can efficiently support different neural networks and achieve a high model complexity with millions of neurons. It allocates almost all of its computational operations optically and achieves extremely high speed of data modulation and large-scale network parameter updating by dynamically programming optical modulators and photodetectors. We demonstrated the reconfiguration of the DPU to implement various diffractive feedforward and recurrent neural networks and developed a novel adaptive training approach to circumvent the system imperfections. We applied the trained networks for high-speed classifying of handwritten digit images and human action videos over benchmark datasets, and the experimental results revealed a comparable classification accuracy to the electronic computing approaches. Furthermore, our prototype system built with off-the-shelf optoelectronic components surpasses the performance of state-of-the-art graphics processing units (GPUs) by several times on computing speed and more than an order of magnitude on system energy efficiency.