Abstract: Photoelectric hybrid artificial intelligence computing chip realizes high-speed and efficient computing through artificial intelligence algorithms in artificial intelligence applications. Particularly, Optical neural networks algorithm is important in realizing a large number of matrix operations among them. We use a fast Fourier transform type optical neural network built with Mach-Zehnder interferometers to achieve high-precision recognition of handwritten digits. In terms of model construction, the linear layer of the neural network is decomposed by singular value decomposition, so as to realize data dimension reduction and main feature extraction. In the training of the optical neural networks, the stochastic gradient descent with momentum algorithm and the root mean square propagation algorithm were used respectively, and the recognition accuracy of the optical neural networks for handwritten digits was analyzed under the different training algorithms. In addition, we also deeply analyze the mathematical theory behind the two training algorithms, and explore the essential reasons for the difference between the experimental results of the two training algorithms. Finally, through experimental comparison, we found that the root mean square propagation algorithm has a high recognition accuracy on the fast Fourier transform type optical neural network, reaching 97.4%.what′s more, the optical neural networks calculation speed using the root mean square propagation algorithm is better than the stochastic gradient descent with momentum algorithm.