Deep neural networks have achieved great success in almost every field of artificial intelligence. However, several weaknesses keep bothering researchers due to its hierarchical structure, particularly when large-scale parallelism, faster learning, better performance, and high reliability are required. Inspired by the parallel and large-scale information processing structures in the human brain, a shallow broad neural network model is proposed on a specially designed multi-order Descartes expansion operation. Such Descartes expansion acts as an efficient feature extraction method for the network, improve the separability of the original pattern by transforming the raw data pattern into a high-dimensional feature space, the multi-order Descartes expansion space. As a result, a single-layer perceptron network will be able to accomplish the classification task. The multi-order Descartes expansion neural network (MODENN) is thus created by combining the multi-order Descartes expansion operation and the single-layer perceptron together, and its capacity is proved equivalent to the traditional multi-layer perceptron and the deep neural networks. Three kinds of experiments were implemented, the results showed that the proposed MODENN model retains great potentiality in many aspects, including implementability, parallelizability, performance, robustness, and interpretability, indicating MODENN would be an excellent alternative to mainstream neural networks.

中文翻译：

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MODENN：基于多阶笛卡尔展开的浅层广泛神经网络模型。

深度神经网络几乎在人工智能的每一个领域都取得了巨大的成功。然而，由于其层次结构，一些弱点一直困扰着研究人员，特别是在需要大规模并行、更快的学习、更好的性能和高可靠性时。受人脑中并行和大规模信息处理结构的启发，在专门设计的多阶笛卡尔展开操作上提出了浅层广义神经网络模型。这种笛卡尔展开作为一种高效的网络特征提取方法，通过将原始数据模式转换为高维特征空间，即多阶笛卡尔展开空间，提高了原始模式的可分性。因此，单层感知器网络就能完成分类任务。多阶笛卡尔展开运算与单层感知器相结合，创建了多阶笛卡尔展开神经网络（MODENN），证明其容量与传统的多层感知器和深度神经网络相当。实施了三种实验，结果表明，所提出的MODENN模型在可实现性、可并行性、性能、鲁棒性和可解释性等许多方面都保留了巨大的潜力，表明MODENN将成为主流神经网络的优秀替代品。多阶笛卡尔展开运算与单层感知器相结合，创建了多阶笛卡尔展开神经网络（MODENN），证明其容量与传统的多层感知器和深度神经网络相当。实施了三种实验，结果表明，所提出的MODENN模型在可实现性、可并行性、性能、鲁棒性和可解释性等许多方面都保留了巨大的潜力，表明MODENN将成为主流神经网络的优秀替代品。多阶笛卡尔展开运算与单层感知器相结合，创建了多阶笛卡尔展开神经网络（MODENN），证明其容量与传统的多层感知器和深度神经网络相当。实施了三种实验，结果表明，所提出的MODENN模型在可实现性、可并行性、性能、鲁棒性和可解释性等许多方面都保留了巨大的潜力，表明MODENN将成为主流神经网络的优秀替代品。