To enrich the diversity of artificial neurons, a type of quadratic neurons was proposed previously, where the inner product of inputs and weights is replaced by a quadratic operation. In this paper, we demonstrate the superiority of such quadratic neurons over conventional counterparts. For this purpose, we train such quadratic neural networks using an adapted backpropagation algorithm and perform a systematic comparison between quadratic and conventional neural networks for classificaiton of Gaussian mixture data, which is one of the most important machine learning tasks. Our results show that quadratic neural networks enjoy remarkably better efficacy and efficiency than conventional neural networks in this context, and potentially extendable to other relevant applications.

中文翻译：

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二次元在高斯混合数据分类中优于传统神经网络

为了丰富人工神经元的多样性，之前提出了一种二次神经元，其中输入和权重的内积被二次运算代替。在本文中，我们证明了这种二次神经元相对于传统神经元的优越性。为此，我们使用自适应反向传播算法训练这种二次神经网络，并在二次神经网络和传统神经网络之间进行系统比较，以对高斯混合数据进行分类，这是最重要的机器学习任务之一。我们的结果表明，在这种情况下，二次神经网络比传统神经网络具有显着更好的功效和效率，并且有可能扩展到其他相关应用。