Convolutional neural networks (CNNs) are the cutting edge model for
supervised machine learning in computer vision. In recent years CNNs have
outperformed traditional approaches in many computer vision tasks such as
object detection, image classification and face recognition. CNNs are
vulnerable to overfitting, and a lot of research focuses on finding
regularization methods to overcome it. One approach is designing task specific
models based on prior knowledge.
Several works have shown that properties of natural images can be easily
captured using complex numbers. Motivated by these works, we present a
variation of the CNN model with complex valued input and weights. We construct
the complex model as a generalization of the real model. Lack of order over the
complex field raises several difficulties both in the definition and in the
training of the network. We address these issues and suggest possible
solutions.
The resulting model is shown to be a restricted form of a real valued CNN
with twice the parameters. It is sensitive to phase structure, and we suggest
it serves as a regularized model for problems where such structure is
important. This suggestion is verified empirically by comparing the performance
of a complex and a real network in the problem of cell detection. The two
networks achieve comparable results, and although the complex model is hard to
train, it is significantly less vulnerable to overfitting. We also demonstrate
that the complex network detects meaningful phase structure in the data.

本文介绍了使用复数输入和权重构造卷积神经网络（CNN）的变形模型，以及提出的正则化方法解决训练 CNN 中的一些问题和困难，通过与真实 CNN 进行比较并应用于细胞检测问题进行实证验证，表明复杂模型比真实模型更不易过拟合且可检测出数据的有意义的相位结构。