On Complex Valued Convolutional Neural Networks

TL;DR

This paper introduces a complex-valued CNN model that captures phase information and acts as a regularizer, showing comparable performance to real CNNs but with reduced overfitting in cell detection tasks.

Contribution

The paper presents a novel complex-valued CNN architecture addressing training challenges and demonstrating its regularization benefits over traditional real-valued CNNs.

Findings

Complex CNNs are less prone to overfitting than real CNNs.

The complex model captures meaningful phase structures in data.

Performance comparable to real CNNs in cell detection.

Abstract

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.