[论文解读] On Complex Valued Convolutional Neural Networks

Nitzan Guberman|arXiv (Cornell University)|Feb 29, 2016

Advanced Neural Network Applications参考文献 29被引用 106

一句话总结

这篇论文提出了一个带有复数输入和权重的复值CNN变体，分析其训练挑战，并展示它在正则化过拟合的同时能捕捉相位结构，通过细胞检测任务进行演示。

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.

研究动机与目标

• Motivate the use of complex numbers to capture structure in natural images and explore their regularization potential in CNNs.
• Develop a complex valued CNN as a generalization of real CNNs with a corresponding training scheme.
• Assess whether complex CNNs regularize better and how they compare to real CNNs on a cell detection task.
• Characterize the role of phase structure in complex networks and its impact on representation learning.

提出的方法

• Define a complex valued extension of CNNs with complex inputs and weights.
• Develop complex calculus tools and backpropagation for training, including Wirtinger derivatives and complex gradients.
• Demonstrate that complex convolutions act as a restricted form of real convolutions with twice as many parameters.
• Implement complex ReLU, pooling, and a projection layer within the network architecture.
• Conduct an empirical study comparing complex and real networks on a cell detection task, including analysis of optimization difficulties and overfitting.
• Provide qualitative analysis of learned complex kernels to illustrate phase sensitivity.

实验结果

研究问题

• RQ1 Can a complex valued CNN achieve comparable performance to a real-valued CNN on a practical vision task?
• RQ2 Does restricting computations to the complex domain function as a regularization that reduces overfitting?
• RQ3 How does phase structure manifest in learned filters and affect representation learning?
• RQ4 What are the numerical and optimization challenges unique to training complex valued CNNs?
• RQ5 In what ways does complex convolution relate to standard real convolutions?

主要发现

• The complex valued CNN is a restricted form of a real CNN with twice the number of parameters.
• The complex model is sensitive to phase structure and can serve as a regularized model for phase-relevant problems.
• Empirically, the complex network and a real network achieve comparable results on cell detection, but the complex network is harder to train.
• The complex network shows reduced vulnerability to overfitting compared to its real counterpart.
• The study provides evidence that complex networks can detect meaningful phase structure in data.