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Published as a conference paper at ICLR 2018

DEEP COMPLEX NETWORKS

ABSTRACT

At present, the vast majority of building blocks, techniques, and architectures for

deep learning are based on real-valued operations and representations. However,

recent work on recurrent neural networks and older fundamental theoretical anal-

ysis suggests that complex numbers could have a richer representational capacity

and could also facilitate noise-robust memory retrieval mechanisms. Despite their

attractive properties and potential for opening up entirely new neural architectures,

complex-valued deep neural networks have been marginalized due to the absence

of the building blocks required to design such models. In this work, we provide

the key atomic components for complex-valued deep neural networks and apply

them to convolutional feed-forward networks and convolutional LSTMs. More

precisely, we rely on complex convolutions and present algorithms for complex

batch-normalization, complex weight initialization strategies for complex-valued

neural nets and we use them in experiments with end-to-end training schemes.

We demonstrate that such complex-valued models are competitive with their real-

valued counterparts. We test deep complex models on several computer vision

tasks, on music transcription using the MusicNet dataset and on Speech Spectrum

Prediction using the TIMIT dataset. We achieve state-of-the-art performance on

these audio-related tasks.

1 INTRODUCTION

Recent research advances have made significant progress in addressing the difficulties involved in

learning deep neural network architectures. Key innovations include normalization techniques (Ioffe

and Szegedy, 2015; Salimans and Kingma, 2016) and the emergence of gating-based feed-forward

neural networks like Highway Networks (Srivastava et al., 2015). Residual networks (He et al.,

2015a; 2016) have emerged as one of the most popular and effective strategies for training very deep

convolutional neural networks (CNNs). Both highway networks and residual networks facilitate

the training of deep networks by providing shortcut paths for easy gradient flow to lower network

layers thereby diminishing the effects of vanishing gradients (Hochreiter, 1991). He et al. (2016)

?Equal first author

?Equal contributions