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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