SurReal: Fr'echet Mean and Distance Transform for Complex-Valued Deep Learning

TitleSurReal: Fr'echet Mean and Distance Transform for Complex-Valued Deep Learning
Publication TypeConference Paper
Year of Publication2019
AuthorsChakraborty, R., Wang J., & Yu S. X.
Published inProceedings of IEEE Conference on Computer Vision and Pattern Recognition

We develop a novel deep learning architecture for naturally complex-valued data, which is often subject to complex scaling ambiguity. We treat each sample as a field in the space of complex numbers. With the polar form of a complex-valued number, the general group that acts in this space is the product of planar rotation and non-zero scaling. This perspective allows us to develop not only a novel convolution operator using weighted Fréchet mean (wFM) on a Riemannian manifold, but also a novel fully connected layer operator using the distance to the wFM, with natural equivariant properties to non-zero scaling and planar rotation for the former and invariance properties for the latter. Compared to the baseline approach of learning realvalued neural network models on the two-channel realvalued representation of complex-valued data, our method achieves surreal performance on two publicly available complex-valued datasets: MSTAR on SAR images and RadioML on radio frequency signals. On MSTAR, at 8% of the baseline model size and with fewer than 45, 000 parameters, our model improves the target classification accuracy from 94% to 98% on this highly imbalanced dataset. On RadioML, our model achieves comparable RF modulation classification accuracy at 10% of the baseline model size. 


This research was supported, in part, by Berkeley Deep Drive and DARPA. The views, opinions and/or findings expressed are those of the author and should not be interpreted as representing the official views or policies of the Department of Defense or the U.S. Government.

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