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SurReal: Fr'echet Mean and Distance Transform for Complex-Valued Deep Learning
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Rudrasis Chakraborty and Jiayun Wang and Stella X. Yu
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Best Paper Award, IEEE Conference on Computer Vision and Pattern Recognition Workshop: Perception Beyond the Visible Spectrum, Long Beach, California, 16 June 2019
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Paper
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Poster
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Code
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arXiv
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Abstract
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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 Fr\'{e}chet 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 real-valued neural network models on the two-channel real-valued 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.
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Keywords
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complex-valued deep learning, Fr\'{e}chet Mean, distance transform, equivariance and invariance
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