A mathematical motivation for complex-valued convolutional networks

A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with complex-valued vectors followed by (2) taking the absolute value of every entry of the resulting vectors followed by (3) local averaging. For processing real-valued random vectors, complex-valued convnets can be viewed as "data-driven multiscale windowed power spectra," "data-driven multiscale windowed absolute spectra," "data-driven multiwavelet absolute values," or (in their most general configuration) "data-driven nonlinear multiwavelet packets.".. (read more)

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