Frequency learning for structured CNN filters with Gaussian fractional derivatives

Frequency information lies at the base of discriminating between textures, and therefore between different objects. Classical CNN architectures limit the frequency learning through fixed filter sizes, and lack a way of explicitly controlling it. Here, we build on the structured receptive field filters with Gaussian derivative basis. Yet, rather than using predetermined derivative orders, which typically result in fixed frequency responses for the basis functions, we learn these. We show that by learning the order of the basis we can accurately learn the frequency of the filters, and hence adapt to the optimal frequencies for the underlying learning task. We investigate the well-founded mathematical formulation of fractional derivatives to adapt the filter frequencies during training. Our formulation leads to parameter savings and data efficiency when compared to the standard CNNs and the Gaussian derivative CNN filter networks that we build upon.