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

Frequency learning for structured CNN filters with Gaussian fractional derivatives