Abstract
For this paper, we proposed the fractional category representation vector (FV) based on fractional calculus (FC), of which one-hot label is only the special case when the derivative order is 0. FV can be considered as a distributional representation when negative probability is considered. FVs can be used either as a regularization method or as a distributed category representation. They gain significantly in the generalization of classification models and representability in generative adversarial networks with conditions (C-GANs). In image classification, the linear combinations of FVs correspond to the mixture of images and can be used as an independent variable of the loss function. Our experiments showed that FVs can also be used as space sampling, with fewer dimensions and less computational overhead than normal distributions.
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