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Polar Prototype Networks

This paper proposes a neural network for classification and regression, without the need to learn layout structures in the output space. Standard solutions such as softmax cross-entropy and mean squared error are effective but parametric, meaning that known inductive structures such as maximum margin separation and simplicity (Occam's Razor) need to be learned for the task at hand. Instead, we propose polar prototype networks, a class of networks that explicitly states the structure, \ie the layout, of the output. The structure is defined by polar prototypes, points on the hypersphere of the output space. For classification, each class is described by a single polar prototype and they are a priori distributed with maximal separation and equal shares on the hypersphere. Classes are assigned to prototypes randomly or based on semantic priors and training becomes a matter of minimizing angular distances between examples and their class prototypes. For regression, we show that training can be performed as a polar interpolation between two prototypes, arriving at a regression with higher-dimensional outputs. From empirical analysis, we find that polar prototype networks benefit from large margin separation and semantic class structure, while only requiring a minimal amount of output dimensions. While the structure is simple, the performance is on par with (classification) or better than (regression) standard network methods. Moreover, we show that we gain the ability to perform regression and classification jointly in the same space, which is disentangled and interpretable by design.

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