  This paper introduces hyperspherical prototype networks, which unify
classification and regression with prototypes on hyperspherical output spaces.
For classification, a common approach is to define prototypes as the mean
output vector over training examples per class. Here, we propose to use
hyperspheres as output spaces, with class prototypes defined a priori with
large margin separation. We position prototypes through data-independent
optimization, with an extension to incorporate priors from class semantics. By
doing so, we do not require any prototype updating, we can handle any training
size, and the output dimensionality is no longer constrained to the number of
classes. Furthermore, we generalize to regression, by optimizing outputs as an
interpolation between two prototypes on the hypersphere. Since both tasks are
now defined by the same loss function, they can be jointly trained for
multi-task problems. Experimentally, we show the benefit of hyperspherical
prototype networks for classification, regression, and their combination over
other prototype methods, softmax cross-entropy, and mean squared error
approaches.
