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Neural networks are widely used as a model for classification in a largevariety of tasks. Typically, a learnable transformation (i.e. the classifier)is placed at the end of such models returning a value for each class used forclassification. This transformation plays an important role in determining howthe generated features change during the learning process.  In this work we argue that this transformation not only can be fixed (i.e.set as non trainable) with no loss of accuracy, but it can also be used tolearn stationary and maximally discriminative embeddings.  We show that the stationarity of the embedding and its maximal discriminativerepresentation can be theoretically justified by setting the weights of thefixed classifier to values taken from the coordinate vertices of three regularpolytopes available in $\mathbb{R}^d$, namely: the $d$-Simplex, the $d$-Cubeand the $d$-Orthoplex. These regular polytopes have the maximal amount ofsymmetry that can be exploited to generate stationary features angularlycentered around their corresponding fixed weights.  Our approach improves and broadens the concept of a fixed classifier,recently proposed in \cite{hoffer2018fix}, to a larger class of fixedclassifier models. Experimental results confirm both the theoretical analysisand the generalization capability of the proposed method.

Fix Your Features: Stationary and Maximally Discriminative Embeddings using Regular Polytope (Fixed Classifier) Networks