  Convolutional Neural Networks (CNNs) trained with the Softmax loss are widely
used classification models for several vision tasks. Typically, a learnable
transformation (i.e. the classifier) is placed at the end of such models
returning class scores that are further normalized into probabilities by
Softmax. This learnable transformation has a fundamental role in determining
the network internal feature representation.
  In this work we show how to extract from CNNs features with the properties of
\emph{maximum} inter-class separability and \emph{maximum} intra-class
compactness by setting the parameters of the classifier transformation as not
trainable (i.e. fixed). We obtain features similar to what can be obtained with
the well-known ``Center Loss'' \cite{wen2016discriminative} and other similar
approaches but with several practical advantages including maximal exploitation
of the available feature space representation, reduction in the number of
network parameters, no need to use other auxiliary losses besides the Softmax.
  Our approach unifies and generalizes into a common approach two apparently
different classes of methods regarding: discriminative features, pioneered by
the Center Loss \cite{wen2016discriminative} and fixed classifiers, firstly
evaluated in \cite{hoffer2018fix}.
  Preliminary qualitative experimental results provide some insight on the
potentialities of our combined strategy.
