  Compatible features enable the direct comparison of old and new learned
features allowing to use them interchangeably over time. In visual search
systems, this eliminates the need to extract new features from the gallery-set
when the representation model is upgraded with novel data. This has a big value
in real applications as re-indexing the gallery-set can be computationally
expensive when the gallery-set is large, or even infeasible due to privacy or
other concerns of the application. In this paper, we propose CoReS, a new
training procedure to learn representations that are \textit{compatible} with
those previously learned, grounding on the stationarity of the features as
provided by fixed classifiers based on polytopes. With this solution, classes
are maximally separated in the representation space and maintain their spatial
configuration stationary as new classes are added, so that there is no need to
learn any mappings between representations nor to impose pairwise training with
the previously learned model. We demonstrate that our training procedure
largely outperforms the current state of the art and is particularly effective
in the case of multiple upgrades of the training-set, which is the typical case
in real applications.
