  CNN feature spaces can be linearly mapped and consequently are often
interchangeable. This equivalence holds across variations in architectures,
training datasets, and network tasks. Specifically, we mapped between 10
image-classification CNNs and between 4 facial-recognition CNNs. When image
embeddings generated by one CNN are transformed into embeddings corresponding
to the feature space of a second CNN trained on the same task, their respective
image classification or face verification performance is largely preserved. For
CNNs trained to the same classes and sharing a common backend-logit (soft-max)
architecture, a linear-mapping may always be calculated directly from the
backend layer weights. However, the case of a closed-set analysis with perfect
knowledge of classifiers is limiting. Therefore, empirical methods of
estimating mappings are presented for both the closed-set image classification
task and the open-set task of face recognition. The results presented expose
the essentially interchangeable nature of CNNs embeddings for two important and
common recognition tasks. The implications are far-reaching, suggesting an
underlying commonality between representations learned by networks designed and
trained for a common task. One practical implication is that face embeddings
from some commonly used CNNs can be compared using these mappings.
