  We present evidence that many common convolutional neural networks (CNNs)
trained for face verification learn functions that are nearly equivalent under
rotation. More specifically, we demonstrate that one face verification model's
embeddings (i.e. last-layer activations) can be compared directly to another
model's embeddings after only a rotation or linear transformation, with little
performance penalty. This finding is demonstrated using IJB-C 1:1 verification
across the combinations of ten modern off-the-shelf CNN-based face verification
models which vary in training dataset, CNN architecture, method of angular loss
calculation, or some combination of the 3. These networks achieve a mean true
accept rate of 0.96 at a false accept rate of 0.01. When instead evaluating
embeddings generated from two CNNs, where one CNN's embeddings are mapped with
a linear transformation, the mean true accept rate drops to 0.95 using the same
verification paradigm. Restricting these linear maps to only perform rotation
produces a mean true accept rate of 0.91. These mappings' existence suggests
that a common representation is learned by models despite variation in training
or structure. We discuss the broad implications a result like this has,
including an example regarding face template security.
