  The complexity of a learning task is increased by transformations in the
input space that preserve class identity. Visual object recognition for example
is affected by changes in viewpoint, scale, illumination or planar
transformations. While drastically altering the visual appearance, these
changes are orthogonal to recognition and should not be reflected in the
representation or feature encoding used for learning. We introduce a framework
for weakly supervised learning of image embeddings that are robust to
transformations and selective to the class distribution, using sets of
transforming examples (orbit sets), deep parametrizations and a novel
orbit-based loss. The proposed loss combines a discriminative, contrastive part
for orbits with a reconstruction error that learns to rectify orbit
transformations. The learned embeddings are evaluated in distance metric-based
tasks, such as one-shot classification under geometric transformations, as well
as face verification and retrieval under more realistic visual variability. Our
results suggest that orbit sets, suitably computed or observed, can be used for
efficient, weakly-supervised learning of semantically relevant image
embeddings.
