  We study the problem of building models that disentangle independent factors
of variation. Such models could be used to encode features that can efficiently
be used for classification and to transfer attributes between different images
in image synthesis. As data we use a weakly labeled training set. Our weak
labels indicate what single factor has changed between two data samples,
although the relative value of the change is unknown. This labeling is of
particular interest as it may be readily available without annotation costs. To
make use of weak labels we introduce an autoencoder model and train it through
constraints on image pairs and triplets. We formally prove that without
additional knowledge there is no guarantee that two images with the same factor
of variation will be mapped to the same feature. We call this issue the
reference ambiguity. Moreover, we show the role of the feature dimensionality
and adversarial training. We demonstrate experimentally that the proposed model
can successfully transfer attributes on several datasets, but show also cases
when the reference ambiguity occurs.
