  We present a principled approach to uncover the structure of visual data by
solving a novel deep learning task coined visual permutation learning. The goal
of this task is to find the permutation that recovers the structure of data
from shuffled versions of it. In the case of natural images, this task boils
down to recovering the original image from patches shuffled by an unknown
permutation matrix. Unfortunately, permutation matrices are discrete, thereby
posing difficulties for gradient-based methods. To this end, we resort to a
continuous approximation of these matrices using doubly-stochastic matrices
which we generate from standard CNN predictions using Sinkhorn iterations.
Unrolling these iterations in a Sinkhorn network layer, we propose DeepPermNet,
an end-to-end CNN model for this task. The utility of DeepPermNet is
demonstrated on two challenging computer vision problems, namely, (i) relative
attributes learning and (ii) self-supervised representation learning. Our
results show state-of-the-art performance on the Public Figures and OSR
benchmarks for (i) and on the classification and segmentation tasks on the
PASCAL VOC dataset for (ii).
