  The Balanced-Pairwise-Affinities (BPA) feature transform is designed to
upgrade the features of a set of input items to facilitate downstream matching
or grouping related tasks. The transformed set encodes a rich representation of
high order relations between the input features. A particular min-cost-max-flow
fractional matching problem, whose entropy regularized version can be
approximated by an optimal transport (OT) optimization, leads to a transform
which is efficient, differentiable, equivariant, parameterless and
probabilistically interpretable. While the Sinkhorn OT solver has been adapted
extensively in many contexts, we use it differently by minimizing the cost
between a set of features to $itself$ and using the transport plan's $rows$ as
the new representation. Empirically, the transform is highly effective and
flexible in its use and consistently improves networks it is inserted into, in
a variety of tasks and training schemes. We demonstrate state-of-the-art
results in few-shot classification, unsupervised image clustering and person
re-identification. Code is available at \url{github.com/DanielShalam/BPA}.
