  Many machine learning tasks require finding per-part correspondences between
objects. In this work we focus on low-level correspondences - a highly
ambiguous matching problem. We propose to use a hierarchical semantic
representation of the objects, coming from a convolutional neural network, to
solve this ambiguity. Training it for low-level correspondence prediction
directly might not be an option in some domains where the ground-truth
correspondences are hard to obtain. We show how transfer from recognition can
be used to avoid such training. Our idea is to mark parts as "matching" if
their features are close to each other at all the levels of convolutional
feature hierarchy (neural paths). Although the overall number of such paths is
exponential in the number of layers, we propose a polynomial algorithm for
aggregating all of them in a single backward pass. The empirical validation is
done on the task of stereo correspondence and demonstrates that we achieve
competitive results among the methods which do not use labeled target domain
data.
