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.

Local Coordinate Coding (LCC) [18] is a method for modeling functions of data lying on non-linear manifolds. It provides a set of anchor points which form a local coordinate system, such that each data point on the manifold can be approximated by a linear combination of its anchor points, and the linear weights become the local coordinate coding. In this paper we propose encoding data using orthogonal anchor planes, rather than anchor points. Our method needs only a few orthogonal anchor planes for coding, and it can linearize any (\alpha,\beta,p)-Lipschitz smooth nonlinear function with a fixed expected value of the upper-bound approximation error on any high dimensional data. In practice, the orthogonal coordinate system can be easily learned by minimizing this upper bound using singular value decomposition (SVD). We apply our method to model the coordinates locally in linear SVMs for classification tasks, and our experiment on MNIST shows that using only 50 anchor planes our method achieves 1.72% error rate, while LCC achieves 1.90% error rate using 4096 anchor points.