  Dense prediction tasks typically employ encoder-decoder architectures, but
the prevalent convolutions in the decoder are not image-adaptive and can lead
to boundary artifacts. Different generalized convolution operations have been
introduced to counteract this. We go beyond these by leveraging guidance data
to redefine their inherent notion of proximity. Our proposed network layer
builds on the permutohedral lattice, which performs sparse convolutions in a
high-dimensional space allowing for powerful non-local operations despite small
filters. Multiple features with different characteristics span this
permutohedral space. In contrast to prior work, we learn these features in a
task-specific manner by generalizing the basic permutohedral operations to
learnt feature representations. As the resulting objective is complex, a
carefully designed framework and learning procedure are introduced, yielding
rich feature embeddings in practice. We demonstrate the general applicability
of our approach in different joint upsampling tasks. When adding our network
layer to state-of-the-art networks for optical flow and semantic segmentation,
boundary artifacts are removed and the accuracy is improved.
