  Proteins perform a large variety of functions in living organisms, thus
playing a key role in biology. As of now, available learning algorithms to
process protein data do not consider several particularities of such data
and/or do not scale well for large protein conformations. To fill this gap, we
propose two new learning operations enabling deep 3D analysis of large-scale
protein data. First, we introduce a novel convolution operator which considers
both, the intrinsic (invariant under protein folding) as well as extrinsic
(invariant under bonding) structure, by using $n$-D convolutions defined on
both the Euclidean distance, as well as multiple geodesic distances between
atoms in a multi-graph. Second, we enable a multi-scale protein analysis by
introducing hierarchical pooling operators, exploiting the fact that proteins
are a recombination of a finite set of amino acids, which can be pooled using
shared pooling matrices. Lastly, we evaluate the accuracy of our algorithms on
several large-scale data sets for common protein analysis tasks, where we
outperform state-of-the-art methods.
