  We address the problem of learning on sets of features, motivated by the need
of performing pooling operations in long biological sequences of varying sizes,
with long-range dependencies, and possibly few labeled data. To address this
challenging task, we introduce a parametrized representation of fixed size,
which embeds and then aggregates elements from a given input set according to
the optimal transport plan between the set and a trainable reference. Our
approach scales to large datasets and allows end-to-end training of the
reference, while also providing a simple unsupervised learning mechanism with
small computational cost. Our aggregation technique admits two useful
interpretations: it may be seen as a mechanism related to attention layers in
neural networks, or it may be seen as a scalable surrogate of a classical
optimal transport-based kernel. We experimentally demonstrate the effectiveness
of our approach on biological sequences, achieving state-of-the-art results for
protein fold recognition and detection of chromatin profiles tasks, and, as a
proof of concept, we show promising results for processing natural language
sequences. We provide an open-source implementation of our embedding that can
be used alone or as a module in larger learning models at
https://github.com/claying/OTK.
