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

A Trainable Optimal Transport Embedding for Feature Aggregation and its Relationship to Attention