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Unordered feature sets are a nonstandard data structure that traditionalneural networks are incapable of addressing in a principled manner. Providing aconcatenation of features in an arbitrary order may lead to the learning ofspurious patterns or biases that do not actually exist. Another complication isintroduced if the number of features varies between each set. We proposeconvolutional deep averaging networks (CDANs) for classifying and learningrepresentations of datasets whose instances comprise variable-size, unorderedfeature sets. CDANs are efficient, permutation-invariant, and capable ofaccepting sets of arbitrary size. We emphasize the importance of nonlinearfeature embeddings for obtaining effective CDAN classifiers and illustratetheir advantages in experiments versus linear embeddings and alternativepermutation-invariant and -equivariant architectures.

Classifying Unordered Feature Sets with Convolutional Deep Averaging Networks