  Feature interaction has been recognized as an important problem in machine
learning, which is also very essential for click-through rate (CTR) prediction
tasks. In recent years, Deep Neural Networks (DNNs) can automatically learn
implicit nonlinear interactions from original sparse features, and therefore
have been widely used in industrial CTR prediction tasks. However, the implicit
feature interactions learned in DNNs cannot fully retain the complete
representation capacity of the original and empirical feature interactions
(e.g., cartesian product) without loss. For example, a simple attempt to learn
the combination of feature A and feature B <A, B> as the explicit cartesian
product representation of new features can outperform previous implicit feature
interaction models including factorization machine (FM)-based models and their
variations. In this paper, we propose a Co-Action Network (CAN) to approximate
the explicit pairwise feature interactions without introducing too many
additional parameters. More specifically, giving feature A and its associated
feature B, their feature interaction is modeled by learning two sets of
parameters: 1) the embedding of feature A, and 2) a Multi-Layer Perceptron
(MLP) to represent feature B. The approximated feature interaction can be
obtained by passing the embedding of feature A through the MLP network of
feature B. We refer to such pairwise feature interaction as feature co-action,
and such a Co-Action Network unit can provide a very powerful capacity to
fitting complex feature interactions. Experimental results on public and
industrial datasets show that CAN outperforms state-of-the-art CTR models and
the cartesian product method. Moreover, CAN has been deployed in the display
advertisement system in Alibaba, obtaining 12\% improvement on CTR and 8\% on
Revenue Per Mille (RPM), which is a great improvement to the business.
