  Transformer is a powerful architecture that achieves superior performance on
various sequence learning tasks, including neural machine translation, language
understanding, and sequence prediction. At the core of the Transformer is the
attention mechanism, which concurrently processes all inputs in the streams. In
this paper, we present a new formulation of attention via the lens of the
kernel. To be more precise, we realize that the attention can be seen as
applying kernel smoother over the inputs with the kernel scores being the
similarities between inputs. This new formulation gives us a better way to
understand individual components of the Transformer's attention, such as the
better way to integrate the positional embedding. Another important advantage
of our kernel-based formulation is that it paves the way to a larger space of
composing Transformer's attention. As an example, we propose a new variant of
Transformer's attention which models the input as a product of symmetric
kernels. This approach achieves competitive performance to the current state of
the art model with less computation. In our experiments, we empirically study
different kernel construction strategies on two widely used tasks: neural
machine translation and sequence prediction.
