  Transformers are expensive to train due to the quadratic time and space
complexity in the self-attention mechanism. On the other hand, although kernel
machines suffer from the same computation bottleneck in pairwise dot products,
several approximation schemes have been successfully incorporated to
considerably reduce their computational cost without sacrificing too much
accuracy. In this work, we leverage the computation methods for kernel machines
to alleviate the high computational cost and introduce Skyformer, which
replaces the softmax structure with a Gaussian kernel to stabilize the model
training and adapts the Nystr\"om method to a non-positive semidefinite matrix
to accelerate the computation. We further conduct theoretical analysis by
showing that the matrix approximation error of our proposed method is small in
the spectral norm. Experiments on Long Range Arena benchmark show that the
proposed method is sufficient in getting comparable or even better performance
than the full self-attention while requiring fewer computation resources.
