  Convolutional models have been widely used in multiple domains. However, most
existing models only use local convolution, making the model unable to handle
long-range dependency efficiently. Attention overcomes this problem by
aggregating global information but also makes the computational complexity
quadratic to the sequence length. Recently, Gu et al. [2021] proposed a model
called S4 inspired by the state space model. S4 can be efficiently implemented
as a global convolutional model whose kernel size equals the input sequence
length. S4 can model much longer sequences than Transformers and achieve
significant gains over SoTA on several long-range tasks. Despite its empirical
success, S4 is involved. It requires sophisticated parameterization and
initialization schemes. As a result, S4 is less intuitive and hard to use. Here
we aim to demystify S4 and extract basic principles that contribute to the
success of S4 as a global convolutional model. We focus on the structure of the
convolution kernel and identify two critical but intuitive principles enjoyed
by S4 that are sufficient to make up an effective global convolutional model:
1) The parameterization of the convolutional kernel needs to be efficient in
the sense that the number of parameters should scale sub-linearly with sequence
length. 2) The kernel needs to satisfy a decaying structure that the weights
for convolving with closer neighbors are larger than the more distant ones.
Based on the two principles, we propose a simple yet effective convolutional
model called Structured Global Convolution (SGConv). SGConv exhibits strong
empirical performance over several tasks: 1) With faster speed, SGConv
surpasses S4 on Long Range Arena and Speech Command datasets. 2) When plugging
SGConv into standard language and vision models, it shows the potential to
improve both efficiency and performance.
