  Energy-efficient spikformer has been proposed by integrating the biologically
plausible spiking neural network (SNN) and artificial Transformer, whereby the
Spiking Self-Attention (SSA) is used to achieve both higher accuracy and lower
computational cost. However, it seems that self-attention is not always
necessary, especially in sparse spike-form calculation manners. In this paper,
we innovatively replace vanilla SSA (using dynamic bases calculating from Query
and Key) with spike-form Fourier Transform, Wavelet Transform, and their
combinations (using fixed triangular or wavelets bases), based on a key
hypothesis that both of them use a set of basis functions for information
transformation. Hence, the Fourier-or-Wavelet-based spikformer (FWformer) is
proposed and verified in visual classification tasks, including both static
image and event-based video datasets. The FWformer can achieve comparable or
even higher accuracies ($0.4\%$-$1.5\%$), higher running speed ($9\%$-$51\%$
for training and $19\%$-$70\%$ for inference), reduced theoretical energy
consumption ($20\%$-$25\%$), and reduced GPU memory usage ($4\%$-$26\%$),
compared to the standard spikformer. Our result indicates the continuous
refinement of new Transformers, that are inspired either by biological
discovery (spike-form), or information theory (Fourier or Wavelet Transform),
is promising.
