Fourier or Wavelet bases as counterpart self-attention in spikformer for efficient visual classification

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 article, 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 graphic processing unit (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.