  In this note we examine the autoregressive generalization of the FNet
algorithm, in which self-attention layers from the standard Transformer
architecture are substituted with a trivial sparse-uniformsampling procedure
based on Fourier transforms. Using the Wikitext-103 benchmark, we
demonstratethat FNetAR retains state-of-the-art performance (25.8 ppl) on the
task of causal language modelingcompared to a Transformer-XL baseline (24.2
ppl) with only half the number self-attention layers,thus providing further
evidence for the superfluity of deep neural networks with heavily
compoundedattention mechanisms. The autoregressive Fourier transform could
likely be used for parameterreduction on most Transformer-based time-series
prediction models.
