  Recently, random feature attentions (RFAs) are proposed to approximate the
softmax attention in linear time and space complexity by linearizing the
exponential kernel. In this paper, we first propose a novel perspective to
understand the bias in such approximation by recasting RFAs as self-normalized
importance samplers. This perspective further sheds light on an \emph{unbiased}
estimator for the whole softmax attention, called randomized attention (RA). RA
constructs positive random features via query-specific distributions and enjoys
greatly improved approximation fidelity, albeit exhibiting quadratic
complexity. By combining the expressiveness in RA and the efficiency in RFA, we
develop a novel linear complexity self-attention mechanism called linear
randomized attention (LARA). Extensive experiments across various domains
demonstrate that RA and LARA significantly improve the performance of RFAs by a
substantial margin.
