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Many efficient approximate self-attention techniques have become prevalentsince the inception of the transformer architecture. Two popular classes ofthese techniques are low-rank and kernel methods. Each of these methods has itsown strengths. We observe these strengths synergistically complement each otherand exploit these synergies to fuse low-rank and kernel methods, producing anew class of transformers: FLuRKA (Fast Low-Rank and Kernel Attention). FLuRKAprovide sizable performance gains over these approximate techniques and are ofhigh quality. We theoretically and empirically evaluate both the runtimeperformance and quality of FLuRKA. Our runtime analysis posits a variety ofparameter configurations where FLuRKA exhibit speedups and our accuracyanalysis bounds the error of FLuRKA with respect to full-attention. Weinstantiate three FLuRKA variants which experience empirical speedups of up to3.3x and 1.7x over low-rank and kernel methods respectively. This translates tospeedups of up to 30x over models with full-attention. With respect to modelquality, FLuRKA can match the accuracy of low-rank and kernel methods on GLUEafter pre-training on wiki-text 103. When pre-training on a fixed time budget,FLuRKA yield better perplexity scores than models with full-attention.

FLuRKA: Fast fused Low-Rank & Kernel Attention