The I/O Complexity of Attention, or How Optimal is Flash Attention?

Self-attention is at the heart of the popular Transformer architecture, yet suffers from quadratic time and memory complexity. The breakthrough FlashAttention algorithm revealed I/O complexity as the true bottleneck in scaling Transformers. Given two levels of memory hierarchy, a fast cache (e.g. GPU on-chip SRAM) and a slow memory (e.g. GPU high-bandwidth memory), the I/O complexity measures the number of accesses to memory. FlashAttention computes attention using $\frac{N^2d^2}{M}$ I/O operations where $N$ is the dimension of the attention matrix, $d$ …

algorithm architecture attention cache chip complexity cs.cc cs.ds cs.it cs.lg flash gpu math.it memory popular scaling self-attention transformer transformer architecture transformers true