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FlashAttention converted that observation into wall-clock speed by combining tiling with recomputation. Blocks of the inputs are loaded into on-chip SRAM, the softmax reduction is performed incrementally across blocks using the online normaliser, and the output is written back without the score matrix ever reaching main memory; for the backward pass, the softmax normalisation factors are kept from the forward pass so that attention can be recomputed on-chip, which the authors state is faster than reading the stored intermediate back from HBM. Their analysis gives O($N^2$ $d^2$ $M^{-1}$) HBM accesses against $\Omega(Nd + N^2)$ for standard attention, with a matching lower bound showing no exact algorithm can do asymptotically better across all SRAM sizes [ 1 ] . The reported results were a 7.6 times speedup on the attention computation itself for GPT-2, 15 per cent faster end-to-end BERT-large training against the MLPerf 1.1 record, 3 times on GPT-2 and 2.4 times on long-range arena, plus qualitatively new capability at length: 61.4 per cent on Path-X at 16K and 63.1 per cent on Path-256 at 64K, both above chance for the first time.