# Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention

Angelos KatharopoulosApoorv VyasNikolaos PappasFrançois Fleuret

Transformers achieve remarkable performance in several tasks but due to their quadratic complexity, with respect to the input's length, they are prohibitively slow for very long sequences. To address this limitation, we express the self-attention as a linear dot-product of kernel feature maps and make use of the associativity property of matrix products to reduce the complexity from $\mathcal{O}\left(N^2\right)$ to $\mathcal{O}\left(N\right)$, where $N$ is the sequence length... (read more)

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