In this work, we improved the analysis of the running time of SparseGPT [Frantar, Alistarh ICML 2023] from $O(d^{3})$ to $O(d^ω + d^{2+a+o(1)} + d^{1+ω(1,1,a)-a})$ for any $a \in [0, 1]$, where $ω$ is the exponent of matrix multiplication. In particular, for the current $ω\approx 2.371$ [Alman, Duan, Williams, Xu, Xu, Zhou 2024], our running time boils down to $O(d^{2.53})$. This running time is due to the analysis of the lazy update behavior in iterative maintenance problems such as [Deng, Song, Weinstein 2022; Brand, Song, Zhou ICML 2024].
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