A Tighter Complexity Analysis of SparseGPT
This work provides a tighter theoretical complexity bound for a specific pruning algorithm, which is incremental to prior analyses.
The paper tackled the problem of improving the running time analysis of SparseGPT, reducing it from O(d^3) to O(d^2.53) for current matrix multiplication exponents, by analyzing lazy update behavior in iterative maintenance problems.
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].