A residual self-attention network with all weight entries bounded by a small η can be approximated by one layer to error O(η)‖X‖∞, so skip connections do not prevent layer collapse.
A Tighter Complexity Analysis of SparseGPT
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abstract
In this work, we improved the analysis of the running time of SparseGPT [Frantar, Alistarh ICML 2023] from $O(d^{3})$ to $O(d^{\omega} + d^{2+a+o(1)} + d^{1+\omega(1,1,a)-a})$ for any $a \in [0, 1]$, where $\omega$ is the exponent of matrix multiplication. In particular, for the current $\omega \approx 2.371$ [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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Only Large Weights (And Not Skip Connections) Can Prevent the Perils of Rank Collapse
A residual self-attention network with all weight entries bounded by a small η can be approximated by one layer to error O(η)‖X‖∞, so skip connections do not prevent layer collapse.