  Pruning large language models (LLMs) is a challenging task due to their
enormous size. The primary difficulty is fine-tuning the model after pruning,
which is needed to recover the lost performance caused by dropping weights.
Recent approaches have either ignored fine-tuning entirely, focusing on
efficient pruning criteria, or attempted layer-wise weight updates, preserving
the behavior of each layer. However, even layer-wise weight updates can be
costly for LLMs, and previous works have resorted to various approximations.
  In our paper, we propose a fast and effective weight update algorithm for
pruned layers based on the Alternating Direction Method of Multipliers (ADMM).
We further extend it with a simple gradual pruning mask selection and achieve
state-of-the-art pruning performance across a wide range of LLMs. Code is
available at https://github.com/fmfi-compbio/admm-pruning.
