Optimal Brain Restoration for Joint Quantization and Sparsification of
  LLMs
Authors: name: Hang Guo, name: Yawei Li, name: Luca Benini

Recent advances in Large Language Model (LLM) compression, such as
quantization and pruning, have achieved notable success. However, as these
techniques gradually approach their respective limits, relying on a single
method for further compression has become increasingly challenging. In this
work, we explore an alternative solution by combining quantization and
sparsity. This joint approach, though promising, introduces new difficulties
due to the inherently conflicting requirements on weight distributions:
quantization favors compact ranges, while pruning benefits from high variance.
To attack this problem, we propose Optimal Brain Restoration (OBR), a general
and training-free framework that aligns pruning and quantization by error
compensation between both. OBR minimizes performance degradation on downstream
tasks by building on a second-order Hessian objective, which is then
reformulated into a tractable problem through surrogate approximation and
ultimately reaches a closed-form solution via group error compensation.
Experiments show that OBR enables aggressive W4A4KV4 quantization with 50%
sparsity on existing LLMs, and delivers up to 4.72x speedup and 6.4x memory
reduction compared to the FP16-dense baseline.