QuIP#: Even Better LLM Quantization with Hadamard Incoherence and
  Lattice Codebooks
Albert Tseng Jerry Chee Qingyao Sun Volodymyr Kuleshov Christopher De Sa
Post-training quantization (PTQ) reduces the memory footprint of LLMs by
quantizing their weights to low-precision. In this work, we introduce QuIP#, a
weight-only PTQ method that achieves state-of-the-art results in extreme
compression regimes ($\le$ 4 bits per weight) using three novel techniques.
First, QuIP# improves the incoherence processing from QuIP by using the
randomized Hadamard transform, which is faster and has better theoretical
properties. Second, QuIP# uses vector quantization techniques to take advantage
of the ball-shaped sub-Gaussian distribution that incoherent weights possess:
specifically, we introduce a set of hardware-efficient codebooks based on the
highly symmetric $E_8$ lattice, which achieves the optimal 8-dimension unit
ball packing. Third, QuIP# uses fine-tuning to improve fidelity to the original
model. Our experiments show that QuIP# outperforms existing PTQ methods,
enables new behaviors in PTQ scaling, and supports fast inference.