Pushing the Limits of Large Language Model Quantization via the Linearity Theorem
Reviewed by Pithpith:K56M2WAOopen to challenge →
read the original abstract
Quantizing large language models has become a standard way to reduce their memory and computational costs. Typically, existing methods focus on breaking down the problem into individual layer-wise sub-problems, and minimizing per-layer error, measured via various metrics. Yet, this approach currently lacks theoretical justification and the metrics employed may be sub-optimal. In this paper, we present a "linearity theorem" establishing a direct relationship between the layer-wise $\ell_2$ reconstruction error and the model perplexity increase due to quantization. This insight enables two novel applications: (1) a simple data-free LLM quantization method using Hadamard rotations and MSE-optimal grids, dubbed HIGGS, which outperforms all prior data-free approaches such as the extremely popular NF4 quantized format, and (2) an optimal solution to the problem of finding non-uniform per-layer quantization levels which match a given compression constraint in the medium-bitwidth regime, obtained by reduction to dynamic programming. On the practical side, we demonstrate improved accuracy-compression trade-offs on Llama-3.1 and 3.2-family models, as well as on Qwen-family models. Further, we show that our method can be efficiently supported in terms of GPU kernels at various batch sizes, advancing both data-free and non-uniform quantization for LLMs.
This paper has not been read by Pith yet.
Forward citations
Cited by 5 Pith papers
-
KV Cache Offloading for Context-Intensive Tasks
KV offloading degrades accuracy on context-intensive tasks due to low-rank key projections and unreliable landmarks; a simpler alternative improves results across models and benchmarks.
-
HyperQuant: A Rate-Distortion-Optimal Quantization Pipeline for Large Language and Diffusion Models
HyperQuant unifies Hadamard transform, optimal lattice quantization, and entropy coding to outperform prior schemes on LLM weight and KV cache quantization down to 1.7 bits per scalar while preserving quality on a 19B...
-
KV Cache Offloading for Context-Intensive Tasks
KV offloading hurts accuracy on context-heavy tasks due to low-rank key projections and bad landmarks, but a simpler strategy recovers performance across models.
-
KV Cache Offloading for Context-Intensive Tasks
KV offloading degrades performance on context-intensive tasks due to low-rank key projections and unreliable landmarks, but a simpler alternative strategy restores accuracy across LLM families.
-
KV Cache Offloading for Context-Intensive Tasks
KV offloading hurts accuracy on context-heavy tasks because of low-rank key projections and bad landmarks, but a simpler strategy improves results across models and benchmarks.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.