https://arxiv.org/abs/2411.17525

Skip to main content
Cornell University
We gratefully acknowledge support from the Simons Foundation, member
institutions, and all contributors. Donate
 
arxiv logo > cs > arXiv:2411.17525
[                    ]

Help | Advanced Search

[All fields        ]
Search
arXiv logo
Cornell University Logo
[                    ] GO
quick links

  * Login
  * Help Pages
  * About

Computer Science > Machine Learning

arXiv:2411.17525 (cs)
[Submitted on 26 Nov 2024]

Title:Pushing the Limits of Large Language Model Quantization via the
Linearity Theorem

Authors:Vladimir Malinovskii, Andrei Panferov, Ivan Ilin, Han Guo,
Peter Richtarik, Dan Alistarh
View a PDF of the paper titled Pushing the Limits of Large Language
Model Quantization via the Linearity Theorem, by Vladimir Malinovskii
and 5 other authors
View PDF HTML (experimental)

    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.

Subjects: Machine Learning (cs.LG)
Cite as:  arXiv:2411.17525 [cs.LG]
          (or arXiv:2411.17525v1 [cs.LG] for this version)
          https://doi.org/10.48550/arXiv.2411.17525
          Focus to learn more
          arXiv-issued DOI via DataCite

Submission history

From: Andrei Panferov [view email]
[v1] Tue, 26 Nov 2024 15:35:44 UTC (1,321 KB)
Full-text links:

Access Paper:

    View a PDF of the paper titled Pushing the Limits of Large
    Language Model Quantization via the Linearity Theorem, by
    Vladimir Malinovskii and 5 other authors
  * View PDF
  * HTML (experimental)
  * TeX Source
  * Other Formats

view license
Current browse context:
cs.LG
< prev   |   next >
new | recent | 2024-11
Change to browse by:
cs

References & Citations

  * NASA ADS
  * Google Scholar
  * Semantic Scholar

a export BibTeX citation Loading...

BibTeX formatted citation

x
[loading...          ]
Data provided by:

Bookmark

BibSonomy logo Reddit logo
(*) Bibliographic Tools

Bibliographic and Citation Tools

[ ] Bibliographic Explorer Toggle
Bibliographic Explorer (What is the Explorer?)
[ ] Connected Papers Toggle
Connected Papers (What is Connected Papers?)
[ ] Litmaps Toggle
Litmaps (What is Litmaps?)
[ ] scite.ai Toggle
scite Smart Citations (What are Smart Citations?)
( ) Code, Data, Media

Code, Data and Media Associated with this Article

[ ] alphaXiv Toggle
alphaXiv (What is alphaXiv?)
[ ] Links to Code Toggle
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
[ ] DagsHub Toggle
DagsHub (What is DagsHub?)
[ ] GotitPub Toggle
Gotit.pub (What is GotitPub?)
[ ] Huggingface Toggle
Hugging Face (What is Huggingface?)
[ ] Links to Code Toggle
Papers with Code (What is Papers with Code?)
[ ] ScienceCast Toggle
ScienceCast (What is ScienceCast?)
( ) Demos

Demos

[ ] Replicate Toggle
Replicate (What is Replicate?)
[ ] Spaces Toggle
Hugging Face Spaces (What is Spaces?)
[ ] Spaces Toggle
TXYZ.AI (What is TXYZ.AI?)
( ) Related Papers

Recommenders and Search Tools

[ ] Link to Influence Flower
Influence Flower (What are Influence Flowers?)
[ ] Core recommender toggle
CORE Recommender (What is CORE?)
[ ] IArxiv recommender toggle
IArxiv Recommender (What is IArxiv?)

  * Author
  * Venue
  * Institution
  * Topic

( ) About arXivLabs

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and
share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have
embraced and accepted our values of openness, community, excellence,
and user data privacy. arXiv is committed to these values and only
works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community?
Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is
MathJax?)

  * About
  * Help

  * Click here to contact arXiv Contact
  * Click here to subscribe Subscribe

  * Copyright
  * Privacy Policy

  * Web Accessibility Assistance
  * arXiv Operational Status
    Get status notifications via email or slack