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arxiv: 2606.04050 · v2 · pith:BEOHIIFUnew · submitted 2026-06-02 · 💻 cs.LG · cs.AI

LiftQuant: Continuous Bit-Width LLM via Dimensional Lifting and Projection

Liulu He , XuanAng Liu , Juntao Liu , Taolue Feng , Ting Lu , Chunsheng Gan , Zhiyv Peng , Yuan Du
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Huanrui Yang Yijiang Liu Li Du
This is my paper

Pith reviewed 2026-06-30 11:14 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords quantizationlarge language modelscontinuous bit-widthdimensional liftingprojectionvector quantizationmodel compressionhardware-friendly decoding
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The pith

LiftQuant achieves continuous non-integer bit-widths for LLMs by lifting weight vectors to a higher dimension, applying 1-bit quantization there, and projecting the result back to the original space.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Existing quantization forces rigid integer bit-widths such as 2 or 3 bits, leaving a gap between what a model needs and what a given GPU memory budget allows. LiftQuant removes that restriction by determining the effective bit-width as the simple ratio of a lifted dimension to the original dimension, so the width can be tuned in small fractional steps. The method works by taking each low-dimensional weight vector, embedding it in a higher-dimensional space, replacing it with the nearest point from a 1-bit lattice, and projecting the result back; the projection step produces a structured non-uniform codebook whose expressiveness matches vector quantization. Because the entire decode path uses only linear transformations and standard 1-bit uniform quantizers, the scheme stays hardware-friendly. The concrete payoff is that a 70B model can be reduced to 2.4 bits and still run on a 24 GB GPU while beating the accuracy of any 2-bit baseline that fits the same device.

Core claim

The paper establishes that low-dimensional weight vectors can be approximated by first embedding them in a higher-dimensional space, replacing each coordinate with a 1-bit value drawn from a uniform lattice, and then projecting the lifted vector back to the original dimension; the ratio of the two dimensions directly sets the effective bit-width, which can therefore be chosen quasi-continuously. This lift-then-project step generates a non-uniform yet structured codebook that retains the representational power of vector quantization, while the decoding operations remain limited to linear maps and 1-bit uniform quantizers.

What carries the argument

The lift-then-project mechanism, whose effective bit-width equals the ratio of lifted dimension to original dimension.

If this is right

  • Bit-width can be set to any rational value determined by the dimension ratio rather than only integers.
  • A 70B model fits inside a 24 GB GPU at 2.4 bits and exceeds the accuracy of 2-bit baselines on the same hardware.
  • The decode path requires only linear transformations and 1-bit uniform quantizers, preserving hardware compatibility.
  • The generated codebook is non-uniform and structured, matching the expressiveness of vector quantization without its typical overhead.
  • Memory budgets can be matched exactly instead of forcing the model into the next lower integer bit-width.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same dimension-ratio control could be applied to vision or multimodal models to achieve fine-grained memory fitting on edge hardware.
  • Because the lifted lattice is always 1-bit, the method might combine with existing integer quantization pipelines without new low-level kernels.
  • If the projection fidelity scales with dimension ratio, one could derive an explicit error bound that predicts the minimal lift needed for a target accuracy drop.

Load-bearing premise

Projecting the higher-dimensional 1-bit lattice points back to the original space preserves enough of the original weight vectors' geometry that downstream model accuracy stays competitive.

What would settle it

Measure whether a 70B-parameter model quantized to exactly 2.4 bits with LiftQuant attains higher zero-shot or few-shot accuracy on standard LLM benchmarks than any published 2-bit method when both are constrained to run inside a 24 GB GPU memory envelope.

Figures

Figures reproduced from arXiv: 2606.04050 by Chunsheng Gan, Huanrui Yang, Juntao Liu, Li Du, Liulu He, Taolue Feng, Ting Lu, XuanAng Liu, Yijiang Liu, Yuan Du, Zhiyv Peng.

Figure 1
Figure 1. Figure 1: Pareto-Optimal Deployment on a 24GB GPU. Perplex￾ity (WikiText-2 and C4) vs. Memory Footprint for Llama-3-70B. While advanced integer-based methods like QTIP and Efficien￾tQAT leave memory wasted or exceed the limit, LiftQuant enables a 2.4-bit model that fully utilizes the available VRAM, significantly outperforming 2-bit baselines. Note that the reserved memory buffer (red zone) is dynamic, varying with … view at source ↗
Figure 2
Figure 2. Figure 2: Visualization of Codewords Generation in LiftQuant. Our method generates a structured, non-uniform codebook by projecting a simple, uniform lattice from a high-dimensional “lifted” space onto a lower-dimensional target subspace [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The LiftQuant Dequant Mechanism. A 1-bit quantized tensor in the high-dimensional lifted space is projected via the mapping matrix M to generate the de-quantized weight tensor. representational capacity and search complexity. Generally, higher coding dimensions yield better coding efficiency; for instance, as shown in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Performance (PPL, Zero-shot, MMLU) vs. Memory Footprint across multiple model families. LiftQuant’s fractional bit widths fill the gaps between integer steps, creating a dense frontier that enables customized, optimal quantization for arbitrary memory constraint. We implemented the linear operation o = diag(s)W(T ∗a) efficiently using torch.compile and BitBLAS (Wang et al., 2024) for UINT1-FP16 GEMV operat… view at source ↗
read the original abstract

Existing quantization methods are fundamentally limited by rigid, integer-based bit-widths (e.g., 2, 3-bit), resulting in a ``deployment gap" where Large Language Models cannot be optimally fitted to specific memory budgets. To bridge this gap, we introduce LiftQuant, a novel framework that enables continuous bit-width control for true Pareto-optimal deployment. The core innovation is a ``lift-then-project" mechanism which approximates low-dimensional weight vectors by projecting a simple 1-bit lattice from a higher-dimensional ``lifted" space. Crucially, the effective bit-width is determined simply by the ratio of the lifted dimension to the original dimension, which allows the bit-width to be tuned quasi-continuous as the dimension is a flexible structural parameter. This projection generates a structured yet non-uniform codebook, capturing the expressive power of Vector Quantization (VQ). While beneficial over VQ, LiftQuant's decoding path relies solely on linear transformations and 1-bit uniform quantizers, retaining hardware-friendly nature. This flexibility is transformative: LiftQuant enables a 70B LLM to be compressed to 2.4 bits to precisely fit a 24GB GPU, where its performance significantly surpasses state-of-the-art 2-bit models fitted on the same device. Our code and ckpt is available at https://github.com/Heliulu/LiftQuant.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper introduces LiftQuant, a quantization framework for LLMs enabling continuous (quasi-continuous) bit-widths via a lift-then-project mechanism: low-dimensional weights are approximated by lifting to a higher-dimensional space, applying a simple 1-bit lattice, and projecting back. The effective bit-width is defined directly as the structural ratio of lifted to original dimension. The abstract asserts that this yields a structured non-uniform codebook with VQ-like expressiveness while remaining hardware-friendly (linear transforms + 1-bit uniform quantizers), and specifically claims that a 70B model can be compressed to exactly 2.4 bits to fit a 24GB GPU with performance significantly exceeding state-of-the-art 2-bit baselines on the same device.

Significance. If the lift-then-project approximation can be shown to preserve sufficient fidelity for 70B-scale weights without hidden capacity loss, the method would address a genuine deployment gap by allowing Pareto-optimal fitting to arbitrary memory budgets rather than discrete bit-widths. The hardware-friendly decoding path is a practical strength. However, the absence of any error analysis, projection construction details, or performance data in the manuscript text prevents assessment of whether the non-uniform codebook actually captures the required expressiveness.

major comments (2)
  1. [Abstract] Abstract (performance claim): the assertion that the 2.4-bit 70B model 'significantly surpasses state-of-the-art 2-bit models fitted on the same device' is presented without any quantitative results, perplexity numbers, task scores, ablation studies, or error bounds. This directly undermines evaluation of the central claim that the projection from the lifted 1-bit lattice approximates original weight vectors with fidelity sufficient to avoid degradation at 70B scale.
  2. [Abstract] Abstract (mechanism): the lift-then-project operation is described at a high level but supplies no explicit construction of the linear transforms, no bound on approximation error relative to vector quantization, and no analysis showing that the resulting codebook remains expressive for the empirical distribution of LLM weights. Without these, it is impossible to verify that the dimension-ratio definition of bit-width produces a faithful approximation rather than an uncontrolled capacity reduction.
minor comments (1)
  1. [Abstract] Abstract: 'Our code and ckpt is available' contains a subject-verb agreement error ('is' should be 'are').

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback. We address each major comment below and will revise the manuscript to improve clarity and completeness.

read point-by-point responses

  1. Referee: [Abstract] Abstract (performance claim): the assertion that the 2.4-bit 70B model 'significantly surpasses state-of-the-art 2-bit models fitted on the same device' is presented without any quantitative results, perplexity numbers, task scores, ablation studies, or error bounds. This directly undermines evaluation of the central claim that the projection from the lifted 1-bit lattice approximates original weight vectors with fidelity sufficient to avoid degradation at 70B scale.

    Authors: The referee correctly notes that the abstract states a performance claim without accompanying numbers. The current manuscript text does not embed the supporting quantitative results (perplexity, task scores) directly alongside the abstract claim. We will revise the abstract to include key quantitative highlights drawn from the experimental evaluations, ensuring the claim is substantiated within the summary itself. revision: yes

  2. Referee: [Abstract] Abstract (mechanism): the lift-then-project operation is described at a high level but supplies no explicit construction of the linear transforms, no bound on approximation error relative to vector quantization, and no analysis showing that the resulting codebook remains expressive for the empirical distribution of LLM weights. Without these, it is impossible to verify that the dimension-ratio definition of bit-width produces a faithful approximation rather than an uncontrolled capacity reduction.

    Authors: We agree that the abstract description is high-level and that explicit construction details, error bounds relative to VQ, and expressiveness analysis are absent from the manuscript text. The methods section provides a conceptual description of the lifting and projection but does not include the requested formal analysis. In revision we will expand the mechanism description with explicit linear transform construction and add a dedicated analysis subsection addressing approximation error and codebook properties for LLM weight distributions. revision: yes

Circularity Check

0 steps flagged

No circularity; bit-width defined structurally by dimension ratio with independent empirical claims

full rationale

The paper's central mechanism defines effective bit-width explicitly as the structural ratio of lifted dimension to original dimension, which is a definitional choice for achieving continuous control rather than a fitted or predicted quantity derived from performance data. No load-bearing step reduces by construction to self-citation, ansatz smuggling, or tautological equivalence (e.g., no 'prediction' of approximation fidelity that is forced by the input definition itself). The lift-then-project is presented as an innovation whose downstream performance superiority is asserted empirically, without the derivation chain collapsing to its own inputs. This is the most common honest outcome for papers whose core contribution is a new parameterization rather than a closed-form derivation.

Axiom & Free-Parameter Ledger

1 free parameters · 0 axioms · 0 invented entities

The central claim rests on the unproven assumption that the projection step preserves sufficient model capacity; no explicit free parameters beyond the structural lift dimension are named, and no new physical entities are introduced.

free parameters (1)
  • lifted dimension
    Chosen to set the desired bit-width ratio; acts as the tunable structural parameter that determines effective precision.

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Reference graph

Works this paper leans on

64 extracted references · 22 canonical work pages · 11 internal anchors

  1. [1]

    Langley , title =

    P. Langley , title =. Proceedings of the 17th International Conference on Machine Learning (ICML 2000) , address =. 2000 , pages =

    2000

  2. [2]

    T. M. Mitchell. The Need for Biases in Learning Generalizations. 1980

    1980

  3. [3]

    M. J. Kearns , title =

  4. [4]

    Machine Learning: An Artificial Intelligence Approach, Vol. I. 1983

    1983

  5. [5]

    R. O. Duda and P. E. Hart and D. G. Stork. Pattern Classification. 2000

    2000

  6. [6]

    Suppressed for Anonymity , author=

  7. [7]

    Newell and P

    A. Newell and P. S. Rosenbloom. Mechanisms of Skill Acquisition and the Law of Practice. Cognitive Skills and Their Acquisition. 1981

    1981

  8. [8]

    A. L. Samuel. Some Studies in Machine Learning Using the Game of Checkers. IBM Journal of Research and Development. 1959

    1959

  9. [9]

    Scaling Learning Algorithms Towards

    Bengio, Yoshua and LeCun, Yann , booktitle =. Scaling Learning Algorithms Towards

  10. [10]

    and Osindero, Simon and Teh, Yee Whye , journal =

    Hinton, Geoffrey E. and Osindero, Simon and Teh, Yee Whye , journal =. A Fast Learning Algorithm for Deep Belief Nets , volume =

  11. [11]

    2016 , publisher=

    Deep learning , author=. 2016 , publisher=

    2016

  12. [12]

    LLaMA: Open and Efficient Foundation Language Models

    Llama: Open and efficient foundation language models , author=. arXiv preprint arXiv:2302.13971 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  13. [13]

    ArXiv , year=

    Qwen Technical Report , author=. ArXiv , year=

  14. [14]

    ArXiv , year=

    The Llama 3 Herd of Models , author=. ArXiv , year=

  15. [15]

    ArXiv , year=

    Llama 2: Open Foundation and Fine-Tuned Chat Models , author=. ArXiv , year=

  16. [16]

    ArXiv , year=

    DeepSeek-V3 Technical Report , author=. ArXiv , year=

  17. [17]

    Qwen2.5 Technical Report

    Qwen2. 5 technical report , author=. arXiv preprint arXiv:2412.15115 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  18. [18]

    ArXiv , year=

    Up or Down? Adaptive Rounding for Post-Training Quantization , author=. ArXiv , year=

  19. [19]

    ArXiv , year=

    BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction , author=. ArXiv , year=

  20. [20]

    2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , year=

    NoisyQuant: Noisy Bias-Enhanced Post-Training Activation Quantization for Vision Transformers , author=. 2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , year=

    2023

  21. [21]

    ArXiv , year=

    FBQuant: FeedBack Quantization for Large Language Models , author=. ArXiv , year=

  22. [22]

    ArXiv , year=

    Outlier Suppression+: Accurate quantization of large language models by equivalent and optimal shifting and scaling , author=. ArXiv , year=

  23. [23]

    ArXiv , year=

    SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models , author=. ArXiv , year=

  24. [24]

    ArXiv , year=

    QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs , author=. ArXiv , year=

  25. [25]

    ArXiv , year=

    SpinQuant: LLM quantization with learned rotations , author=. ArXiv , year=

  26. [26]

    ArXiv , year=

    OstQuant: Refining Large Language Model Quantization with Orthogonal and Scaling Transformations for Better Distribution Fitting , author=. ArXiv , year=

  27. [27]

    ArXiv , year=

    OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models , author=. ArXiv , year=

  28. [28]

    ArXiv , year=

    AffineQuant: Affine Transformation Quantization for Large Language Models , author=. ArXiv , year=

  29. [29]

    Pointer Sentinel Mixture Models

    Pointer sentinel mixture models , author=. arXiv preprint arXiv:1609.07843 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  30. [30]

    Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge

    Think you have solved question answering? try arc, the ai2 reasoning challenge , author=. arXiv preprint arXiv:1803.05457 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  31. [31]

    BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions

    Boolq: Exploring the surprising difficulty of natural yes/no questions , author=. arXiv preprint arXiv:1905.10044 , year=

    work page internal anchor Pith review Pith/arXiv arXiv 1905

  32. [32]

    HellaSwag: Can a Machine Really Finish Your Sentence?

    Hellaswag: Can a machine really finish your sentence? , author=. arXiv preprint arXiv:1905.07830 , year=

    work page internal anchor Pith review Pith/arXiv arXiv 1905

  33. [33]

    OpenAI blog , volume=

    Language models are unsupervised multitask learners , author=. OpenAI blog , volume=

  34. [34]

    Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering

    Can a suit of armor conduct electricity? a new dataset for open book question answering , author=. arXiv preprint arXiv:1809.02789 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  35. [35]

    Proceedings of the AAAI conference on artificial intelligence , volume=

    Piqa: Reasoning about physical commonsense in natural language , author=. Proceedings of the AAAI conference on artificial intelligence , volume=

  36. [36]

    SocialIQA: Commonsense Reasoning about Social Interactions

    Socialiqa: Commonsense reasoning about social interactions , author=. arXiv preprint arXiv:1904.09728 , year=

    work page internal anchor Pith review Pith/arXiv arXiv 1904

  37. [37]

    Communications of the ACM , volume=

    Winogrande: An adversarial winograd schema challenge at scale , author=. Communications of the ACM , volume=. 2021 , publisher=

    2021

  38. [38]

    arXiv preprint arXiv:2410.09426 , year=

    Flatquant: Flatness matters for llm quantization , author=. arXiv preprint arXiv:2410.09426 , year=

    work page arXiv

  39. [39]

    Proceedings of Machine Learning and Systems , volume=

    Awq: Activation-aware weight quantization for on-device llm compression and acceleration , author=. Proceedings of Machine Learning and Systems , volume=

  40. [40]

    Advances in Neural Information Processing Systems , volume=

    Duquant: Distributing outliers via dual transformation makes stronger quantized llms , author=. Advances in Neural Information Processing Systems , volume=

  41. [41]

    Quip#: Even better llm quantization with hadamard incoherence and lattice codebooks,

    Quip\#: Even better llm quantization with hadamard incoherence and lattice codebooks , author=. arXiv preprint arXiv:2402.04396 , year=

    work page arXiv

  42. [42]

    Advances in Neural Information Processing Systems , volume=

    Quip: 2-bit quantization of large language models with guarantees , author=. Advances in Neural Information Processing Systems , volume=

  43. [43]

    ArXiv , year=

    GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers , author=. ArXiv , year=

  44. [44]

    doi:10.5281/zenodo.12608602 , url =

    Gao, Leo and Tow, Jonathan and Abbasi, Baber and Biderman, Stella and Black, Sid and DiPofi, Anthony and Foster, Charles and Golding, Laurence and Hsu, Jeffrey and Le Noac'h, Alain and Li, Haonan and McDonell, Kyle and Muennighoff, Niklas and Ociepa, Chris and Phang, Jason and Reynolds, Laria and Schoelkopf, Hailey and Skowron, Aviya and Sutawika, Lintang...

    work page doi:10.5281/zenodo.12608602

  45. [45]

    Thomas Wolf and Lysandre Debut and Victor Sanh and Julien Chaumond and Clement Delangue and Anthony Moi and Pierric Cistac and Tim Rault and Rémi Louf and Morgan Funtowicz and Joe Davison and Sam Shleifer and Patrick von Platen and Clara Ma and Yacine Jernite and Julien Plu and Canwen Xu and Teven Le Scao and Sylvain Gugger and Mariama Drame and Quentin L...

    2020

  46. [46]

    fast-hadamard-transform

    Tri Dao. fast-hadamard-transform. 2023 , note =

    2023

  47. [47]

    Vptq: Extreme low-bit vector post-training quantization for large language models,

    Vptq: Extreme low-bit vector post-training quantization for large language models , author=. arXiv preprint arXiv:2409.17066 , year=

    work page arXiv

  48. [48]

    Egiazarian, A

    Extreme compression of large language models via additive quantization , author=. arXiv preprint arXiv:2401.06118 , year=

    work page arXiv

  49. [49]

    arXiv preprint arXiv:2407.11062 , year=

    Efficientqat: Efficient quantization-aware training for large language models , author=. arXiv preprint arXiv:2407.11062 , year=

    work page arXiv

  50. [50]

    Advances in neural information processing systems , volume=

    Qlora: Efficient finetuning of quantized llms , author=. Advances in neural information processing systems , volume=

  51. [51]

    arXiv preprint arXiv:2402.04291 , year=

    Billm: Pushing the limit of post-training quantization for llms , author=. arXiv preprint arXiv:2402.04291 , year=

    work page arXiv

  52. [52]

    61: Push the real limit of extremely low-bit post-training quantization methods for large language models , author=

    Ptq1. 61: Push the real limit of extremely low-bit post-training quantization methods for large language models , author=. arXiv preprint arXiv:2502.13179 , year=

    work page arXiv

  53. [53]

    Journal of machine learning research , volume=

    Exploring the limits of transfer learning with a unified text-to-text transformer , author=. Journal of machine learning research , volume=

  54. [54]

    18th USENIX Symposium on Operating Systems Design and Implementation (OSDI 24) , pages=

    Ladder: Enabling efficient \ Low-Precision \ deep learning computing through hardware-aware tensor transformation , author=. 18th USENIX Symposium on Operating Systems Design and Implementation (OSDI 24) , pages=

  55. [55]

    Advances in Neural Information Processing Systems , volume=

    Qtip: Quantization with trellises and incoherence processing , author=. Advances in Neural Information Processing Systems , volume=

  56. [56]

    arXiv preprint arXiv:2310.16836 , year=

    Llm-fp4: 4-bit floating-point quantized transformers , author=. arXiv preprint arXiv:2310.16836 , year=

    work page arXiv

  57. [57]

    Alternating Multi-bit Quantization for Recurrent Neural Networks

    Alternating multi-bit quantization for recurrent neural networks , author=. arXiv preprint arXiv:1802.00150 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  58. [58]

    arXiv preprint arXiv:2506.03781 , year=

    Unifying Uniform and Binary-coding Quantization for Accurate Compression of Large Language Models , author=. arXiv preprint arXiv:2506.03781 , year=

    work page arXiv

  59. [59]

    Journal of Machine Learning Research , volume=

    Bitnet: 1-bit pre-training for large language models , author=. Journal of Machine Learning Research , volume=

  60. [60]

    arXiv preprint arXiv:2509.20214 , year=

    Q-Palette: Fractional-Bit Quantizers Toward Optimal Bit Allocation for Efficient LLM Deployment , author=. arXiv preprint arXiv:2509.20214 , year=

    work page arXiv

  61. [61]

    The annals of statistics , pages=

    Asymptotics of graphical projection pursuit , author=. The annals of statistics , pages=. 1984 , publisher=

    1984

  62. [62]

    Measuring Massive Multitask Language Understanding

    Measuring massive multitask language understanding , author=. arXiv preprint arXiv:2009.03300 , year=

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  63. [63]

    Qwen3 Technical Report

    Qwen3 technical report , author=. arXiv preprint arXiv:2505.09388 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  64. [64]

    int8 (): 8-bit matrix multiplication for transformers at scale , author=

    Gpt3. int8 (): 8-bit matrix multiplication for transformers at scale , author=. Advances in neural information processing systems , volume=