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We introduce the Banach-Butterfly Invariant (BBT), an influence-adaptive Banach geometry on the Walsh-Hadamard butterfly factorization. For a Boolean function $f:\{-1,+1\}^n\to\{-1,+1\}$ with coordinate influences $\mathrm{Inf}_\ell(f)$,…

Machine Learning · Computer Science 2026-05-05 Gorgi Pavlov

Large language models (LLMs) have driven major progress in NLP, yet their substantial memory and compute demands still hinder practical deployment. Binarization can compress weights to 1 bit, fundamentally lowering compute and bandwidth…

Machine Learning · Computer Science 2026-05-04 Zhixiong Zhao , Zukang Xu , Dawei Yang

Rotation-based Post-Training Quantization (PTQ) has emerged as a promising solution for mitigating activation outliers in the quantization of Large Language Models (LLMs). Global rotation methods achieve inference efficiency by fusing…

Computer Vision and Pattern Recognition · Computer Science 2026-05-29 Suyoung Kim , Sunghyun Wee , Hyeonjin Kim , Kyomin Hwang , Hyunho Lee , Nojun Kwak

Quantizing LLM weights and activations is a standard approach for efficient deployment, but a few extreme outliers can stretch the dynamic range and amplify low-bit quantization errors. Prior transform-based mitigations (e.g., Hadamard…

Machine Learning · Computer Science 2026-02-03 Jiale Chen , Vage Egiazarian , Roberto L. Castro , Torsten Hoefler , Dan Alistarh

We introduce QuaRot, a new Quantization scheme based on Rotations, which is able to quantize LLMs end-to-end, including all weights, activations, and KV cache in 4 bits. QuaRot rotates LLMs in a way that removes outliers from the hidden…

We identify the Spectral Energy Gain in extreme model compression, where low-rank binary approximations outperform tiny-rank floating-point baselines for heavy-tailed spectra. However, prior attempts fail to realize this potential, trailing…

Machine Learning · Computer Science 2026-05-05 Banseok Lee , Youngmin Kim

Post-training quantization (PTQ) techniques applied to weights, activations, and the KV cache greatly reduce memory usage, latency, and power consumption of Large Language Models (LLMs), but may lead to large quantization errors when…

Quantizing large language models (LLMs) to 1-bit precision significantly reduces computational costs, but existing quantization techniques suffer from noticeable performance degradation when using weight and activation precisions below 4…

Machine Learning · Computer Science 2025-07-01 Siqing Song , Chuang Wang , Ruiqi Wang , Yi Yang , Xu-Yao Zhang

We study weight-only post-training quantization (PTQ), which quantizes the weights of a large language model (LLM) without retraining, using little or no calibration data. Weight-only PTQ is crucial for reducing the memory footprint and…

Machine Learning · Computer Science 2025-10-23 Deokjae Lee , Hyun Oh Song

Fine-tuning pre-trained diffusion models under limited budgets has gained great success. In particular, the recent advances that directly fine-tune the quantized weights using Low-rank Adaptation (LoRA) further reduces training costs.…

Computer Vision and Pattern Recognition · Computer Science 2025-05-20 Hang Guo , Yawei Li , Tao Dai , Shu-Tao Xia , Luca Benini

Large Language Models (LLMs) excel in NLP, but their demands hinder their widespread deployment. While Quantization-Aware Training (QAT) offers a solution, its extensive training costs make Post-Training Quantization (PTQ) a more practical…

Computation and Language · Computer Science 2024-04-09 Jing Liu , Ruihao Gong , Xiuying Wei , Zhiwei Dong , Jianfei Cai , Bohan Zhuang

The deployment of large language models (LLMs) is frequently hindered by prohibitive memory and computational requirements. While quantization mitigates these bottlenecks, maintaining model fidelity in the sub-1-bit regime remains a…

Machine Learning · Computer Science 2026-02-06 Banseok Lee , Dongkyu Kim , Youngcheon You , Youngmin Kim

We present ITQ3_S (Interleaved Ternary Quantization -- Specialized), a novel 3-bit weight quantization format for LLMs integrating TurboQuant (TQ), a rotation-domain strategy based on the Fast Walsh-Hadamard Transform (FWHT). Conventional…

Machine Learning · Computer Science 2026-04-01 Edward J. Yoon

Ultra low-bit quantization brings substantial efficiency for Transformer-based models, but the accuracy degradation and limited GPU support hinder its wide usage. In this paper, we analyze zero-point distortion in binarization and propose a…

Machine Learning · Computer Science 2026-04-07 Yifu Ding , Xianglong Liu , Shenghao Jin , Jinyang Guo , Jiwen Lu

Post training quantization is essential for deploying large language models (LLMs) on resource constrained hardware, yet state of the art methods enforce uniform bit widths across layers, yielding suboptimal accuracy efficiency trade offs.…

Machine Learning · Computer Science 2026-03-19 Arpit Singh Gautam , Saurabh Jha

The demand for efficient deployment of large language models (LLMs) has driven interest in quantization, which reduces inference cost, and parameter-efficient fine-tuning (PEFT), which lowers training overhead. This motivated the…

Computation and Language · Computer Science 2026-05-20 Hyesung Jeon , Seojune Lee , Beomseok Kang , Yulhwa Kim , Jae-Joon Kim

Quantization is an effective approach to reduce the memory footprint and inference cost of large language models (LLMs), yet maintaining performance in the ultra-low-bit regime remains challenging. Existing post-training methods often…

Machine Learning · Computer Science 2026-05-27 Phong Nam Huu Nguyen , Khoi M. Le , Cong-Duy T Nguyen , Anh Tuan Luu , Thong Thanh Nguyen , Tho Quan

Scalar post-training quantizers discard pairwise coordinate structure within weight rows. We introduce QAM-W (Quadrature Amplitude Modulation for Weights), a codec that recovers this structure: each row is L2-normalized, block-Hadamard…

Machine Learning · Computer Science 2026-05-27 Preetam Sharma , Kacper Dobek

The emergence of accurate open large language models (LLMs) has sparked a push for advanced quantization techniques to enable efficient deployment on end-user devices. In this paper, we revisit the challenge of extreme LLM compression --…

Machine Learning · Computer Science 2026-04-09 Zhixiong Zhao , Fangxin Liu , Junjie Wang , Chenyang Guan , Zongwu Wang , Li Jiang , Haibing Guan

We construct an efficient classical analogue of the quantum matrix inversion algorithm (HHL) for low-rank matrices. Inspired by recent work of Tang, assuming length-square sampling access to input data, we implement the pseudoinverse of a…

Data Structures and Algorithms · Computer Science 2018-11-13 András Gilyén , Seth Lloyd , Ewin Tang
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