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The $\mu$-parameterization ($\mu$P) provides a principled foundation for large language model (LLM) training by prescribing width-independent learning dynamics, which in turn enables predictable scaling behavior and robust hyperparameter…

Machine Learning · Computer Science 2026-01-08 John Zhao

Modern Large Language Model (LLM) training is fundamentally bottlenecked by pathologically flat saddle points in extreme high-dimensional landscapes. Motivated by this challenge, we analyze the saddle-point escape dynamics of the emerging…

Machine Learning · Computer Science 2026-05-12 Yanlin Long , Yufei Gu , Zeke Xie

Muon and related normalized optimizers decouple the choice of update direction from the choice of step scale, but their practical performance remains sensitive to the scale of the normalized step. We study adaptive scaling rules for Muon in…

Machine Learning · Computer Science 2026-05-20 Yury Demidovich , Abhishek Chakraborty , Grigory Malinovsky , Angelia Nedić , Peter Richtárik

A central challenge in continual learning for large language models (LLMs) is catastrophic forgetting, where adapting to new tasks can substantially degrade performance on previously learned ones. Existing projection-based methods mitigate…

Machine Learning · Computer Science 2026-05-18 Binghang Lu , Zheyuan Deng , Runyu Zhang , Bing Hu , Yunhan Zhao , Yuan Tian , Changhong Mou , Guang Lin , Xiaomin Li

Large language models (LLMs) deliver impressive results for a variety of tasks, but state-of-the-art systems require fast GPUs with large amounts of memory. To reduce both the memory and latency of these systems, practitioners quantize…

Computer Vision and Pattern Recognition · Computer Science 2026-01-22 Gautom Das , Vincent La , Ethan Lau , Abhinav Shrivastava , Matthew Gwilliam

Large language models (LLMs) show excellent performance but are compute- and memory-intensive. Quantization can reduce memory and accelerate inference. However, existing methods cannot maintain accuracy and hardware efficiency at the same…

Computation and Language · Computer Science 2024-04-03 Guangxuan Xiao , Ji Lin , Mickael Seznec , Hao Wu , Julien Demouth , Song Han

Quantization has become one of the most effective methodologies to compress LLMs into smaller size. However, the existing quantization solutions still show limitations of either non-negligible accuracy drop or low system efficiency. In this…

Machine Learning · Computer Science 2026-04-23 Zhen Zheng , Xiaonan Song , Chuanjie Liu

The quality of Large Language Model (LLM) pretraining depends on multiple factors, including the compute budget and the choice of optimization algorithm. Empirical scaling laws are widely used to predict loss as model size and training data…

Machine Learning · Computer Science 2026-02-25 Alexandra Volkova , Mher Safaryan , Christoph H. Lampert , Dan Alistarh

Orthonormalized updates accelerate training, improve stability, and enable robust hyperparameter transfer, but existing methods like Muon rely on dense matrix operations that clash with sharded weights in large-scale LLM training, causing…

Machine Learning · Computer Science 2025-09-16 Kwangjun Ahn , Byron Xu , Natalie Abreu , Ying Fan , Gagik Magakyan , Pratyusha Sharma , Zheng Zhan , John Langford

We propose a new variant of the Adam optimizer called MicroAdam that specifically minimizes memory overheads, while maintaining theoretical convergence guarantees. We achieve this by compressing the gradient information before it is fed…

Machine Learning · Computer Science 2024-11-06 Ionut-Vlad Modoranu , Mher Safaryan , Grigory Malinovsky , Eldar Kurtic , Thomas Robert , Peter Richtarik , Dan Alistarh

The severe on-chip memory limitations are currently preventing the deployment of the most accurate Deep Neural Network (DNN) models on tiny MicroController Units (MCUs), even if leveraging an effective 8-bit quantization scheme. To tackle…

Machine Learning · Computer Science 2020-08-13 Manuele Rusci , Marco Fariselli , Alessandro Capotondi , Luca Benini

Large Language Models (LLMs) stand out for their impressive performance in intricate language modeling tasks. However, their demanding computational and memory needs pose obstacles for broad use on edge devices. Quantization is then…

Machine Learning · Computer Science 2025-04-22 Xuan Shen , Peiyan Dong , Lei Lu , Zhenglun Kong , Zhengang Li , Ming Lin , Chao Wu , Yanzhi Wang

A range of recent optimizers have emerged that approximate the same "matrix-whitening" transformation in various ways. In this work, we systematically deconstruct such optimizers, aiming to disentangle the key components that explain…

Machine Learning · Computer Science 2025-10-30 Kevin Frans , Pieter Abbeel , Sergey Levine

Large language models have achieved significant advancements in complex mathematical reasoning benchmarks, such as MATH. However, their substantial computational requirements present challenges for practical deployment. Model quantization…

Computation and Language · Computer Science 2025-02-25 Zhen Li , Yupeng Su , Runming Yang , Congkai Xie , Zheng Wang , Zhongwei Xie , Ngai Wong , Hongxia Yang

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

Large Language Models (LLMs) have demonstrated remarkable success across a wide range of language tasks, but their deployment on edge devices remains challenging due to the substantial memory requirements imposed by their large parameter…

Computation and Language · Computer Science 2025-02-05 Zihan Chen , Bike Xie , Jundong Li , Cong Shen

Combinatorial optimization problems have wide-ranging applications in industry and academia. Quantum computers may help solve them by sampling from carefully prepared Ansatz quantum circuits. However, current quantum computers are limited…

Quantum Physics · Physics 2025-11-07 Sabina Drăgoi , Alberto Baiardi , Daniel J. Egger

Large language models (LLMs) have achieved outstanding performance across a wide range of natural language processing tasks, but their enormous parameter counts impose ubstantial memory and computational overheads. This challenge is…

Machine Learning · Computer Science 2026-04-07 Seoungsub Lee , In Seo Kim , Seon Wook Kim

Large Language Models (LLMs) pose significant hardware challenges related to memory requirements and computational ability. There are two mainstream quantization schemes for LLMs: coarse-grained ($\textit{e.g.,}$ channel-wise) quantization…

Artificial Intelligence · Computer Science 2023-10-10 Luoming Zhang , Wen Fei , Weijia Wu , Yefei He , Zhenyu Lou , Hong Zhou

Low-bit quantization emerges as one of the most promising compression approaches for deploying deep neural networks on edge devices. Mixed-precision quantization leverages a mixture of bit-widths to unleash the accuracy and efficiency…

Machine Learning · Computer Science 2024-05-24 Wei Huang , Haotong Qin , Yangdong Liu , Jingzhuo Liang , Yulun Zhang , Ying Li , Xianglong Liu