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We study the training of deep neural networks by gradient descent where floating-point arithmetic is used to compute the gradients. In this framework and under realistic assumptions, we demonstrate that it is highly unlikely to find ReLU…

Machine Learning · Computer Science 2023-11-16 Clemens Karner , Vladimir Kazeev , Philipp Christian Petersen

The rapid advancement of large language models (LLMs) has significantly advanced the capabilities of artificial intelligence across various domains. However, their massive scale and high computational costs render them unsuitable for direct…

Computer Vision and Pattern Recognition · Computer Science 2025-10-01 Miao Rang , Zhenni Bi , Hang Zhou , Hanting Chen , An Xiao , Tianyu Guo , Kai Han , Xinghao Chen , Yunhe Wang

Parameter-Efficient Fine-Tuning (PEFT) is a popular class of techniques that strive to adapt large models in a scalable and resource-efficient manner. Yet, the mechanisms underlying their training performance and generalization remain…

Machine Learning · Computer Science 2026-02-10 Zahra Rahimi Afzal , Tara Esmaeilbeig , Mojtaba Soltanalian , Mesrob I. Ohannessian

General-purpose Large Language Models (LLMs) are frequently fine-tuned through supervised fine-tuning (SFT) to enhance performance in specific domains. Better results can be achieved by distilling the chain-of-thought of a larger model at…

Machine Learning · Computer Science 2026-03-24 Andrey Goncharov , Daniil Vyazhev , Petr Sychev , Edvard Khalafyan , Alexey Zaytsev

The success of Transformer-based Language Models (LMs) stems from their attention mechanism. While this mechanism has been extensively studied in explainability research, particularly through the attention values obtained during the forward…

Computation and Language · Computer Science 2024-12-24 Shahar Katz , Lior Wolf

In this paper, we aim at providing an introduction to the gradient descent based optimization algorithms for learning deep neural network models. Deep learning models involving multiple nonlinear projection layers are very challenging to…

Machine Learning · Computer Science 2019-03-12 Jiawei Zhang

Large language models exhibit remarkable performance across diverse tasks through pre-training and fine-tuning paradigms. However, continual fine-tuning on sequential tasks induces catastrophic forgetting, where newly acquired knowledge…

Machine Learning · Computer Science 2026-01-27 Olaf Yunus Laitinen Imanov

Despite their success in many natural language tasks, solving math problems remains a significant challenge for large language models (LLMs). A large gap exists between LLMs' pass-at-one and pass-at-N performance in solving math problems,…

Computation and Language · Computer Science 2023-10-17 Yixin Liu , Avi Singh , C. Daniel Freeman , John D. Co-Reyes , Peter J. Liu

A major challenge in training large-scale machine learning models is configuring the training process to maximize model performance, i.e., finding the best training setup from a vast design space. In this work, we unlock a gradient-based…

Machine Learning · Statistics 2025-03-19 Logan Engstrom , Andrew Ilyas , Benjamin Chen , Axel Feldmann , William Moses , Aleksander Madry

When using supervised fine-tuning (SFT) to adapt large language models (LLMs) to specific domains, a significant challenge arises: should we use the entire SFT dataset for fine-tuning? Common practice often involves fine-tuning directly on…

Computation and Language · Computer Science 2025-05-26 Xiang Liu , Zhaoxiang Liu , Peng Wang , Kohou Wang , Huan Hu , Kai Wang , Shiguo Lian

Recent advancements highlight the success of instruction tuning with large language models (LLMs) utilizing Chain-of-Thought (CoT) data for mathematical reasoning tasks. Despite the fine-tuned LLMs, challenges persist, such as incorrect,…

Computation and Language · Computer Science 2024-03-28 Yongwei Zhou , Tiejun Zhao

Despite the significant improvements achieved by large language models (LLMs) in English reasoning tasks, these models continue to struggle with multilingual reasoning. Recent studies leverage a full-parameter and two-stage training…

Computation and Language · Computer Science 2025-01-08 Yuchun Fan , Yongyu Mu , Yilin Wang , Lei Huang , Junhao Ruan , Bei Li , Tong Xiao , Shujian Huang , Xiaocheng Feng , Jingbo Zhu

As Large Language Models (LLMs) grow dramatically in size, there is an increasing trend in compressing and speeding up these models. Previous studies have highlighted the usefulness of gradients for importance scoring in neural network…

Computation and Language · Computer Science 2024-07-17 Hongrong Cheng , Miao Zhang , Javen Qinfeng Shi

In the era of Large Language Models (LLMs), alignment has emerged as a fundamental yet challenging problem in the pursuit of more reliable, controllable, and capable machine intelligence. The recent success of reasoning models and…

Machine Learning · Computer Science 2025-07-18 Hao Sun , Mihaela van der Schaar

Despite significant progress in transformer interpretability, an understanding of the computational mechanisms of large language models (LLMs) remains a fundamental challenge. Many approaches interpret a network's hidden representations but…

Machine Learning · Computer Science 2025-10-14 James R. Golden

The success of current Large-Language Models (LLMs) hinges on extensive training data that is collected and stored centrally, called Centralized Learning (CL). However, such a collection manner poses a privacy threat, and one potential…

Machine Learning · Computer Science 2025-11-18 Huiwen Wu , Xiaogang Xu , Deyi Zhang , Xiaohan Li , Jiafei Wu , Zhe Liu

Fine-tuning Large Language Models (LLMs) typically involves either full fine-tuning, which updates all model parameters, or Parameter-Efficient Fine-Tuning (PEFT), which adjusts a small subset of parameters. However, both approaches have…

Artificial Intelligence · Computer Science 2026-04-14 Shaocong Ma , Peiran Yu , Heng Huang

The evolving sophistication and intricacies of Large Language Models (LLMs) yield unprecedented advancements, yet they simultaneously demand considerable computational resources and incur significant costs. To alleviate these challenges,…

Computation and Language · Computer Science 2023-10-03 Hongye Jin , Xiaotian Han , Jingfeng Yang , Zhimeng Jiang , Chia-Yuan Chang , Xia Hu

In this paper, we explore FP8 low-bit data formats for efficient training of large language models (LLMs). Our key insight is that most variables, such as gradients and optimizer states, in LLM training can employ low-precision data formats…

We present a general framework for training deep neural networks without backpropagation. This substantially decreases training time and also allows for construction of deep networks with many sorts of learners, including networks whose…

Machine Learning · Statistics 2017-06-09 Chris Hettinger , Tanner Christensen , Ben Ehlert , Jeffrey Humpherys , Tyler Jarvis , Sean Wade
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