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This work presents BAdam, an optimization method that leverages the block coordinate descent (BCD) framework with Adam's update rule. BAdam offers a memory efficient approach to the full parameter finetuning of large language models. We…

Machine Learning · Computer Science 2024-11-18 Qijun Luo , Hengxu Yu , Xiao Li

Deep Feedforward Neural Networks' (DFNNs) weights estimation relies on the solution of a very large nonconvex optimization problem that may have many local (no global) minimizers, saddle points and large plateaus. As a consequence,…

Optimization and Control · Mathematics 2020-06-16 Laura Palagi , Ruggiero Seccia

We present LLMQ, an end-to-end CUDA/C++ implementation for medium-sized language-model training, e.g. 3B to 32B parameters, on affordable, commodity GPUs. These devices are characterized by low memory availability and slow communication…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-12-18 Erik Schultheis , Dan Alistarh

The advent of large language models (LLMs) has revolutionized the deep learning paradigm, yielding impressive results across a wide array of tasks. However, the pre-training or fine-tuning of LLMs within a federated learning (FL) framework…

Machine Learning · Computer Science 2024-07-22 Lin Wang , Zhichao Wang , Xiaoying Tang

Machine learning (ML) is a key technique for big-data-driven modelling and analysis of massive Internet of Things (IoT) based intelligent and ubiquitous computing. For fast-increasing applications and data amounts, distributed learning is a…

Machine Learning · Computer Science 2022-02-08 Hao Chen , Yu Ye , Ming Xiao , Mikael Skoglund

In this paper, we consider a block coordinate descent (BCD) algorithm for training deep neural networks and provide a new global convergence guarantee under strictly monotonically increasing activation functions. While existing works…

Machine Learning · Statistics 2025-10-28 Shunta Akiyama

Although Federated Learning has been widely studied in recent years, there are still high overhead expenses in each communication round for large-scale models such as Vision Transformer. To lower the communication complexity, we propose a…

Machine Learning · Computer Science 2026-04-21 Junkang Liu , Fanhua Shang , Yuanyuan Liu , Hongying Liu , Yuangang Li , YunXiang Gong

Training Large Language Models(LLMs) is one of the most compute-intensive tasks in high-performance computing. Predicting end-to-end training time for multi-billion parameter models distributed across hundreds of GPUs remains challenging…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-09-30 Biyao Zhang , Mingkai Zheng , Debargha Ganguly , Xuecen Zhang , Vikash Singh , Vipin Chaudhary , Zhao Zhang

Block coordinate descent (BCD) methods are widely used for large-scale numerical optimization because of their cheap iteration costs, low memory requirements, amenability to parallelization, and ability to exploit problem structure. Three…

Optimization and Control · Mathematics 2022-08-02 Julie Nutini , Issam Laradji , Mark Schmidt

Block-coordinate descent (BCD) is the method of choice to solve numerous large scale optimization problems, however their theoretical study for non-convex optimization, has received less attention. In this paper, we present a new…

Machine Learning · Computer Science 2026-01-30 Guillaume Lauga

Coordinate descent algorithms are widely used in machine learning and large-scale data analysis due to their strong optimality guarantees and impressive empirical performance in solving non-convex problems. In this work, we introduce Block…

Optimization and Control · Mathematics 2024-12-17 Zhijie Yuan , Ganzhao Yuan , Lei Sun

Dramatic increases in the capabilities of neural network models in recent years are driven by scaling model size, training data, and corresponding computational resources. To develop the exceedingly large networks required in modern…

Machine Learning · Computer Science 2025-04-15 Jared Fernandez , Luca Wehrstedt , Leonid Shamis , Mostafa Elhoushi , Kalyan Saladi , Yonatan Bisk , Emma Strubell , Jacob Kahn

Large language models (LLMs) have achieved significant success across various domains. However, training these LLMs typically involves substantial memory and computational costs during both forward and backward propagation. While…

Machine Learning · Computer Science 2025-03-03 Sunghyeon Woo , Baeseong Park , Byeongwook Kim , Minjung Jo , Se Jung Kwon , Dongsuk Jeon , Dongsoo Lee

Training large language models (LLMs) for pretraining or adapting to new tasks and domains has become increasingly critical as their applications expand. However, as the model and the data sizes grow, the training process presents…

Machine Learning · Computer Science 2024-12-17 Amrutha Varshini Ramesh , Vignesh Ganapathiraman , Issam H. Laradji , Mark Schmidt

Training with larger mini-batches improves the convergence rate and can yield superior performance. However, training with large mini-batches becomes prohibitive for Large Language Models (LLMs), due to the large GPU memory requirement. To…

Machine Learning · Computer Science 2025-05-29 Dang Nguyen , Wenhan Yang , Rathul Anand , Yu Yang , Baharan Mirzasoleiman

Training deep neural networks (DNNs) efficiently is a challenge due to the associated highly nonconvex optimization. The backpropagation (backprop) algorithm has long been the most widely used algorithm for gradient computation of…

Machine Learning · Statistics 2018-03-28 Tim Tsz-Kit Lau , Jinshan Zeng , Baoyuan Wu , Yuan Yao

Large language models (LLMs) are computationally intensive. The computation workload and the memory footprint grow quadratically with the dimension (layer width). Most of LLMs' parameters come from the linear layers of the transformer…

Machine Learning · Computer Science 2024-02-22 Xiao-Yang Liu , Jie Zhang , Guoxuan Wang , Weiqing Tong , Anwar Walid

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…

By lifting the ReLU function into a higher dimensional space, we develop a smooth multi-convex formulation for training feed-forward deep neural networks (DNNs). This allows us to develop a block coordinate descent (BCD) training algorithm…

Machine Learning · Statistics 2017-11-21 Ziming Zhang , Matthew Brand

This paper introduces a deep reinforcement learning-based block coordinate descent (DRL-based BCD) algorithm to address the nonconvex weighted sum-rate maximization (WSRM) problem with a total power constraint. Firstly, we present an…

Networking and Internet Architecture · Computer Science 2026-02-25 Siya Chen , Chee Wei Tan , H. Vincent Poor
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