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It is widely believed that stochastic gradient descent (SGD) performs significantly worse than adaptive optimizers such as Adam in pre-training Large Language Models (LLMs). Yet the underlying reason for this gap remains unclear. In this…

Training large language models requires optimization algorithms that are not only statistically effective, but also computationally and memory efficient at extreme scale. Although Adam remains the dominant optimizer for large-scale…

Training large language models (LLMs) relies on adaptive optimizers such as Adam, which introduce extra operations and require significantly more memory to maintain first- and second-order moments than SGD. While recent works such as…

Stochastic gradient-based descent (SGD), have long been central to training large language models (LLMs). However, their effectiveness is increasingly being questioned, particularly in large-scale applications where empirical evidence…

Large Language Models (LLMs) are typically fine-tuned for reasoning tasks through a two-stage pipeline of Supervised Fine-Tuning (SFT) followed by Reinforcement Learning (RL), a process fraught with catastrophic forgetting and suboptimal…

In recent years, training methods centered on Reinforcement Learning (RL) have markedly enhanced the reasoning and alignment performance of Large Language Models (LLMs), particularly in understanding human intents, following user…

Large language models (LLMs) are notoriously memory-intensive during training, particularly with the popular AdamW optimizer. This memory burden necessitates using more or higher-end GPUs or reducing batch sizes, limiting training…

Adaptive optimizers such as Adam (Kingma & Ba, 2015) have been central to the success of large language models. However, they often require to maintain optimizer states throughout training, which can result in memory requirements several…

Adaptive gradient methods (AGMs) have become popular in optimizing the nonconvex problems in deep learning area. We revisit AGMs and identify that the adaptive learning rate (A-LR) used by AGMs varies significantly across the dimensions of…

Training large language models (LLMs) poses challenges due to their massive scale and heterogeneous architectures. While adaptive optimizers like AdamW help address gradient variations, they still struggle with efficient and effective…

With the rapid development of natural language processing technology, large-scale language models (LLM) have achieved remarkable results in a variety of tasks. However, how to effectively train these huge models and improve their…

Large Language Models (LLMs) often struggle with problems that require multi-step reasoning. For small-scale open-source models, Reinforcement Learning with Verifiable Rewards (RLVR) fails when correct solutions are rarely sampled even…

Training and fine-tuning large language models (LLMs) come with challenges related to memory and computational requirements due to the increasing size of the model weights and the optimizer states. Various techniques have been developed to…

SGD and AdamW are the two most used optimizers for fine-tuning large neural networks in computer vision. When the two methods perform the same, SGD is preferable because it uses less memory (12 bytes/parameter with momentum and 8…

We introduce AdamS, a simple yet effective alternative to Adam for large language model (LLM) pretraining and post-training. By leveraging a novel denominator, i.e., the root of weighted sum of squares of the momentum and the current…

Adam is widely adopted in practical applications due to its fast convergence. However, its theoretical analysis is still far from satisfactory. Existing convergence analyses for Adam rely on the bounded smoothness assumption, referred to as…

Large language models (LLMs) excel at mathematical reasoning and logical problem-solving. The current popular training paradigms primarily use supervised fine-tuning (SFT) and reinforcement learning (RL) to enhance the models' reasoning…

Training large language models (LLMs) typically relies on adaptive optimizers like Adam (Kingma & Ba, 2015) which store additional state information to accelerate convergence but incur significant memory overhead. Recent efforts, such as…

Recent advances in reasoning capabilities of large language models (LLMs) are largely driven by reinforcement learning (RL), yet the underlying parameter dynamics during RL training remain poorly understood. This work identifies two…

Enhancing the reasoning capabilities of Large Language Models (LLMs) with efficiency and scalability remains a fundamental challenge in artificial intelligence research. This paper presents a rigorous experimental investigation into how…