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The Warmup Stable Decay (WSD) learning rate scheduler has recently become popular, largely due to its good performance and flexibility when training large language models. It remains an open question whether the remarkable performance of…

Learning rate scheduling is crucial for training large language models, yet understanding the optimal annealing strategies across different model configurations remains challenging. In this work, we investigate the transferability of…

Training language models currently requires pre-determining a fixed compute budget because the typical cosine learning rate schedule depends on the total number of steps. In contrast, the Warmup-Stable-Decay (WSD) schedule uses a constant…

We investigate the role of learning rate scheduling in the large-scale pre-training of large language models, focusing on its influence on downstream performance after supervised fine-tuning (SFT). Decay-based learning rate schedulers are…

It is common in deep learning to warm up the learning rate $\eta$, often by a linear schedule between $\eta_{\text{init}} = 0$ and a predetermined target $\eta_{\text{trgt}}$. In this paper, we show through systematic experiments using SGD…

Large-batch training has been essential in leveraging large-scale datasets and models in deep learning. While it is computationally beneficial to use large batch sizes, it often requires a specially designed learning rate (LR) schedule to…

We show that learning-rate schedules for large model training behave surprisingly similar to a performance bound from non-smooth convex optimization theory. We provide a bound for the constant schedule with linear cooldown; in particular,…

Learning rate (LR) schedules in large language model (LLM) training often follow empirical templates: warm-up, constant plateau/stable phase, and decay (WSD). However, the mechanistic explanation for this strategy remains underexplored, and…

Learning rate warm-up - increasing the learning rate at the beginning of training - has become a ubiquitous heuristic in modern deep learning, yet its theoretical foundations remain poorly understood. In this work, we provide a principled…

A basic unanswered question in neural network training is: what is the best learning rate schedule shape for a given workload? The choice of learning rate schedule is a key factor in the success or failure of the training process, but…

Setting the learning rate (LR) for a deep learning model is a critical part of successful training. Choosing LRs is often done empirically with trial and error. In this work, we explore a solvable model of optimal LR schedules for a…

Learning rate schedules used in practice bear little resemblance to those recommended by theory. We close much of this theory/practice gap, and as a consequence are able to derive new problem-adaptive learning rate schedules. Our main…

Neural scaling laws, which in some domains can predict the performance of large neural networks as a function of model, data, and compute scale, are the cornerstone of building foundation models in Natural Language Processing and Computer…

We study adaptive learning rate scheduling for norm-constrained optimizers (e.g., Muon and Lion). We introduce a generalized smoothness assumption under which local curvature decreases with the suboptimality gap and empirically verify that…

The Transformer is widely used in natural language processing tasks. To train a Transformer however, one usually needs a carefully designed learning rate warm-up stage, which is shown to be crucial to the final performance but will slow…

We study optimal learning-rate schedules (LRSs) under the functional scaling law (FSL) framework introduced in Li et al. (2025), which accurately models the loss dynamics of both linear regression and large language model (LLM)…

Curvature information -- particularly, the largest eigenvalue of the loss Hessian, known as the sharpness -- often forms the basis for learning rate tuners. However, recent work has shown that the curvature information undergoes complex…

As both model and dataset sizes continue to scale rapidly, conventional pretraining strategies with fixed compute budgets-such as cosine learning rate schedules-are increasingly inadequate for large-scale training. Recent alternatives,…

In this work, we study the evolution of the loss Hessian across many classification tasks in order to understand the effect the curvature of the loss has on the training dynamics. Whereas prior work has focused on how different learning…

In practice, the hyperparameters $(\beta_1, \beta_2)$ and weight-decay $\lambda$ in AdamW are typically kept at fixed values. Is there any reason to do otherwise? We show that for large-scale language model training, the answer is yes: by…