SOAP, Muon, and Beyond: Pushing LLM Pretraining Scales

• URL: http://arxiv.org/abs/2607.20548v1
• Date: Mon, 13 Jul 2026 21:47:08 GMT
• Title: SOAP, Muon, and Beyond: Pushing LLM Pretraining Scales
• Abstract summary: Higher-order LLMs such as Muon and SOAP offer faster convergence than AdamW, but their computational cost and numerical stability challenges have limited adoption at scale.<n>We adapt and enhance preconditioned methods to overcome the practical challenges of large-scale LLM pretraining regimes.
• Score: 48.03325171473355
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Higher-order optimizers such as Muon and SOAP offer faster convergence than AdamW, but their computational cost and numerical stability challenges have limited adoption at scale. In this work, we adapt and enhance preconditioned gradient methods to overcome the practical challenges of large-scale LLM pretraining. We first identify instabilities in SOAP at large batch sizes and propose algorithmic modifications including per-step QR orthogonalization and improved preconditioning strategies that eliminate loss spikes and enable stable training in these regimes. We then present a unified empirical study of SOAP, Muon, and AdamW using update-RMS matching to ensure fair learning rate transfer across optimizers. As part of this analysis, we empirically evaluate the orthogonalization quality of Muon. Our experiments on multi-billion-parameter models trained on trillions of tokens reveal that SOAP and Muon consistently outperform AdamW at the scales we tested. Notably, at batch sizes of up to 100M tokens for next-token prediction, these optimizers maintain training stability and quality while AdamW degrades. To enable efficient training at large scale, we introduce a layer-wise distributed optimizer compatible with Megatron-LM. Our implementation balances memory and hides communication while avoiding approximations to the optimizer computations, thus retaining their convergence benefits. Additionally, we identify and build specific system-level improvements to further accelerate our layer-wise implementation. To support the research community, we release a codebase that contains emerging algorithms for optimization: https://github.com/NVIDIA-NeMo/Emerging-Optimizers

Related papers

• Beyond Adam: SOAP and Muon for Faster, Label-Efficient Training of Machine Learning Interatomic Potentials [0.5714512533033075]
  We implement and compare a class of recently proposed matrix-structureds, including Muon, SOAP, and the hybrid SOAP-Muon, for training NequIP and Allegro MLIP models.<n>We find that theses can substantially outperform Adam in both convergence speed and final accuracy.
  arXiv  Detail & Related papers  (2026-07-02T17:57:31Z)
• Hyperparameter Transfer Enables Consistent Gains of Matrix-Preconditioned Optimizers Across Scales [55.91454326946738]
  We study how the optimal learning rate and weight decay should scale with model width and depth for a wide range of languages.<n>We find that scaling the learning rate according to $$P improves transfer, but can still suffer from significant finite-width deviations.<n>For compute-optimal scaling, we find scaling independent weight decay as $1/mathrmwidth$ is nearly optimal across languages.
  arXiv  Detail & Related papers  (2025-12-05T11:03:41Z)
• NorMuon: Making Muon more efficient and scalable [71.49702449498085]
  We propose NorMuon (Neuron-wise Normalized Muon) as a successor to Adam.<n>We show NorMuon consistently outperforms both Adam and Muon, achieving 21.74% better training efficiency than Adam and 11.31% improvement over Muon on 1.1 B pretraining setting.
  arXiv  Detail & Related papers  (2025-10-07T01:13:41Z)
• Leveraging Coordinate Momentum in SignSGD and Muon: Memory-Optimized Zero-Order [39.25335214877435]
  Fine-tuning Large Language Models (LLMs) is essential for adapting pre-trained models to downstream tasks.<n>Traditional first-order algorithms incur prohibitive memory and computational costs that scale poorly with model size.<n>We propose zero-order (ZO) optimization methods as a memory- and compute-efficient alternative.
  arXiv  Detail & Related papers  (2025-06-04T20:27:17Z)
• Gradient Multi-Normalization for Stateless and Scalable LLM Training [16.037614012166063]
  Training large language models (LLMs) typically relies on adaptives like Adam which store additional state information to accelerate convergence but incur significant memory overhead.<n>Recent efforts, such as SWAN (Ma et al., 2024) address this by eliminating the need for states while achieving performance comparable to Adam via a multi-step preprocessing procedure applied to instantaneous gradients.<n>We introduce a novel framework for designing stateless gradients that normalizes gradients according to multiple norms. Experiments on pre-training LLaMA models with up to 1 billion parameters demonstrate a 3X speedup over Adam with significantly reduced memory requirements, outperforming other memory-efficient baseline
  arXiv  Detail & Related papers  (2025-02-10T18:09:53Z)
• MARS: Unleashing the Power of Variance Reduction for Training Large Models [56.67982828148859]
  We propose a unified training framework for deep neural networks.<n>We introduce three instances of MARS that leverage preconditioned gradient optimization.<n>Results indicate that the implementation of MARS consistently outperforms Adam.
  arXiv  Detail & Related papers  (2024-11-15T18:57:39Z)
• Simplicity Prevails: Rethinking Negative Preference Optimization for LLM Unlearning [45.64632177923583]
  This work studies the problem of large language model (LLM) unlearning, aiming to remove unwanted data influences.<n>Despite the increasing demand for unlearning, a technically-grounded optimization framework is lacking.<n>We propose a simple yet effective unlearning optimization framework, called SimNPO, showing that simplicity' in removing the reliance on a reference model benefits unlearning.
  arXiv  Detail & Related papers  (2024-10-09T17:58:12Z)
• AdaLomo: Low-memory Optimization with Adaptive Learning Rate [59.64965955386855]
  We introduce low-memory optimization with adaptive learning rate (AdaLomo) for large language models. AdaLomo results on par with AdamW, while significantly reducing memory requirements, thereby lowering the hardware barrier to training large language models.
  arXiv  Detail & Related papers  (2023-10-16T09:04:28Z)
• MaxVA: Fast Adaptation of Step Sizes by Maximizing Observed Variance of Gradients [112.00379151834242]
  We propose adaptive learning rate principle, in which the running mean of squared gradient in Adam is replaced by a weighted mean, with weights chosen to maximize the estimated variance each coordinate. This results in faster adaptation, which leads more desirable empirical convergence behaviors.
  arXiv  Detail & Related papers  (2020-06-21T21:47:43Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.