Related papers: What Really Matters in Matrix-Whitening Optimizers…

As the use of artificial intelligence rapidly increases, the development of trustworthy artificial intelligence has become important. However, recent studies have shown that deep neural networks are susceptible to learn spurious…

Different gradient-based methods for optimizing overparameterized models can all achieve zero training error yet converge to distinctly different solutions inducing different generalization properties. We provide the first complete…

The Muon optimizer has recently demonstrated remarkable empirical success in training large language models. However, the theoretical understanding of its mechanisms remains limited. Current convergence guarantees for Muon rely heavily on…

Muon is a matrix-aware optimizer that leverages Newton-Schulz (NS) iterations to enforce spectral gradient orthogonalization by driving all singular values of the momentum matrix toward 1. While this uniform spectral whitening enhances…

Recent advances in spectral optimization, notably Muon, have demonstrated that constraining update steps to the Stiefel manifold can significantly accelerate training and improve generalization. However, Muon implicitly assumes an isotropic…

Matrix-based optimizers have attracted growing interest for improving LLM training efficiency, with significant progress centered on orthogonalization/whitening based methods. While yielding substantial performance gains, a fundamental…

Muon updates matrix parameters via the matrix sign of the gradient and has shown strong empirical gains, yet its dynamics and scaling behavior remain unclear in theory. We study Muon in a linear associative memory model with softmax…

The muon optimizer has picked up much attention as of late as a possible replacement to the seemingly omnipresent Adam optimizer. Recently, care has been taken to document the scaling laws of hyper-parameters under muon such as weight decay…

The rapid scaling of large language models (LLMs) has made low-precision training essential for reducing memory, improving efficiency, and enabling larger models and datasets. Existing convergence theories for adaptive optimizers, however,…

Sharpness-Aware Minimization (SAM) has emerged as a promising alternative optimizer to stochastic gradient descent (SGD). The originally-proposed motivation behind SAM was to bias neural networks towards flatter minima that are believed to…

Gradient orthogonalization is a simple strategy that shows great utility in speeding up gradient descent. The Muon optimizer (Jordan, Jin, et al., 2024) combines gradient orthogonalization with first-order momentum and achieves significant…

Optimization lies at the core of modern deep learning, yet existing methods often face a fundamental trade-off between adapting to problem geometry and leveraging curvature utilization. Steepest descent algorithms adapt to different…

We study the problem of estimating a large, low-rank matrix corrupted by additive noise of unknown covariance, assuming one has access to additional side information in the form of noise-only measurements. We study the Whiten-Shrink-reColor…

Selecting an optimizer is a central step in the contemporary deep learning pipeline. In this paper, we demonstrate the sensitivity of optimizer comparisons to the hyperparameter tuning protocol. Our findings suggest that the hyperparameter…

The Gauss-Newton matrix is widely viewed as a positive semidefinite approximation of the Hessian, yet mounting empirical evidence shows that Gauss-Newton descent outperforms Newton's method. We adopt a function space perspective to analyze…

In this work, we take an experimentally grounded look at neural network optimization. Building on the Shampoo family of algorithms, we identify and alleviate three key issues, resulting in the proposed SPlus method. First, we find that…

We present a comprehensive theoretical and empirical study of the Muon optimizer for training transformers only with a small to medium decoder (30M - 200M parameters), with an emphasis on its mathematical foundations, convergence properties…

Muon has emerged as an efficient alternative to Adam for pretraining, yet remains underused for fine-tuning. A key obstacle is that most open models are pretrained with Adam, and naively switching to Muon for fine-tuning leads to degraded…

Optimizers play an important role in both pretraining and finetuning stages when training large language models (LLMs). In this paper, we present an observation that full finetuning with the same optimizer as in pretraining achieves a…

Foundation models achieve state-of-the-art performance across different tasks, but their size and computational demands raise concerns about accessibility and sustainability. Existing efficiency methods often require additional retraining…