Related papers: PolarGrad: A Class of Matrix-Gradient Optimizers f…

This paper investigates the impact of different optimizers on the grokking phenomenon, where models exhibit delayed generalization. We conducted experiments across seven numerical tasks (primarily modular arithmetic) using a modern…

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…

In this paper, we revisit stochastic gradient descent (SGD) with AdaGrad-type preconditioning. Our contributions are twofold. First, we develop a unified convergence analysis of SGD with adaptive preconditioning under anisotropic or matrix…

Algebraic multigrid (AMG) methods are among the most efficient solvers for linear systems of equations and they are widely used for the solution of problems stemming from the discretization of Partial Differential Equations (PDEs). The most…

This paper studies a class of adaptive gradient based momentum algorithms that update the search directions and learning rates simultaneously using past gradients. This class, which we refer to as the "Adam-type", includes the popular…

End-to-end deep learning has achieved impressive results but remains limited by its reliance on large labeled datasets, poor generalization to unseen scenarios, and growing computational demands. In contrast, classical optimization methods…

From a simplified analysis of adaptive methods, we derive AvaGrad, a new optimizer which outperforms SGD on vision tasks when its adaptability is properly tuned. We observe that the power of our method is partially explained by a decoupling…

Muon improves neural-network training by orthogonalizing matrix-valued updates, but it leaves each layer's update magnitude controlled mostly by a global learning rate. We introduce OrScale, a trust-ratio extension of Muon built on a simple…

Adam has been widely adopted for training deep neural networks due to less hyperparameter tuning and remarkable performance. To improve generalization, Adam is typically used in tandem with a squared $\ell_2$ regularizer (referred to as…

The Muon optimizer has recently offered a promising alternative to AdamW for large language model training, leveraging matrix orthogonalization to produce geometry-aware updates. However, like all first-order methods, Muon can become…

In the Data-Centric Artificial Intelligence (AI) paradigm, improving data quality is essential for robust machine learning. However, many denoising methods rely on rigid statistical assumptions or require clean reference data, which limits…

We propose PRISM, an optimizer that enhances first-order spectral descent methods like Muon with partial second-order information. It constructs an efficient, low-rank quasi-second-order preconditioner via innovation-augmented polar…

We present PEARL (Preconditioner Enhancement through Actor-critic Reinforcement Learning), a novel approach to learning matrix preconditioners. Existing preconditioners such as Jacobi, Incomplete LU, and Algebraic Multigrid methods offer…

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…

The recent success of Shampoo in the AlgoPerf contest has sparked renewed interest in Kronecker-factorization-based optimization algorithms for training neural networks. Despite its success, Shampoo relies heavily on several heuristics such…

Geometry-aware optimizers such as Newton and natural gradient can improve conditioning in deep learning, but scalable variants such as K-FAC, Shampoo, and related preconditioners usually impose structural approximations early, often…

Adaptive gradient methods, especially Adam-type methods (such as Adam, AMSGrad, and AdaBound), have been proposed to speed up the training process with an element-wise scaling term on learning rates. However, they often generalize poorly…

Deep learning classifiers face significant challenges when dealing with heterogeneous multi-modal and multi-organ biomedical datasets. The low-level feature distinguishability limited to imaging-modality hinders the classifiers' ability to…

In this paper, we introduce a model for analyzing deep learning optimization over a single iteration by leveraging the matrix structure of the weights. We derive the model by assuming isotropy of curvature, including the second-order…

Self-supervised learning has shown its great potential to extract powerful visual representations without human annotations. Various works are proposed to deal with self-supervised learning from different perspectives: (1) contrastive…