Related papers: Dion2: A Simple Method to Shrink Matrix in Muon
Preconditioned adaptive methods have gained significant attention for training deep neural networks, as they capture rich curvature information of the loss landscape. The central challenge in this field lies in balancing preconditioning…
The Muon optimizer has recently attracted considerable attention for its strong empirical performance and use of orthogonalized updates on matrix-shaped parameters, yet its underlying mechanisms and relationship to adaptive optimizers such…
The Muon optimizer has demonstrated strong empirical performance in pre-training large language models by performing matrix-level gradient (or momentum) orthogonalization in each layer independently. In this work, we propose TEON, a…
Muon, a recently proposed optimizer that leverages the inherent matrix structure of neural network parameters, has demonstrated strong empirical performance, indicating its potential as a successor to standard optimizers such as AdamW. This…
The Muon optimizer has received considerable attention for its strong performance in training large language models, yet the design principle behind its matrix-gradient orthogonalization remains largely elusive. In this paper, we introduce…
The Muon optimizer has rapidly emerged as a powerful, geometry-aware alternative to AdamW, demonstrating strong performance in large-scale training of neural networks. However, a critical theory-practice disconnect exists: Muon's efficiency…
Modern optimizers, like Muon, impose matrix-wise geometry constraints on their updates. These matrix-wise constraints can be unified under Linear Minimization Oracle (LMO) theory. However, all current methods impose fixed LMO geometries for…
Muon and related normalized optimizers decouple the choice of update direction from the choice of step scale, but their practical performance remains sensitive to the scale of the normalized step. We study adaptive scaling rules for Muon in…
The pursuit of faster optimization algorithms remains an active and important research direction in deep learning. Recently, the Muon optimizer [JJB+24] has demonstrated promising empirical performance, but its theoretical foundation…
Muon-style optimizers take a matrix-valued momentum or preconditioned update $B = U \operatorname{diag}(\sigma_1,\ldots,\sigma_r) V^\top$ and replace it with its canonical partial polar factor $\operatorname{Pol}(B) = U V^\top$. This maps…
In large-scale optimization, the cheapness and effectiveness of update steps are the most crucial factors for a successful optimizer. Sign-based optimizers like Lion or Signum produce cheap per-step updates, whereas Muon's spectral…
To define a steepest descent method over a neural network, we need to choose a norm for each layer, a way to aggregate these norms across layers, and whether to use normalization. We systematically explore different alternatives for…
Recommender systems (RecSys) are increasingly emphasizing scaling, leveraging larger architectures and more interaction data to improve personalization. Yet, despite the optimizer's pivotal role in training, modern RecSys pipelines almost…
Conventional wisdom in deep learning optimization dictates updating all layers at every step-a principle followed by all recent state-of-the-art optimizers such as Muon. In this work, we challenge this assumption, showing that full-network…
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…
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…
Muon updates weight matrices along (approximate) polar factors of the gradients and has shown strong empirical performance in large-scale training. Existing attempts at explaining its performance largely focus on single-step comparisons (on…
Muon orthogonalizes the momentum buffer before each update, replacing its singular values with ones via Newton-Schulz iterations. This simple change lets Muon tolerate far larger learning rates and converge faster than other optimizers, but…
The Muon optimizer has demonstrated remarkable empirical success in handling matrix-structured parameters for training neural networks. However, a significant gap remains between its practical performance and theoretical understanding.…
Generalisation of a deep neural network (DNN) is one major concern when employing the deep learning approach for solving practical problems. In this paper we propose a new technique, named approximated orthonormal normalisation (AON), to…