Related papers: Turbo-Muon: Accelerating Orthogonality-Based Optim…

Recently, a new optimization method based on the linear minimization oracle (LMO), called Muon, has been attracting increasing attention since it can train neural networks faster than existing adaptive optimization methods, such as Adam. In…

Superlinear convergence has been an elusive goal for black-box nonsmooth optimization. Even in the convex case, the subgradient method is very slow, and while some cutting plane algorithms, including traditional bundle methods, are popular…

Modern deep learning commonly relies on AdamW with prescribed learning rate schedules, but recent works challenge both components: Schedule-Free optimization removes explicit schedules via iterate averaging, and Muon improves the update…

AdamW has long been the dominant optimizer in language model pretraining, despite numerous claims that alternative optimizers offer 1.4 to 2x speedup. We posit that two methodological shortcomings have obscured fair comparisons and hindered…

We propose AdaMuon, a novel optimizer that combines element-wise adaptivity with orthogonal updates for large-scale neural network training. AdaMuon incorporates two tightly coupled mechanisms: (1) an element-wise second momentum estimator…

In [19], a general, inexact, efficient proximal quasi-Newton algorithm for composite optimization problems has been proposed and a sublinear global convergence rate has been established. In this paper, we analyze the convergence properties…

Inspired by the concept of preconditioning, we propose a novel method to increase adaptation speed for gradient-based meta-learning methods without incurring extra parameters. We demonstrate that recasting the optimization problem to a…

Distributed training of large neural networks is bottlenecked by full-precision gradient communication and by coordinatewise optimizers that ignore the matrix structure of weight tensors. We propose Sign-Muon, a 1-bit, matrix-aware…

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…

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.…

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…

The rapid progress of large language models (LLMs) is increasingly constrained by memory and deployment costs, motivating compression methods for practical deployment. Many state-of-the-art compression pipelines leverage the low-rank…

A central challenge in continual learning for large language models (LLMs) is catastrophic forgetting, where adapting to new tasks can substantially degrade performance on previously learned ones. Existing projection-based methods mitigate…

High-fidelity physics simulations are powerful tools in the design and optimization of charged particle accelerators. However, the computational burden of these simulations often limits their use in practice for design optimization and…

The optimisation of neural networks can be sped up by orthogonalising the gradients before the optimisation step, ensuring the diversification of the learned representations. We orthogonalise the gradients of the layer's components/filters…

The ever-growing scale of deep learning models and training data underscores the critical importance of efficient optimization methods. While preconditioned gradient methods such as Adam and AdamW are the de facto optimizers for training…

Multi-Task Learning (MTL) is a foundational machine learning problem that has seen extensive development over the past decade. Recently, various optimization-based MTL approaches have been proposed to learn multiple tasks simultaneously by…

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…

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…

One of the widespread solutions for non-rigid tracking has a nested-loop structure: with Gauss-Newton to minimize a tracking objective in the outer loop, and Preconditioned Conjugate Gradient (PCG) to solve a sparse linear system in the…