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

This paper develops the proximal method of multipliers for a class of nonsmooth convex optimization. The method generates a sequence of minimization problems (subproblems). We show that the sequence of approximations to the solutions of the…

With the growing use of machine learning algorithms and ubiquitous sensors, many `perception-to-control' systems are being developed and deployed. To ensure their trustworthiness, improving their robustness through adversarial training is…

Recent developments in deep learning optimization have brought about radically new algorithms based on the Linear Minimization Oracle (LMO) framework, such as $\sf Muon$ and $\sf Scion$. After over a decade of $\sf Adam$'s dominance, these…

Optimization with orthogonality constraints frequently arises in various fields such as machine learning. Riemannian optimization offers a powerful framework for solving these problems by equipping the constraint set with a Riemannian…

The classical work of (Arora et al., 1999) provides a scheme that gives, for any $\epsilon>0$, a polynomial time $1-\epsilon$ approximation algorithm for dense instances of a family of $\mathcal{NP}$-hard problems, such as Max-CUT and…

Recent trends towards training ever-larger language models have substantially improved machine learning performance across linguistic tasks. However, the huge cost of training larger models can make tuning them prohibitively expensive,…

Autoregressive next-token training offers a unified formulation for image generation and text understanding, but it also creates strong modality competition that destabilizes optimization and limits large-batch scaling. We show that…

As the computational demands for pre-training Large Language Models (LLMs) continue to surge, the need for efficient training paradigms becomes critical. Despite the vast resources already invested in existing pre-trained checkpoints, these…

Muon has emerged as a strong competitor to AdamW for language model pre-training, yet its behavior at scale is sensitive to weight decay. Recent work has observed that, for Muon without decoupled weight decay, the spectral norm of weight…

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…

In this paper, we introduce faster accelerated primal-dual algorithms for minimizing a convex function subject to strongly convex function constraints. Prior to our work, the best complexity bound was $\mathcal{O}(1/{\varepsilon})$,…

Achieving faster execution with shorter compilation time can foster further diversity and innovation in neural networks. However, the current paradigm of executing neural networks either relies on hand-optimized libraries, traditional…

We study a Newton-like method for the minimization of an objective function that is the sum of a smooth convex function and an l-1 regularization term. This method, which is sometimes referred to in the literature as a proximal Newton…

Many machine learning models involve solving optimization problems. Thus, it is important to deal with a large-scale optimization problem in big data applications. Recently, subsampled Newton methods have emerged to attract much attention…

Cross-modal alignment aims to map heterogeneous modalities into a shared latent space, as exemplified by models like CLIP, which benefit from large-scale image-text pretraining for strong recognition capabilities. However, when operating in…

Primal-Dual Hybrid Gradient (PDHG) and Alternating Direction Method of Multipliers (ADMM) are two widely-used first-order optimization methods. They reduce a difficult problem to simple subproblems, so they are easy to implement and have…

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…

We consider (stochastic) subgradient methods for strongly convex but potentially nonsmooth non-Lipschitz optimization. We provide new equivalent dual descriptions (in the style of dual averaging) for the classic subgradient method, the…

In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…

Spectral optimizers such as Muon have recently shown strong empirical performance in large-scale language model training, but the source and extent of their advantage remain poorly understood. We study this question through the linear…