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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…

The training and generalization dynamics of the Transformer's core mechanism, namely the Attention mechanism, remain under-explored. Besides, existing analyses primarily focus on single-head attention. Inspired by the demonstrated benefits…

The recent empirical success of the Muon optimizer has renewed interest in non-Euclidean optimization, typically justified by similarities with second-order methods, and linear minimization oracle (LMO) theory. In this paper, we challenge…

Large models recently are widely applied in artificial intelligence, so efficient training of large models has received widespread attention. More recently, a useful Muon optimizer is specifically designed for matrix-structured parameters…

Large Language Models (LLMs), built on Transformer architectures, exhibit remarkable generalization across a wide range of tasks. However, fine-tuning these models for specific tasks remains resource-intensive due to their extensive…

Orthonormalized updates accelerate training, improve stability, and enable robust hyperparameter transfer, but existing methods like Muon rely on dense matrix operations that clash with sharded weights in large-scale LLM training, causing…

Zeroth-order (ZO) optimization provides a gradient-free alternative to first-order (FO) methods by estimating gradients via finite differences of function evaluations, and has recently emerged as a memory-efficient paradigm for fine-tuning…

Multi-head attentive neural architectures have achieved state-of-the-art results on a variety of natural language processing tasks. Evidence has shown that they are overparameterized; attention heads can be pruned without significant…

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…

Recent advances in multimodal foundation models have achieved state-of-the-art performance across a range of tasks. These breakthroughs are largely driven by new pre-training paradigms that leverage large-scale, unlabeled multimodal data,…

In this paper, we propose DeMuon, a method for decentralized matrix optimization over a given communication topology. DeMuon incorporates matrix orthogonalization via Newton-Schulz iterations-a technique inherited from its centralized…

In Multi-Task Learning (MTL), it is a common practice to train multi-task networks by optimizing an objective function, which is a weighted average of the task-specific objective functions. Although the computational advantages of this…

Multi-query attention (MQA), which only uses a single key-value head, drastically speeds up decoder inference. However, MQA can lead to quality degradation, and moreover it may not be desirable to train a separate model just for faster…

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…

Physics-informed neural networks and neural operators often suffer from severe optimization difficulties caused by ill-conditioned gradients, multi-scale spectral behavior, and stiffness induced by physical constraints. Recently, the Muon…

Recent studies show that the attention heads in Transformer are not equal. We relate this phenomenon to the imbalance training of multi-head attention and the model dependence on specific heads. To tackle this problem, we propose a simple…

We introduce a novel architecture design that enhances expressiveness by incorporating multiple head classifiers (\ie, classification heads) instead of relying on channel expansion or additional building blocks. Our approach employs…

Multi-head attention mechanism is capable of learning various representations from sequential data while paying attention to different subsequences, e.g., word-pieces or syllables in a spoken word. From the subsequences, it retrieves richer…

Parameter-efficient fine-tuning (PEFT) of vision-language models (VLMs) excels in various vision tasks thanks to the rich knowledge and generalization ability of VLMs. However, recent studies revealed that such fine-tuned VLMs are…

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…