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Transformers have achieved state-of-the-art performance in language modeling tasks. However, the reasons behind their tremendous success are still unclear. In this paper, towards a better understanding, we train a Transformer model on a…

Machine Learning · Statistics 2024-06-06 Michael E. Sander , Raja Giryes , Taiji Suzuki , Mathieu Blondel , Gabriel Peyré

Adaptive moment methods such as Adam use a diagonal, coordinate-wise preconditioner based on exponential moving averages of squared gradients. This diagonal scaling is coordinate-system dependent and can struggle with dense or rotated…

Machine Learning · Computer Science 2026-04-09 Devender Singh , Tarun Sheel

NLP research has explored different neural model architectures and sizes, datasets, training objectives, and transfer learning techniques. However, the choice of optimizer during training has not been explored as extensively. Typically,…

Computation and Language · Computer Science 2024-02-13 Nefeli Gkouti , Prodromos Malakasiotis , Stavros Toumpis , Ion Androutsopoulos

We propose a variational framework that interprets transformer layers as iterations of an optimization algorithm acting on token embeddings. In this view, self-attention implements a gradient step of an interaction energy, while MLP layers…

Machine Learning · Computer Science 2026-03-06 Aleksandr Zimin , Yury Polyanskiy , Philippe Rigollet

We evaluate three simple, normalization-centric changes to improve Transformer training. First, we show that pre-norm residual connections (PreNorm) and smaller initializations enable warmup-free, validation-based training with large…

Computation and Language · Computer Science 2020-01-01 Toan Q. Nguyen , Julian Salazar

During pretraining, the Pre-LayerNorm transformer suffers from a gradient magnitude mismatch: gradients at early layers are much larger than at later layers. These issues can be alleviated by our proposed NormFormer architecture, which adds…

Computation and Language · Computer Science 2021-11-02 Sam Shleifer , Jason Weston , Myle Ott

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…

Machine Learning · Computer Science 2025-12-25 Chongjie Si , Debing Zhang , Wei Shen

Topology optimization enables the design of highly efficient and complex structures, but conventional iterative methods, such as SIMP-based approaches, often suffer from high computational costs and sensitivity to initial conditions.…

Computational Engineering, Finance, and Science · Computer Science 2025-09-18 Aaron Lutheran , Srijan Das , Alireza Tabarraei

Structured dropout approaches, such as attention dropout and DropHead, have been investigated to regularize the multi-head attention mechanism in Transformers. In this paper, we propose a new regularization scheme based on token-level…

Computation and Language · Computer Science 2023-10-31 Yangjun Wu , Kebin Fang , Dongxiang Zhang , Han Wang , Hao Zhang , Gang Chen

Next-generation wireless networks are expected to leverage multi-modal data sources to execute various wireless communication tasks such as beamforming and blockage prediction with situational-awareness. To do so, multi-modal transformers…

Systems and Control · Electrical Eng. & Systems 2026-04-22 Minsu Kim , Walid Saad , Kui Wang , Zongdian Li , Tao Yu , Kei Sakaguchi

Transformers are difficult to optimize with stochastic gradient descent (SGD) and largely rely on adaptive optimizers such as Adam. Despite their empirical success, the reasons behind Adam's superior performance over SGD remain poorly…

Machine Learning · Computer Science 2026-02-19 Akiyoshi Tomihari , Issei Sato

The primary objective of this research is to build a Momentum Transformer that is expected to outperform benchmark time-series momentum and mean-reversion trading strategies. We extend the ideas introduced in the paper Trading with the…

Computational Finance · Quantitative Finance 2024-12-18 Max Mason , Waasi A Jagirdar , David Huang , Rahul Murugan

The Adam optimizer is widely used for transformer optimization in practice, which makes understanding the underlying optimization mechanisms an important problem. However, due to the Adam's complexity, theoretical analysis of how it…

Machine Learning · Computer Science 2025-03-04 Bingrui Li , Wei Huang , Andi Han , Zhanpeng Zhou , Taiji Suzuki , Jun Zhu , Jianfei Chen

Attention-based transformers have been remarkably successful at modeling generative processes across various domains and modalities. In this paper, we study the behavior of transformers on data drawn from \kth Markov processes, where the…

Machine Learning · Computer Science 2024-07-26 Nived Rajaraman , Marco Bondaschi , Kannan Ramchandran , Michael Gastpar , Ashok Vardhan Makkuva

While the Self-Attention mechanism in the Transformer model has proven to be effective in many domains, we observe that it is less effective in more diverse settings (e.g. multimodality) due to the varying granularity of each token and the…

Computer Vision and Pattern Recognition · Computer Science 2024-06-06 Wayner Barrios , SouYoung Jin

Autoregressive language models are next-token predictors and have been criticized for only optimizing surface plausibility (i.e., local coherence) rather than maintaining correct latent-state representations (i.e., global coherence).…

Computation and Language · Computer Science 2026-01-21 Xucong Hu , Jian-Qiao Zhu

Training large language models requires optimization algorithms that are not only statistically effective, but also computationally and memory efficient at extreme scale. Although Adam remains the dominant optimizer for large-scale…

Machine Learning · Computer Science 2026-05-12 Aditya Ranganath

Matrix-based preconditioned optimizers, such as Muon, have recently been shown to be more efficient than scalar-based optimizers for training large-scale neural networks, including large language models (LLMs). Recent benchmark studies of…

Machine Learning · Computer Science 2026-02-02 Yifeng Liu , Angela Yuan , Quanquan Gu

Prior methods propose to offset the escalating costs of modern foundation models by dropping specific parts of their contexts with hand-designed rules, while attempting to preserve their original performance. We overcome this trade-off with…

Machine Learning · Computer Science 2025-02-14 Edoardo Cetin , Qi Sun , Tianyu Zhao , Yujin Tang

Autoregressively trained transformers have brought a profound revolution to the world, especially with their in-context learning (ICL) ability to address downstream tasks. Recently, several studies suggest that transformers learn a…

Machine Learning · Computer Science 2024-10-29 Chenyu Zheng , Wei Huang , Rongzhen Wang , Guoqiang Wu , Jun Zhu , Chongxuan Li