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Selecting a layer normalization (LN) strategy that stabilizes training and speeds convergence in Transformers remains difficult, even for today's large language models (LLM). We present a comprehensive analytical foundation for…

Despite their widespread use, training deep Transformers can be unstable. Layer normalization, a standard component, improves training stability, but its placement has often been ad-hoc. In this paper, we conduct a principled study on the…

Machine Learning · Computer Science 2025-10-14 Kelvin Kan , Xingjian Li , Benjamin J. Zhang , Tuhin Sahai , Stanley Osher , Krishna Kumar , Markos A. Katsoulakis

Transformer networks have become the preferred architecture for many tasks due to their state-of-the-art performance. However, the optimal way to implement residual connections in Transformer, which are essential for effective training, is…

Computation and Language · Computer Science 2023-05-01 Shufang Xie , Huishuai Zhang , Junliang Guo , Xu Tan , Jiang Bian , Hany Hassan Awadalla , Arul Menezes , Tao Qin , Rui Yan

Large language model (LLM) scaling is hitting a wall. Widening models yields diminishing returns, and extending context length does not improve fundamental expressivity. In contrast, depth scaling offers theoretically superior expressivity,…

Machine Learning · Computer Science 2026-02-02 Chen Chen , Lai Wei

Large Language Models (LLMs) have achieved remarkable success, yet recent findings reveal that their deeper layers often contribute minimally and can be pruned without affecting overall performance. While some view this as an opportunity…

Machine Learning · Computer Science 2025-08-05 Pengxiang Li , Lu Yin , Shiwei Liu

The success of Large Language Models (LLMs) hinges on the stable training of deep Transformer architectures. A critical design choice is the placement of normalization layers, leading to a fundamental trade-off: the ``PreNorm'' architecture…

Computation and Language · Computer Science 2026-02-02 Chao Wang , Bei Li , Jiaqi Zhang , Xinyu Liu , Yuchun Fan , Linkun Lyu , Xin Chen , Jingang Wang , Tong Xiao , Peng Pei , Xunliang Cai

In this paper, we propose a simple yet effective method to stabilize extremely deep Transformers. Specifically, we introduce a new normalization function (DeepNorm) to modify the residual connection in Transformer, accompanying with…

Computation and Language · Computer Science 2022-03-02 Hongyu Wang , Shuming Ma , Li Dong , Shaohan Huang , Dongdong Zhang , Furu Wei

The Transformer is widely used in natural language processing tasks. To train a Transformer however, one usually needs a carefully designed learning rate warm-up stage, which is shown to be crucial to the final performance but will slow…

Machine Learning · Computer Science 2020-06-30 Ruibin Xiong , Yunchang Yang , Di He , Kai Zheng , Shuxin Zheng , Chen Xing , Huishuai Zhang , Yanyan Lan , Liwei Wang , Tie-Yan Liu

Pre-Layer Normalization (Pre-LN) is the de facto choice for large language models (LLMs) and is crucial for stable pretraining and effective transfer learning. However, Pre-LN is inefficient due to repeated statistical calculations and…

Computation and Language · Computer Science 2026-02-04 Hoyoon Byun , Youngjun Choi , Taero Kim , Sungrae Park , Kyungwoo Song

Despite their impressive performance, contemporary neural networks often lack structural safeguards that promote stable learning and interpretable behavior. In this work, we introduce a reformulation of layer-level transformations that…

Machine Learning · Computer Science 2025-08-04 Saleh Nikooroo , Thomas Engel

LLM post-training typically propagates task gradients through the full depth of the model. Although this end-to-end structure is simple and general, it couples task adaptation to full-depth activation storage, long-range backward…

Computation and Language · Computer Science 2026-05-11 Hengyu Shi , Tianyang Han , Peizhe Wang , Zhiling Wang , Xu Yang , Junhao Su

In spite of their huge success, transformer models remain difficult to scale in depth. In this work, we develop a unified signal propagation theory and provide formulae that govern the moments of the forward and backward signal through the…

Computation and Language · Computer Science 2024-07-19 Akhil Kedia , Mohd Abbas Zaidi , Sushil Khyalia , Jungho Jung , Harshith Goka , Haejun Lee

Transformers have become the de facto architecture for a wide range of machine learning tasks, particularly in large language models (LLMs). Despite their remarkable performance, many challenges remain in training deep transformer networks,…

Computation and Language · Computer Science 2025-12-09 Zhijian Zhuo , Yutao Zeng , Ya Wang , Sijun Zhang , Jian Yang , Xiaoqing Li , Xun Zhou , Jinwen Ma

Scaling deep reinforcement learning networks is challenging and often results in degraded performance, yet the root causes of this failure mode remain poorly understood. Several recent works have proposed mechanisms to address this, but…

A big convergence of model architectures across language, vision, speech, and multimodal is emerging. However, under the same name "Transformers", the above areas use different implementations for better performance, e.g., Post-LayerNorm…

Selective layer-wise updates are essential for low-cost continued pre-training of Large Language Models (LLMs), yet determining which layers to freeze or train remains an empirical black-box problem due to the lack of interpretable…

Computation and Language · Computer Science 2026-05-25 Yu-Hang Wu , Qin-Yuan Liu , Qiu-Yang Zhao , Bo Jiang , Jiang-Feng Yang , Qing-Wei Cong

We present a new training methodology for transformers using a multilevel, layer-parallel approach. Through a neural ODE formulation of transformers, our application of a multilevel parallel-in-time algorithm for the forward and…

Machine Learning · Computer Science 2026-01-27 Shuai Jiang , Marc Salvadó-Benasco , Eric C. Cyr , Alena Kopaničáková , Rolf Krause , Jacob B. Schroder

We study Latent Recurrent Transformer (LRT), a lightweight augmentation of autoregressive transformers that reuses a high-level source-layer hidden state from the previous token as recurrent memory for the next token. Because this source…

Understanding whether deep neural networks are effectively optimized remains challenging, as training occurs in highly nonconvex landscapes and standard metrics provide limited visibility into layer-wise learning quality. This challenge is…

Machine Learning · Computer Science 2026-05-05 Arian Eamaz , Farhang Yeganegi , Mojtaba Soltanalian

Teams that have trained large Transformer-based models have reported training instabilities at large scale that did not appear when training with the same hyperparameters at smaller scales. Although the causes of such instabilities are of…

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