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Mixture-of-experts (MoE) model incorporates the power of multiple submodels via gating functions to achieve greater performance in numerous regression and classification applications. From a theoretical perspective, while there have been…

Machine Learning · Statistics 2024-06-25 Huy Nguyen , Pedram Akbarian , TrungTin Nguyen , Nhat Ho

The softmax gating function is arguably the most popular choice in mixture of experts modeling. Despite its widespread use in practice, the softmax gating may lead to unnecessary competition among experts, potentially causing the…

Machine Learning · Statistics 2024-11-05 Huy Nguyen , Nhat Ho , Alessandro Rinaldo

Mixture of experts (MoE) has recently emerged as an effective framework to advance the efficiency and scalability of machine learning models by softly dividing complex tasks among multiple specialized sub-models termed experts. Central to…

Machine Learning · Statistics 2025-03-06 Huy Nguyen , Nhat Ho , Alessandro Rinaldo

With the growing prominence of the Mixture of Experts (MoE) architecture in developing large-scale foundation models, we investigate the Hierarchical Mixture of Experts (HMoE), a specialized variant of MoE that excels in handling complex…

Machine Learning · Statistics 2025-03-10 Huy Nguyen , Xing Han , Carl Harris , Suchi Saria , Nhat Ho

Mixture of experts (MoE) model is a statistical machine learning design that aggregates multiple expert networks using a softmax gating function in order to form a more intricate and expressive model. Despite being commonly used in several…

Machine Learning · Statistics 2024-06-25 Huy Nguyen , Nhat Ho , Alessandro Rinaldo

Dense-to-sparse gating mixture of experts (MoE) has recently become an effective alternative to a well-known sparse MoE. Rather than fixing the number of activated experts as in the latter model, which could limit the investigation of…

Machine Learning · Statistics 2024-06-25 Huy Nguyen , Pedram Akbarian , Nhat Ho

Mixture-of-Experts (MoE) architectures combine specialized predictors through a learned gate and are effective across regression and classification, but for classification with softmax multinomial-logistic gating, rigorous guarantees for…

Machine Learning · Statistics 2026-02-10 TrungKhang Tran , TrungTin Nguyen , Md Abul Bashar , Nhat Ho , Richi Nayak , Christopher Drovandi

Mixture of experts (MoE) methods are a key component in most large language model architectures, including the recent series of DeepSeek models. Compared to other MoE implementations, DeepSeekMoE stands out because of two unique features:…

Machine Learning · Computer Science 2026-02-03 Huy Nguyen , Thong T. Doan , Quang Pham , Nghi D. Q. Bui , Nhat Ho , Alessandro Rinaldo

The application of mixture-of-experts (MoE) is gaining popularity due to its ability to improve model's performance. In an MoE structure, the gate layer plays a significant role in distinguishing and routing input features to different…

Machine Learning · Computer Science 2024-02-05 Zhitian Xie , Yinger Zhang , Chenyi Zhuang , Qitao Shi , Zhining Liu , Jinjie Gu , Guannan Zhang

The softmax-contaminated mixture of experts (MoE) model is deployed when a large-scale pre-trained model, which plays the role of a fixed expert, is fine-tuned for learning downstream tasks by including a new contamination part, or prompt,…

Machine Learning · Statistics 2025-11-25 Fanqi Yan , Huy Nguyen , Dung Le , Pedram Akbarian , Nhat Ho , Alessandro Rinaldo

Mixture of experts (MoE), introduced over 20 years ago, is the simplest gated modular neural network architecture. There is renewed interest in MoE because the conditional computation allows only parts of the network to be used during each…

Machine Learning · Computer Science 2023-03-01 Yamuna Krishnamurthy , Chris Watkins , Thomas Gaertner

Understanding the parameter estimation of softmax gating Gaussian mixture of experts has remained a long-standing open problem in the literature. It is mainly due to three fundamental theoretical challenges associated with the softmax…

Machine Learning · Statistics 2023-10-31 Huy Nguyen , TrungTin Nguyen , Nhat Ho

Mixture of Experts (MoE) models are well known for effectively scaling model capacity while preserving computational overheads. In this paper, we establish a rigorous relation between MoE and the self-attention mechanism, showing that each…

Machine Learning · Statistics 2025-07-10 Pedram Akbarian , Huy Nguyen , Xing Han , Nhat Ho

We develop a unified statistical framework for softmax-gated Gaussian mixture of experts (SGMoE) that addresses three long-standing obstacles in parameter estimation and model selection: (i) non-identifiability of gating parameters up to…

Machine Learning · Statistics 2025-10-15 Do Tien Hai , Trung Nguyen Mai , TrungTin Nguyen , Nhat Ho , Binh T. Nguyen , Christopher Drovandi

Contaminated mixture of experts (MoE) is motivated by transfer learning methods where a pre-trained model, acting as a frozen expert, is integrated with an adapter model, functioning as a trainable expert, in order to learn a new task.…

Statistics Theory · Mathematics 2026-02-03 Fanqi Yan , Dung Le , Trang Pham , Huy Nguyen , Nhat Ho

Product search is the most common way for people to satisfy their shopping needs on e-commerce websites. Products are typically annotated with one of several broad categorical tags, such as "Clothing" or "Electronics", as well as…

Machine Learning · Computer Science 2021-03-03 Zhuojian Xiao , Yunjiang jiang , Guoyu Tang , Lin Liu , Sulong Xu , Yun Xiao , Weipeng Yan

Effectively managing missing modalities is a fundamental challenge in real-world multimodal learning scenarios, where data incompleteness often results from systematic collection errors or sensor failures. Sparse Mixture-of-Experts (SMoE)…

Machine Learning · Computer Science 2026-05-12 Liangwei Nathan Zheng , Wei Emma Zhang , Mingyu Guo , Olaf Maennel , Weitong Chen

The Mixture-of-Experts (MoE) model uses a set of expert networks that specialize on subsets of a dataset under the supervision of a gating network. A common issue in MoE architectures is ``expert collapse'' where overlapping class…

Neural and Evolutionary Computing · Computer Science 2026-03-31 Abien Fred Agarap , Arnulfo P. Azcarraga

In a distributed mixture-of-experts (MoE) system, a server collaborates with multiple specialized expert clients to perform inference. The server extracts features from input data and dynamically selects experts based on their areas of…

Machine Learning · Computer Science 2025-04-02 Qiuchen Song , Shusen Jing , Shuai Zhang , Songyang Zhang , Chuan Huang

Originally introduced as a neural network for ensemble learning, mixture of experts (MoE) has recently become a fundamental building block of highly successful modern deep neural networks for heterogeneous data analysis in several…

Machine Learning · Statistics 2024-02-12 Huy Nguyen , TrungTin Nguyen , Khai Nguyen , Nhat Ho
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