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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

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

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

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

The sigmoid gate in mixture-of-experts (MoE) models has been empirically shown to outperform the softmax gate across several tasks, ranging from approximating feed-forward networks to language modeling. Additionally, recent efforts have…

Machine Learning · Statistics 2026-02-03 Tuan Minh Pham , Thinh Cao , Viet Nguyen , Huy Nguyen , Nhat Ho , Alessandro Rinaldo

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

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 models provide a flexible framework for learning complex probabilistic input-output relationships by combining multiple expert models through an input-dependent gating mechanism. These models have become increasingly…

Machine Learning · Statistics 2026-04-23 Nicola Bariletto , 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

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

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) models constitute a widely utilized class of ensemble learning approaches in statistics and machine learning, known for their flexibility and computational efficiency. They have become integral components in…

Machine Learning · Statistics 2025-05-26 Tuan Thai , TrungTin Nguyen , Dat Do , Nhat Ho , Christopher Drovandi

Mixture-of-Experts (MoE) is a flexible framework that combines multiple specialized submodels (``experts''), by assigning covariate-dependent weights (``gating functions'') to each expert, and have been commonly used for analyzing…

Methodology · Statistics 2026-01-06 Qicheng Zhao , Celia M. T. Greenwood , Qihuang Zhang

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

Mixture-of-Experts (MoE) architectures decompose prediction tasks into specialized expert sub-networks selected by a gating mechanism. This letter adopts a communication-theoretic view of MoE gating, modeling the gate as a stochastic…

Machine Learning · Statistics 2026-03-27 Ali Khalesi , Mohammad Reza Deylam Salehi

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

Top-K sparse softmax gating mixture of experts has been widely used for scaling up massive deep-learning architectures without increasing the computational cost. Despite its popularity in real-world applications, the theoretical…

Machine Learning · Statistics 2024-02-27 Huy Nguyen , Pedram Akbarian , Fanqi Yan , Nhat Ho

The traditional viewpoint on Sparse Mixture of Experts (MoE) models is that instead of training a single large expert, which is computationally expensive, we can train many small experts. The hope is that if the total parameter count of the…

Machine Learning · Computer Science 2024-09-04 Youngseog Chung , Dhruv Malik , Jeff Schneider , Yuanzhi Li , Aarti Singh

As machine learning models in critical fields increasingly grapple with multimodal data, they face the dual challenges of handling a wide array of modalities, often incomplete due to missing elements, and the temporal irregularity and…

Machine Learning · Computer Science 2025-04-10 Xing Han , Huy Nguyen , Carl Harris , Nhat Ho , Suchi Saria

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
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