# A Comprehensive Survey of Mixture-of-Experts: Algorithms, Theory, and Applications

arXiv: https://arxiv.org/abs/2503.07137 · HTML: https://mlsanity.com/paper/2503.07137/

## Key facts

- Cited by 91 papers in the map (data through 14 Oct 2026).
- Placed in MoE theory and gating functions, one of 12 directions in Mixture-of-experts.
- Builds on 114 of its 305 references that are in the map.
- First posted on arXiv 10 Mar 2025.

## Placed in

- Mixture-of-experts / [MoE theory and gating functions](https://mlsanity.com/moe/moe-theory-and-gating-functions/)

## Builds on (most cited first, 30 of 114)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translation](https://mlsanity.com/paper/1609.08144/) (2016)
- [No Language Left Behind: Scaling Human-Centered Machine Translation](https://mlsanity.com/paper/2207.04672/) (2022)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [Neural Architectures for Named Entity Recognition](https://mlsanity.com/paper/1603.01360/) (2016)
- [Towards a Human-like Open-Domain Chatbot](https://mlsanity.com/paper/2001.09977/) (2020)
- [Meta-Learning for Semi-Supervised Few-Shot Classification](https://mlsanity.com/paper/1803.00676/) (2018)
- [Jamba: A Hybrid Transformer-Mamba Language Model](https://mlsanity.com/paper/2403.19887/) (2024)
- [ST-MoE: Designing Stable and Transferable Sparse Expert Models](https://mlsanity.com/paper/2202.08906/) (2022)
- [A Neural Attention Model for Abstractive Sentence Summarization](https://mlsanity.com/paper/1509.00685/) (2015)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [Time-MoE: Billion-Scale Time Series Foundation Models with Mixture of Experts](https://mlsanity.com/paper/2409.16040/) (2024)
- [Learning Factored Representations in a Deep Mixture of Experts](https://mlsanity.com/paper/1312.4314/) (2013)

## Built on by (most cited first, 30 of 91)

- [Advancing Open-source World Models](https://mlsanity.com/paper/2601.20540/) (2026)
- [InstructVLA: Vision-Language-Action Instruction Tuning from Understanding to Manipulation](https://mlsanity.com/paper/2507.17520/) (2025)
- [Unveiling Super Experts in Mixture-of-Experts Large Language Models](https://mlsanity.com/paper/2507.23279/) (2025)
- [Mixture of Experts in Large Language Models](https://mlsanity.com/paper/2507.11181/) (2025)
- [MINGLE: Mixture of Null-Space Gated Low-Rank Experts for Test-Time Continual Model Merging](https://mlsanity.com/paper/2505.11883/) (2025)
- [Optimus-3: Dual-Router Aligned Mixture-of-Experts Agent with Dual-Granularity Reasoning-Aware Policy Optimization](https://mlsanity.com/paper/2506.10357/) (2025)
- [Sparse Models, Sparse Safety: Unsafe Routes in Mixture-of-Experts LLMs](https://mlsanity.com/paper/2602.08621/) (2026)
- [Unbiased Gradient Low-Rank Projection](https://mlsanity.com/paper/2510.17802/) (2025)
- [Steer2Adapt: Dynamically Composing Steering Vectors Elicits Efficient Adaptation of LLMs](https://mlsanity.com/paper/2602.07276/) (2026)
- [Can AI Truly Represent Your Voice in Deliberations? A Comprehensive Study of Large-Scale Opinion Aggregation with LLMs](https://mlsanity.com/paper/2510.05154/) (2025)
- [GEMINUS: Dual-aware Global and Scene-Adaptive Mixture-of-Experts for End-to-End Autonomous Driving](https://mlsanity.com/paper/2507.14456/) (2025)
- [The Unseen Frontier: Pushing the Limits of LLM Sparsity with Surrogate-Free ADMM](https://mlsanity.com/paper/2510.01650/) (2025)
- [A Reasoning-Enabled Vision-Language Foundation Model for Chest X-ray Interpretation](https://mlsanity.com/paper/2604.00493/) (2026)
- [φ-Balancing for Mixture-of-Experts Training](https://mlsanity.com/paper/2605.15403/) (2026)
- [Mixture-of-Shape-Experts (MoSE): End-to-End Shape Dictionary Framework to Prompt SAM for Generalizable Medical Segmentation](https://mlsanity.com/paper/2504.09601/) (2025)
- [On the Expressive Power of Mixture-of-Experts for Structured Complex Tasks](https://mlsanity.com/paper/2505.24205/) (2025)
- [AB-PINNs: Adaptive-Basis Physics-Informed Neural Networks for Residual-Driven Domain Decomposition](https://mlsanity.com/paper/2510.08924/) (2025)
- [Variational Inference, Entropy, and Orthogonality: A Unified Theory of Mixture-of-Experts](https://mlsanity.com/paper/2601.03577/) (2026)
- [Sparsity is Combinatorial Depth: Quantifying MoE Expressivity via Tropical Geometry](https://mlsanity.com/paper/2602.03204/) (2026)
- [Knowing When to Quit: Probabilistic Early Exits for Speech Separation](https://mlsanity.com/paper/2507.09768/) (2025)
- [A Mixture of Experts Gating Network for Enhanced Surrogate Modeling in External Aerodynamics](https://mlsanity.com/paper/2508.21249/) (2025)
- [One-Prompt Strikes Back: Sparse Mixture of Experts for Prompt-based Continual Learning](https://mlsanity.com/paper/2509.24483/) (2025)
- [REN: Anatomically-Informed Mixture-of-Experts for Interstitial Lung Disease Diagnosis](https://mlsanity.com/paper/2510.04923/) (2025)
- [Sparsity and Superposition in Mixture of Experts](https://mlsanity.com/paper/2510.23671/) (2025)
- [Metacognitive Sensitivity for Test-Time Dynamic Model Selection](https://mlsanity.com/paper/2512.10451/) (2025)
- [RepetitionCurse: Measuring and Understanding Router Imbalance in Mixture-of-Experts LLMs under DoS Stress](https://mlsanity.com/paper/2512.23995/) (2025)
- [The Rise of Sparse Mixture-of-Experts: A Survey from Algorithmic Foundations to Decentralized Architectures and Vertical Domain Applications](https://mlsanity.com/paper/2602.08019/) (2026)
- [Minimizing Modality Gap from the Input Side: Your Speech LLM Can Be a Prosody-Aware Text LLM](https://mlsanity.com/paper/2605.05927/) (2026)
- [Bridging the Detection-to-Abstention Gap in Reasoning Models under Insufficient Information](https://mlsanity.com/paper/2605.28070/) (2026)
- [Harnessing Routing Foresight for Micro-step-level MoE load balancing in RL Post-training](https://mlsanity.com/paper/2606.11867/) (2026)

## Abstract (arXiv)

Artificial intelligence (AI) has achieved astonishing successes in many domains, especially with the recent breakthroughs in the development of foundational large models. These large models, leveraging their extensive training data, provide versatile solutions for a wide range of downstream tasks. However, as modern datasets become increasingly diverse and complex, the development of large AI models faces two major challenges: (1) the enormous consumption of computational resources and deployment difficulties, and (2) the difficulty in fitting heterogeneous and complex data, which limits the usability of the models. Mixture of Experts (MoE) models has recently attracted much attention in addressing these challenges, by dynamically selecting and activating the most relevant sub-models to process input data. It has been shown that MoEs can significantly improve model performance and efficiency with fewer resources, particularly excelling in handling large-scale, multimodal data. Given the tremendous potential MoE has demonstrated across various domains, it is urgent to provide a comprehensive summary of recent advancements of MoEs in many important fields. Existing surveys on MoE have their limitations, e.g., being outdated or lacking discussion on certain key areas, and we aim to address these gaps. In this paper, we first introduce the basic design of MoE, including gating functions, expert networks, routing mechanisms, training strategies, and system design. We then explore the algorithm design of MoE in important machine learning paradigms such as continual learning, meta-learning, multi-task learning, and reinforcement learning. Additionally, we summarize theoretical studies aimed at understanding MoE and review its applications in computer vision and natural language processing. Finally, we discuss promising future research directions.