# MoH: Multi-Head Attention as Mixture-of-Head Attention

arXiv: https://arxiv.org/abs/2410.11842 · HTML: https://mlsanity.com/paper/2410.11842/

## Key facts

- Cited by 44 papers in the map (data through 14 Oct 2026).
- Placed in Expert routing strategies, one of 12 directions in Mixture-of-experts.
- Builds on 88 of its 103 references that are in the map.
- First posted on arXiv 15 Oct 2024.

## Placed in

- Mixture-of-experts / [Expert routing strategies](https://mlsanity.com/moe/expert-routing-strategies/)

## Builds on (most cited first, 30 of 88)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [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)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)

## Built on by (most cited first, 30 of 44)

- [ImgEdit: A Unified Image Editing Dataset and Benchmark](https://mlsanity.com/paper/2505.20275/) (2025)
- [A Comprehensive Survey of Mixture-of-Experts: Algorithms, Theory, and Applications](https://mlsanity.com/paper/2503.07137/) (2025)
- [WISA: World Simulator Assistant for Physics-Aware Text-to-Video Generation](https://mlsanity.com/paper/2503.08153/) (2025)
- [A Survey on Inference Optimization Techniques for Mixture of Experts Models](https://mlsanity.com/paper/2412.14219/) (2024)
- [Mitigating Hallucinations in Vision-Language Models through Image-Guided Head Suppression](https://mlsanity.com/paper/2505.16411/) (2025)
- [DSV: Exploiting Dynamic Sparsity to Accelerate Large-Scale Video DiT Training](https://mlsanity.com/paper/2502.07590/) (2025)
- [Mixture of Sparse Attention: Content-Based Learnable Sparse Attention via Expert-Choice Routing](https://mlsanity.com/paper/2505.00315/) (2025)
- [PVChat: Personalized Video Chat with One-Shot Learning](https://mlsanity.com/paper/2503.17069/) (2025)
- [GMAR: Gradient-Driven Multi-Head Attention Rollout for Vision Transformer Interpretability](https://mlsanity.com/paper/2504.19414/) (2025)
- [Learning to Skip the Middle Layers of Transformers](https://mlsanity.com/paper/2506.21103/) (2025)
- [MISA: Mixture of Indexer Sparse Attention for Long-Context LLM Inference](https://mlsanity.com/paper/2605.07363/) (2026)
- [UMoE: Unifying Attention and FFN with Shared Experts](https://mlsanity.com/paper/2505.07260/) (2025)
- [Route Experts by Sequence, not by Token](https://mlsanity.com/paper/2511.06494/) (2025)
- [Raven: High-Recall Sequence Modeling with Sparse Memory Routing](https://mlsanity.com/paper/2607.25357/) (2026)
- [Sigmoid Self-Attention has Lower Sample Complexity than Softmax Self-Attention: A Mixture-of-Experts Perspective](https://mlsanity.com/paper/2502.00281/) (2025)
- [Safe-VAR: Safe Visual Autoregressive Model for Text-to-Image Generative Watermarking](https://mlsanity.com/paper/2503.11324/) (2025)
- [KV Admission: Learning What to Write for Efficient Long-Context LLM Inference](https://mlsanity.com/paper/2512.17452/) (2025)
- [HeadHunt-VAD: Hunting Robust Anomaly-Sensitive Heads in MLLM for Tuning-Free Video Anomaly Detection](https://mlsanity.com/paper/2512.17601/) (2025)
- [SynPO: Synergizing Descriptiveness and Preference Optimization for Video Detailed Captioning](https://mlsanity.com/paper/2506.00835/) (2025)
- [Adaptive Shared Experts with LoRA-Based Mixture of Experts for Multi-Task Learning](https://mlsanity.com/paper/2510.00570/) (2025)
- [Making Training-Free Diffusion Segmentors Scale with the Generative Power](https://mlsanity.com/paper/2603.06178/) (2026)
- [Sparse Growing Transformer: Training-Time Sparse Depth Allocation via Progressive Attention Looping](https://mlsanity.com/paper/2603.23998/) (2026)
- [Improving Reasoning Capabilities in Small Models through Mixture-of-Layers Distillation with Stepwise Attention on Key Information](https://mlsanity.com/paper/2604.15701/) (2026)
- [DoRAN: Stabilizing Weight-Decomposed Low-Rank Adaptation via Noise Injection and Auxiliary Networks](https://mlsanity.com/paper/2510.04331/) (2025)
- [A2-Edit: Precise Reference-Guided Image Editing of Arbitrary Objects and Ambiguous Masks](https://mlsanity.com/paper/2603.10685/) (2026)
- [Grouped Query Experts: Mixture-of-Experts on GQA Self-Attention](https://mlsanity.com/paper/2606.20945/) (2026)
- [LoSA-Net: A Localized and Scale-Adaptive Network for Boundary-Sensitive Prediction of Perineural Invasion in 3D MRI](https://mlsanity.com/paper/2607.10992/) (2026)
- [Mixture of Weight-shared Heterogeneous Group Attention Experts for Dynamic Token-wise KV Optimization](https://mlsanity.com/paper/2506.13541/) (2025)
- [Knocking-Heads Attention](https://mlsanity.com/paper/2510.23052/) (2025)
- [Improving MoE Compute Efficiency by Composing Weight and Data Sparsity](https://mlsanity.com/paper/2601.15370/) (2026)

## Abstract (arXiv)

In this work, we upgrade the multi-head attention mechanism, the core of the Transformer model, to improve efficiency while maintaining or surpassing the previous accuracy level. We show that multi-head attention can be expressed in the summation form. Drawing on the insight that not all attention heads hold equal significance, we propose Mixture-of-Head attention (MoH), a new architecture that treats attention heads as experts in the Mixture-of-Experts (MoE) mechanism. MoH has two significant advantages: First, MoH enables each token to select the appropriate attention heads, enhancing inference efficiency without compromising accuracy or increasing the number of parameters. Second, MoH replaces the standard summation in multi-head attention with a weighted summation, introducing flexibility to the attention mechanism and unlocking extra performance potential. Extensive experiments on ViT, DiT, and LLMs demonstrate that MoH outperforms multi-head attention by using only 50%-90% of the attention heads. Moreover, we demonstrate that pre-trained multi-head attention models, such as LLaMA3-8B, can be further continue-tuned into our MoH models. Notably, MoH-LLaMA3-8B achieves an average accuracy of 64.0% across 14 benchmarks, outperforming LLaMA3-8B by 2.4% by utilizing only 75% of the attention heads. We believe the proposed MoH is a promising alternative to multi-head attention and provides a strong foundation for developing advanced and efficient attention-based models.