# Mixture of Group Experts for Learning Invariant Representations

arXiv: https://arxiv.org/abs/2504.09265 · HTML: https://mlsanity.com/paper/2504.09265/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Vision mixture-of-experts, one of 12 directions in Mixture-of-experts.
- Builds on 33 of its 53 references that are in the map.
- First posted on arXiv 12 Apr 2025.

## Placed in

- Mixture-of-experts / [Vision mixture-of-experts](https://mlsanity.com/moe/vision-mixture-of-experts/)

## Builds on (most cited first, 30 of 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Pyramid Vision Transformer: A Versatile Backbone for Dense Prediction without Convolutions](https://mlsanity.com/paper/2102.12122/) (2021)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [Swin Transformer V2: Scaling Up Capacity and Resolution](https://mlsanity.com/paper/2111.09883/) (2021)
- [Scaling Vision with Sparse Mixture of Experts](https://mlsanity.com/paper/2106.05974/) (2021)
- [Mixture-of-Experts with Expert Choice Routing](https://mlsanity.com/paper/2202.09368/) (2022)
- [Sparse Upcycling: Training Mixture-of-Experts from Dense Checkpoints](https://mlsanity.com/paper/2212.05055/) (2022)
- [Tutel: Adaptive Mixture-of-Experts at Scale](https://mlsanity.com/paper/2206.03382/) (2022)
- [Vision Transformer for Small-Size Datasets](https://mlsanity.com/paper/2112.13492/) (2021)
- [Mixture of Cluster-conditional LoRA Experts for Vision-language Instruction Tuning](https://mlsanity.com/paper/2312.12379/) (2023)
- [A Unified Theory of Diversity in Ensemble Learning](https://mlsanity.com/paper/2301.03962/) (2023)
- [Multi-Task Dense Prediction via Mixture of Low-Rank Experts](https://mlsanity.com/paper/2403.17749/) (2024)
- [Straight to Zero: Why Linearly Decaying the Learning Rate to Zero Works Best for LLMs](https://mlsanity.com/paper/2502.15938/) (2025)
- [SwitchHead: Accelerating Transformers with Mixture-of-Experts Attention](https://mlsanity.com/paper/2312.07987/) (2023)
- [HMoE: Heterogeneous Mixture of Experts for Language Modeling](https://mlsanity.com/paper/2408.10681/) (2024)
- [Drop-Upcycling: Training Sparse Mixture of Experts with Partial Re-initialization](https://mlsanity.com/paper/2502.19261/) (2025)
- [Heterogeneous Multi-task Learning with Expert Diversity](https://mlsanity.com/paper/2106.10595/) (2021)
- [OMoE: Diversifying Mixture of Low-Rank Adaptation by Orthogonal Finetuning](https://mlsanity.com/paper/2501.10062/) (2025)
- [Experts Weights Averaging: A New General Training Scheme for Vision Transformers](https://mlsanity.com/paper/2308.06093/) (2023)
- [Mixture of Experts in Image Classification: What's the Sweet Spot?](https://mlsanity.com/paper/2411.18322/) (2024)

## Built on by (most cited first, 1 of 1)

- [LAR-MoE: Latent-Aligned Routing for Mixture of Experts in Robotic Imitation Learning](https://mlsanity.com/paper/2603.08476/) (2026)

## Abstract (arXiv)

Sparsely activated Mixture-of-Experts (MoE) models effectively increase the number of parameters while maintaining consistent computational costs per token. However, vanilla MoE models often suffer from limited diversity and specialization among experts, constraining their performance and scalability, especially as the number of experts increases. In this paper, we present a novel perspective on vanilla MoE with top-k routing inspired by sparse representation. This allows us to bridge established theoretical insights from sparse representation into MoE models. Building on this foundation, we propose a group sparse regularization approach for the input of top-k routing, termed Mixture of Group Experts (MoGE). MoGE indirectly regularizes experts by imposing structural constraints on the routing inputs, while preserving the original MoE architecture. Furthermore, we organize the routing input into a 2D topographic map, spatially grouping neighboring elements. This structure enables MoGE to capture representations invariant to minor transformations, thereby significantly enhancing expert diversity and specialization. Comprehensive evaluations across various Transformer models for image classification and language modeling tasks demonstrate that MoGE substantially outperforms its MoE counterpart, with minimal additional memory and computation overhead. Our approach provides a simple yet effective solution to scale the number of experts and reduce redundancy among them. The source code is included in the supplementary material and will be publicly released.