Mixture of Group Experts for Learning Invariant Representations

Abstract

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.