On Expert Estimation in Hierarchical Mixture of Experts: Beyond Softmax Gating Functions

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 inputs and improving performance on targeted tasks. Our investigation highlights the advantages of using varied gating functions, moving beyond softmax gating within HMoE frameworks. We theoretically demonstrate that applying tailored gating functions to each expert group allows HMoE to achieve robust results, even when optimal gating functions are applied only at select hierarchical levels. Empirical validation across diverse scenarios supports these theoretical claims. This includes large-scale multimodal tasks, image classification, and latent domain discovery and prediction tasks, where our modified HMoE models show great performance improvements.