Mixture-of-Experts (MoE) based large language models (LLMs) have gained popularity due to their multi-task capability, where each input token activates only a subset of "expert" subnetworks. However, whether each expert can truly specialize to a certain task remains poorly understood, while activation analysis shows frequent cross-layer co-activation of experts for the same input, resembling a collaborative behavior. In this paper, we use a dictionary learning approach to show that experts in MoE LLMs form hierarchical and semantically coherent collaborative groups that correspond to specific linguistic and cognitive functions (e.g., mathematical reasoning, syntactic processing), mirroring specialized functional region observed in neuroscience. Furthermore, leveraging these discovered expert groups enables significant model compression with minimal performance degradation, outperforming existing methods by 2.5% while enabling up to 50% expert reduction. These findings provide the first systematic analysis of expert collaboration mechanisms in MoE LLMs, revealing that specialization emerges from joint activation of experts across all layers. We further developed an interactive visualization platform that enables researchers to explore expert collaboration patterns and their semantic associations.