Sparse Mixture-of-Experts (SMoE) models represent a significant breakthrough in large language model development. These models enable performance improvements without a proportional increase in inference costs. By selectively activating a small set of parameters during task execution, SMoEs enhance model capacity. However, their deployment remains challenging due to the substantial memory footprint required to accommodate the growing number of experts. To address this challenge, we propose Hierarchical Clustering for Sparsely activated Mixture of Experts (HC-SMoE), a task-agnostic expert merging framework that reduces SMoE model parameters without retraining. Unlike previous methods, HC-SMoE employs hierarchical clustering based on expert outputs. This approach ensures that the merging process remains unaffected by routing decisions. We validate our approach through extensive experiments on eight zero-shot language tasks and demonstrate its effectiveness in large-scale SMoE models such as Qwen and Mixtral. Our comprehensive results demonstrate that HC-SMoE consistently achieves strong performance, which highlights its potential for real-world deployment. The exponential growth in model parameters for Transformer-based architectures in natural language processing (NLP) has led to significant performance improvements across various tasks (Chowdhery et al., 2022; OpenAI et al., 2024; Team et al., 2024). Nevertheless, this increase in size has resulted in challenges for real-world deployment and accessibility due to heightened inference latency and computational requirements (Bommasani et al., 2022) Sparsely activated Mixture of Experts (SMoE) models have emerged as a promising solution to this challenge.

In this paper, we introduce a new concept of incorporating factorized flow maps as mid-level representations, for bridging the perception and the control modules in modular learning based robotic frameworks. To investigate the advantages of factorized flow maps and examine their interplay with the other types of mid-level representations, we further develop a configurable framework, along with four different environments that contain both static and dynamic objects, for analyzing the impacts of factorized optical flow maps on the performance of deep reinforcement learning agents. Based on this framework, we report our experimental results on various scenarios, and offer a set of analyses to justify our hypothesis. Finally, we validate flow factorization in real world scenarios.