Large language models (LLMs) like Mixtral have revolutionized how we interact with AI, exhibiting remarkable abilities in understanding and generating human-like text. However, their massive size presents a challenge, especially for deployment on resource-constrained devices. Mixture-of-Experts (MoE) models offer a clever solution, activating only specific parts of the model for a given task. Think of it like having a team of specialists, each an expert in a different domain, called upon only when their expertise is required. This specialization allows LLMs to scale while keeping computational costs in check. However, MoE introduces a new bottleneck: the on-demand loading of these expert modules. Imagine needing to call in a specific expert, but they're not readily available—it creates a delay, impacting overall performance. AdapMoE, a new algorithm-system co-design framework, tackles this challenge head-on. It introduces a system of adaptive 'gating,' dynamically adjusting the number of experts needed for each task. This approach reduces the overhead of loading experts, much like optimizing a team's workflow to avoid unnecessary calls. AdapMoE also employs a predictive prefetching technique, anticipating which experts will be required for upcoming tasks. This foresight further minimizes delays, analogous to having the right experts on standby, ready to contribute when needed. Furthermore, AdapMoE introduces adaptive caching, intelligently managing which experts are stored in readily accessible memory. Combined, these innovations lead to significant performance improvements, reducing the number of active experts by 25% and delivering a 1.35x speed boost. AdapMoE represents a leap forward in making powerful LLMs accessible on a wider range of devices, opening doors to more efficient and seamless AI interactions. The research points towards a future where AI is readily available, responding to our needs with speed and intelligence, regardless of the device we use.