Large language models (LLMs) are impressive, but deploying them efficiently on various devices with different resource constraints is a huge challenge. Imagine an LLM that could instantly morph its internal structure to fit perfectly on anything from a powerful server to a tiny smartphone, maximizing performance without sacrificing accuracy. That’s the promise of AmoebaLLM, a groundbreaking new framework. Current methods for deploying LLMs involve compressing or pruning the model for each specific device, which is time-consuming and inefficient. AmoebaLLM takes a radically different approach. It trains a single LLM that can instantly generate smaller, specialized subnets tailored to any device's specific needs. Like an amoeba changing its shape, these subnets adapt their depth and width, achieving the ideal balance between accuracy and efficiency. The secret sauce lies in three key innovations: First, a clever subnet selection strategy preserves crucial knowledge from the original LLM during the shrinking process. This strategy uses dynamic programming to strategically retain essential layers and an importance-driven method to keep only the most impactful neurons, ensuring the smaller subnets don’t lose critical reasoning abilities. Second, AmoebaLLM introduces a novel adapter called SMoL (Shape-aware Mixture of LoRAs). This adapter is a collection of smaller modules that are selectively activated depending on the subnet's shape. This targeted activation minimizes conflicts between different subnets during training, leading to significantly improved performance. Once the optimal subnet is chosen for a specific device, the activated parts of SMoL can be merged directly into the subnet, making it even more efficient. Finally, AmoebaLLM uses a refined training objective that balances the contributions of different subnet shapes. This balancing act prevents smaller subnets from dominating the training process, which can hurt the performance of larger ones. This careful orchestration of training ensures that all subnets, regardless of size, reach their full potential. Extensive testing shows that AmoebaLLM produces subnets that outperform existing state-of-the-art compression methods, offering both superior accuracy and efficiency. Moreover, when used simply as a compression tool, it also achieves top results. AmoebaLLM represents a giant leap towards making powerful AI accessible everywhere, enabling a new wave of applications across a wide range of devices.