Collaborative Inference and Learning between Edge SLMs and Cloud LLMs: A Survey of Algorithms, Execution, and Open Challenges

As large language models (LLMs) evolve, deploying them solely in the cloud or compressing them for edge devices is increasingly inadequate due to latency, privacy, cost, and personalization concerns. This survey examines a collaborative paradigm in which cloud-based LLMs and edge-deployed small language models (SLMs) cooperate for both inference and training. We propose a unified taxonomy of edge-cloud collaboration strategies. For inference, we categorize approaches into task assignment, task division, and mixture-based collaboration at both task- and token-levels, encompassing adaptive scheduling, resource-aware offloading, speculative decoding, and modular routing. For training, we review distributed adaptation techniques, including parameter alignment, pruning, bidirectional distillation, and small-model-guided optimization. We further summarize datasets, benchmarks, and deployment practices, and highlight privacy-preserving methods and vertical applications. This survey aims to establish a systematic foundation for LLM-SLM collaboration, bridging system-algorithm co-design toward efficient, scalable, and trustworthy edge-cloud intelligence.