arXiv:2611.10292v2 Announce Type: replace Abstract: Large language models (LLMs) are increasingly explored for resource management across the Cloud-Edge continuum. However, embedding LLMs directly inside latency-sensitive control loops places inference latency, execution jitter, and hallucination risks on the critical path. This study argues for a different use of LLMs: a continually instruction-tuned intent compiler that runs once per management intent or declared context change, above a fast, deterministic tactical controller that handles all low-latency runtime actions. We formulate intent compilation as a continual instruction tuning problem, because management intents arrive sequentially and accumulate while infrastructure and workload contexts drift. Unlike recent LLM-based management frameworks, our design scores the model's outputs by execution, so that catastrophic forgetting can be measured in the executed objective of the underlying controller. On a continuum simulator with a 2B backbone and parameter-efficient adapters, preliminary results show that naive sequential tuning forgets earlier intents in the executed objective, that replay of stored examples nearly prevents this forgetting, and that the tuned compact compiler performs on par with simpler translators while being more robust than a grammar parser to rephrased intents.