让弱模型在线学习强模型的解题思路，提升效率与准确率。

Standard LLM cascades improve efficiency by deferring difficult queries from weak to strong models. However, these systems are typically static: when faced with repeated or semantically similar queries, they redundantly consult the expensive model, failing to adapt during inference. To address this, we propose Inter-Cascade, an online, interactive framework that transforms the strong model from a temporary helper into a long-term teacher. In our approach, when the strong model resolves a deferred query, it generates a generalized, reusable problem-solving strategy. These strategies are stored in a dynamic repository and retrieved via similarity matching to augment the weak model's context for future queries. This enables the weak model to learn on the job without expensive parameter fine-tuning. We theoretically show that this mechanism improves the weak model's confidence calibration. Empirically, Inter-Cascade outperforms standard cascades on multiple benchmarks, improving weak model and overall system accuracy by up to 33.06 percent and 6.35 percent, while reducing strong model calls by up to 48.05 percent and saving fee by up to 49.63 percent. Inter-Cascade demonstrates effective in-context knowledge transfer between LLMs and provides a general, scalable framework applicable to both open-source and API-based LLMs.