无需训练数据和参数，用任务嵌入实现高效适配器路由。

Parameter-efficient fine-tuning (PEFT) has led to model ecosystems in which a single backbone is paired with many task-specialized adapters. Given such a library, routing aims to select the most appropriate adapter for a user query. While existing adapter routers typically require access to adapter weights or supervised training, we develop training-free semantic adapter routing methods using task embeddings. In ARIADNE, we reframe adapter selection as a classification problem, where PEFT adapters are represented by task embeddings and an unlabeled query is routed to the nearest adapter in the encoder's latent space. Evaluated on 23 tasks, ARIADNE recovers 97.4% of Oracle task performance and scales to 44 adapters at 89.7% selection accuracy, without touching a single adapter parameter. However, training data needed for ARIADNE may not be available when adapters come from public hubs or third-party providers. To overcome this limitation, we introduce GRACE, which recovers an adapter's fine-tuning data from its output logits alone via a modified contrastive decoding diffing (CDD) procedure. Synthetic data generated from CDD-UM is then used to construct task embeddings. Across three backbones (Llama-3.2-1B, Qwen2.5-3B, Qwen2.5-32B), GRACE recovers 72--100\% of Oracle task accuracy and matches or exceeds ARROW on 48 of 69 task/backbone combinations, while requiring neither training data nor model weights. Overall, we demonstrate that fine-tuning task embeddings provide an accurate and efficient path to semantic adapter routing.