Task-specific LoRA adapters offer a modular way to specialize large language and vision-language models. However, existing adapter composition methods are mostly static and cannot adapt to individual test inputs. To address these issues, we propose LiST, a label-free test-time LoRA fusion framework that converts an existing LoRA bank into a target-conditioned local simplex and searches sample-specific fusion weights at inference time. LiST builds joint task representations from LoRA parameter anchors and prompt-level behavior vectors, retrieves neighboring adapters as a local search space, and performs branch-preserving fusion without updating the backbone or adapters. Candidate weights are selected by a prompt-level energy with prior, geometric, and stochastic-consistency constraints, and are deployed only when they pass a safe acceptance rule. Otherwise, LiST falls back to a target-conditioned prior. Experiments on multimodal and language benchmarks show that LiST outperforms static LoRA merging and conventional test-time adaptation baselines, while preserving task-specific adapter utility and improving robustness on unseen tasks.

Large language models (LLMs) exhibit substantial variability in performance and computational cost across tasks and queries, motivating routing systems that select models to meet user-specific cost–performance trade-offs. However, existing routers generalize poorly in cold-start scenarios where in-domain training data is unavailable. We address this limitation with a multi-level task-profile–guided data synthesis framework that constructs a hierarchical task taxonomy and produces diverse question–answer pairs to approximate the test-time query distribution. Building on this, we introduce TRouter, a task-type–aware router approach that models query-conditioned cost and performance via latent task-type variables, with prior regularization derived from the synthesized task taxonomy. This design enhances TRouter’s routing utility under both cold-start and in-domain settings. Across multiple benchmarks, we show that our synthesis framework alleviates cold-start issues and that TRouter delivers effective LLM routing.