arXiv:2610.28638v1 Announce Type: new Abstract: As urban residents demand higher-quality instant delivery services, demand forecasting, estimated time of arrival prediction, and next-stop prediction have become critical tasks in urban delivery systems. However, the three tasks rely on historical evidence with substantially different structures and granularities. Meanwhile, their prediction targets differ in output form, making it difficult to integrate retrieved evidence through a single fusion mechanism without causing mismatch or negative transfer. These issues can increase prediction errors and subsequently lead to imbalanced resource allocation, where some regions experience unmet demand. In contrast, others suffer from underutilization, ultimately degrading overall efficiency and service quality. To address these challenges, we propose TAGR, a Task-Adaptive Geo-Semantic Retrieval framework across heterogeneous urban delivery tasks. TAGR constructs an LLM-based geo-semantic shared prior and task-specific retrieval banks to share regional knowledge while preserving heterogeneous task-specific evidence. The LLM-derived regional representations encode geographic context and semantic relations among regions, providing transferable knowledge for all three tasks without requiring online LLM inference. It further introduces a task-adaptive retrieval augmentation module to accommodate heterogeneous output structures, thereby mitigating information mismatch and negative transfer caused by a uniform retrieval-fusion strategy. Experiments on three city datasets demonstrate that TAGR consistently outperforms state-of-the-art baselines across multiple tasks.