Bridge: Retrieval-Augmented Spatiotemporal Modeling for Urban Delivery Demand

Accurate station-level demand forecasting is essential for the efficient operation of bike-sharing systems, yet it remains challenging due to complex spatio-temporal dependencies and the large scale of urban networks. This paper presents STAGformer, a Spatio-Temporal Agent Graph Transformer that achieves efficient global modeling with linear computational complexity. The model introduces a two-step agent attention mechanism, where a small set of learnable spatial and temporal agent tokens first aggregate global information and then broadcast it back to individual stations and time steps, effectively capturing long-range interactions while reducing the quadratic cost of standard self-attention to O(NT). STAGformer integrates four core modules: a spatio-temporal encoder that fuses dynamic node features with external contextual factors (weather, time, points of interest), a graph propagation module for spatial neighbor aggregation, a temporal convolution module for local pattern extraction, and the agent attention module for global dependency modeling. Extensive experiments on two real-world datasets -- NYC Citi-Bike and Chicago Divvy-Bike -- demonstrate that STAGformer consistently outperforms state-of-the-art baselines across multiple prediction horizons, achieving significant improvements in both RMSE and MAE. Ablation studies validate the contribution of each component, with the agent attention mechanism proving critical for modeling global spatio-temporal dependencies.

Accurate spatiotemporal pattern analysis is critical in fields such as urban traffic, meteorology, and public health monitoring. However, existing methods face performance bottlenecks, typically yielding only incremental gains and often exhibiting limited cross-domain transferability. We analyze this bottleneck through spatial and temporal entropy measures, which are used as diagnostic indicators of spatiotemporal complexity mismatch rather than as guarantees that entropy alignment alone yields better forecasting. Empirically, larger mismatch is often accompanied by higher prediction uncertainty, especially under a fixed model-capacity budget. Guided by this diagnostic, we propose a scalable, adaptive framework that harmonizes spatial and temporal feature representations. Spatial dimensionality is compressed via low-rank matrix embedding to preserve essential structure, while an extended temporal horizon captures long-range dependencies and mitigates cumulative errors arising from temporal heterogeneity. Extensive experiments on urban traffic, meteorological, and epidemic datasets demonstrate substantial accuracy gains and broad applicability across the evaluated domains, suggesting that the framework is promising for a wide range of spatiotemporal tasks beyond the current study. The code is available on GitHub at https://github.com/ST-Balance/ST-Balance.

Urban traffic forecasting often relies on information distributed across stakeholders who may be unable to share raw data due to privacy or commercial constraints, motivating federated spatial-temporal approaches. In such federated settings, each client observes traffic over a distinct sensor subgraph with its own spatial topology and temporal dynamics, leading to significant heterogeneity across clients. Existing federated spatial-temporal methods typically rely on model parameter aggregation and provide limited mechanisms for recovering spatial dependencies across client boundaries. This introduces two key limitations. Specifically, parameter aggregation across heterogeneous graph domains tends to dilute client-specific representations, while road network partitioning breaks the propagation of traffic dynamics across client boundaries. To address these challenges, we propose FedeRICo, a federated traffic forecasting framework that combines gradient-level collaboration with boundary-aware residual communication. FedeRICo employs a dual-branch forecasting architecture in which a globally guided branch captures transferable forecasting structure, while a private residual branch preserves client-specific corrections and incorporates boundary residual signals. The global branch is coordinated through gradient alignment across all clients, enabling collaborative optimisation without destructive parameter interference. To recover cross-client spatial dependencies, boundary messages are extracted through a trend-residual decomposition that suppresses periodic structure and communicates only transient spatial-temporal residual signals between physically adjacent clients. Experiments across four real-world traffic forecasting benchmarks demonstrate that FedeRICo consistently outperforms state-of-the-art federated spatial-temporal baselines while maintaining competitive training runtime.