DRAN: A Distribution and Relation Adaptive Network for Spatio-temporal Forecasting

Distribution shift severely degrades the performance of deep forecasting models. While this issue is well-studied for individual time series, it remains a significant challenge in the spatio-temporal domain. Effective solutions like instance normalization and its variants can mitigate temporal shifts by standardizing statistics. However, distribution shift on a graph is far more complex, involving not only the drift of individual node series but also heterogeneity across the spatial network where different nodes exhibit distinct statistical properties. To tackle this problem, we propose Reversible Residual Normalization (RRN), a novel framework that performs spatially-aware invertible transformations to address distribution shift in both spatial and temporal dimensions. Our approach integrates graph convolutional operations within invertible residual blocks, enabling adaptive normalization that respects the underlying graph structure while maintaining reversibility. By combining Center Normalization with spectral-constrained graph neural networks, our method captures and normalizes complex Spatio-Temporal relationships in a data-driven manner. The bidirectional nature of our framework allows models to learn in a normalized latent space and recover original distributional properties through inverse transformation, offering a robust and model-agnostic solution for forecasting on dynamic spatio-temporal systems.

Spatial-temporal (ST) forecasting underpins many real-world systems such as traffic, climate, and energy networks. While existing methods implicitly assume strong spatiotemporal coupling, we observe that real-world ST data exhibits distinct coupling regimes, ranging from temporal-dominated and spatial-dominated to strongly coupled patterns. This mismatch causes current models to suffer from spurious dependencies and degraded performance when one correlation dominates. To overcome this limitation, we aim to dynamically modulate spatial and temporal modeling based on the data's inherent coupling structure. However, three key challenges exist: unknown coupling structure, heterogeneous coupling dynamics, and suboptimal spatial modeling. We propose AdaST, an adaptive ST forecasting framework that tackles these challenges through a decompose-recompose paradigm. AdaST factorizes inputs into components capturing different coupling patterns using heterogeneity-aware experts. Each component is processed by role-aligned modules, and a correlation-informed adaptive recomposer integrates them for final prediction. Extensive experiments confirm that AdaST significantly outperforms state-of-the-art baselines, validating the necessity of an adaptive approach.

Real-world traffic data exhibit heterogeneous spatial correlations and nonlinear temporal dynamics, posing substantial challenges for accurate spatio-temporal forecasting. Existing approaches have developed increasingly sophisticated graph, attention, and decomposition architectures, while the influence of the underlying nonlinear function approximator has received comparatively less attention. In this work, we propose STKAN, a spatio-temporal forecasting architecture that introduces Taylor-polynomial Kolmogorov--Arnold Network modules into spatial and temporal token mixing. STKAN first constructs high-level spatial representations through a learnable soft node-group assignment mechanism, applies group-wise spatial mixing, and subsequently models temporal dependencies over the compressed sequence. Spatial and temporal self-attention layers are further employed to capture long-range interactions. Experiments on five traffic forecasting benchmarks show that STKAN achieves competitive performance and performs better than the evaluated MLP-based variant in the tested settings. These results suggest that the design of nonlinear function approximators can serve as a useful complement to architectural design in spatio-temporal forecasting.