Conditional independence (CI) is central to causal inference, feature selection, and graphical modeling, yet it is untestable in many settings without additional assumptions. Existing CI tests often rely on restrictive structural conditions, limiting their validity on real-world data. Kernel methods using the partial covariance operator offer a more principled approach but suffer from limited adaptivity, slow convergence, and poor scalability. In this work, we explore whether representation learning can help address these limitations. Specifically, we focus on representations derived from the singular value decomposition of the partial covariance operator and use them to construct a simple test statistic, reminiscent of the Hilbert-Schmidt Independence Criterion (HSIC). We also introduce a practical bi-level contrastive algorithm to learn these representations. Our theory links representation learning error to test performance and establishes asymptotic validity and power guarantees. Preliminary experiments suggest that this approach offers a practical and statistically grounded path toward scalable CI testing, bridging kernel-based theory with modern representation learning.

In this paper, we propose a novel Spatial Balance Attention block for spatiotemporal forecasting. To strike a balance between obeying spatial proximity and capturing global correlation, we partition the spatial graph into a set of subgraphs and instantiate Intra-subgraph Attention to learn local spatial correlation within each subgraph; to capture the global spatial correlation, we further aggregate the nodes to produce subgraph representations and achieve message passing among the subgraphs via Inter-subgraph Attention. Building on the proposed Spatial Balance Attention block, we develop a multiscale spatiotemporal forecasting model by progressively increasing the subgraph scales. The resulting model is both scalable and able to produce structured spatial correlation, and meanwhile, it is easy to implement. We evaluate its efficacy and efficiency against the existing models on real-world spatiotemporal datasets from medium to large sizes. The experimental results show that it can achieve performance improvements up to 7.7% over the baseline methods at low running costs.