Graphs model latent variable relationships in many real-world systems, and Message Passing Neural Networks (MPNNs) are widely used to learn such structures for downstream tasks. While edge-based MPNNs effectively capture local interactions, their expressive power is theoretically bounded, limiting the discovery of higher-order relationships. We introduce the Higher-Order Graph Attention (HoGA) module, which constructs a k-order attention matrix by sampling subgraphs to maximize diversity among feature vectors. Unlike existing higher-order attention methods that greedily resample similar k-order relationships, HoGA targets diverse modalities in higher-order topology, reducing redundancy and expanding the range of captured substructures. Applied to two single-hop attention models, HoGA achieves at least a 5% accuracy gain on all benchmark node classification datasets and outperforms recent baselines on six of eight datasets. Code is available at https://github.com/TB862/Higher_Order.

Global Climate Models (GCMs) simulate low resolution climate projections on a global scale. The native resolution of GCMs is generally too low for societal-level decision-making. To enhance the spatial resolution, downscaling is often applied to GCM output. Statistical downscaling techniques, in particular, are well-established as a cost-effective approach. They require significantly less computational time than physics-based dynamical downscaling. In recent years, deep learning has gained prominence in statistical downscaling, demonstrating significantly lower error rates compared to traditional statistical methods. However, a drawback of regression-based deep learning techniques is their tendency to overfit to the mean sample intensity. Extreme values as a result are often underestimated. Problematically, extreme events have the largest societal impact. We propose Quantile-Regression-Ensemble (QRE), an innovative deep learning algorithm inspired by boosting methods. Its primary objective is to avoid trade-offs between fitting to sample means and extreme values by training independent models on a partitioned dataset. Our QRE is robust to redundant models and not susceptible to explosive ensemble weights, ensuring a reliable training process. QRE achieves lower Mean Squared Error (MSE) compared to various baseline models. In particular, our algorithm has a lower error for high-intensity precipitation events over New Zealand, highlighting the ability to represent extreme events accurately.