Although data that can be naturally represented as graphs is widespread in realworld applications across diverse industries, popular graph ML benchmarks for node property prediction only cover a surprisingly narrow set of data domains, and graph neural networks (GNNs) are often evaluated on just a few academic citation networks. This issue is particularly pressing in light of the recent growing interest in designing graph foundation models. These models are supposed to be able to transfer to diverse graph datasets from different domains, and yet the proposed graph foundation models are often evaluated on a very limited set of datasets from narrow applications. To alleviate this issue, we introduce GraphLand: a benchmark of 14 diverse graph datasets for node property prediction from a range of different industrial applications. GraphLand allows evaluating graph ML models on a wide range of graphs with diverse sizes, structural characteristics, and feature sets, all in a unified setting. Further, GraphLand allows investigating such previously underexplored research questions as how realistic temporal distributional shifts under transductive and inductive settings influence graph ML model performance. To mimic realistic industrial settings, we use GraphLand to compare GNNs with gradient-boosted decision trees (GBDT) models that are popular in industrial applications and show that GBDTs provided with additional graph-based input features can sometimes be very strong baselines. Further, we evaluate current general-purpose graph foundation models and find that they fail to produce competitive results on our proposed datasets.

Optimal transport between graphs, based on Gromov-Wasserstein and other extensions, is a powerful tool for comparing and aligning graph structures. However, solving the associated non-convex optimization problems is computationally expensive, which limits the scalability of these methods to large graphs. In this work, we present Unbalanced Learning of Optimal Transport (ULOT), a deep learning method that predicts optimal transport plans between two graphs. Our method is trained by minimizing the fused unbalanced Gromov-Wasserstein (FUGW) loss. We propose a novel neural architecture with cross-attention that is conditioned on the FUGW tradeoff hyperparameters. We evaluate ULOT on synthetic stochastic block model (SBM) graphs and on real cortical surface data obtained from fMRI. ULOT predicts transport plans with competitive loss up to two orders of magnitude faster than classical solvers. Furthermore, the predicted plan can be used as a warm start for classical solvers to accelerate their convergence. Finally, the predicted transport plan is fully differentiable with respect to the graph inputs and FUGW hyperparameters, enabling the optimization of functionals of the ULOT plan.

In real-world applications, node features in graphs often contain noise from various sources, leading to significant performance degradation in GNNs. Although several methods have been developed to enhance robustness, they rely on the unrealistic assumption that noise in node features is independent of the graph structure and node labels, thereby limiting their applicability. To this end, we introduce a more realistic noise scenario, dependency-aware noise on graphs (DANG), where noise in node features create a chain of noise dependencies that propagates to the graph structure and node labels. We propose a novel robust GNN, DA-GNN, which captures the causal relationships among variables in the data generating process (DGP) of DANG using variational inference. In addition, we present new benchmark datasets that simulate DANG in real-world applications, enabling more practical research on robust GNNs. Extensive experiments demonstrate that DA-GNN consistently outperforms existing baselines across various noise scenarios, including both DANG and conventional noise models commonly considered in this field.

Graph Neural Networks learn on graph-structured data by iteratively aggregating local neighborhood information. While this local message passing paradigm imparts a powerful inductive bias and exploits graph sparsity, it also yields three key challenges: (i) oversquashing of long-range information, (ii) oversmoothing of node representations, and (iii) limited expressive power. In this work we inject randomized global embeddings of node features, which we term Sketched Random Features, into standard GNNs, enabling them to efficiently capture long-range dependencies. The embeddings are unique, distance-sensitive, and topology-agnostic--properties which we analytically and empirically show alleviate the aforementioned limitations when injected into GNNs. Experimental results on real-world graph learning tasks confirm that this strategy consistently improves performance over baseline GNNs, offering both a standalone solution and a complementary enhancement to existing techniques such as graph positional encodings.

The problem of over-smoothing has emerged as a fundamental issue for Graph Convolutional Networks (GCNs). While existing efforts primarily focus on enhancing the discriminability of node representations for node classification, they tend to overlook the over-smoothing at the graph level, significantly influencing the performance of graph classification. In this paper, we provide an explanation of the graph-level over-smoothing phenomenon and propose a novel Adaptive MultiViewed Subgraph Convolutional Network (MultiNet) to address this challenge. Specifically, the MultiNet introduces a local subgraph convolution module that adaptively divides each input graph into multiple subgraph views. Then a number of subgraph-based view-specific convolution operations are applied to constrain the extent of node information propagation over the original global graph structure, not only mitigating the over-smoothing issue but also generating more discriminative local node representations. Moreover, we develop an alignment-based readout that establishes correspondences between nodes over different graphs, thereby effectively preserving the local node-level structure information and improving the discriminative ability of the resulting graph-level representations. Theoretical analysis and empirical studies show that the MultiNet mitigates the graph-level over-smoothing and achieves excellent performance for graph classification.

It also tolerates no prediction errors on the labeled nodes, so the trade-off parameter can be set to infinity. Local and Global Consistency (LGC) [82] relaxes the GRF method by eliminating the restriction of zero empirical risk on labeled nodes and exploits the normalized Laplacian matrix for smoothing instead. Random Walk Smoothing [83] extends LRC for directed graphs by indirectly operating LGC on a modified undirected graph with a new normalized Laplacian matrix L . Tikhonov Smoothing [4] only uses the labeled nodes in the quadratic error term. Hub & Authority Smoothing [84] proposes another random-walk-based strategy on directed graphs that is motivated by the hub and authority web model. Its smoothing matrix is more complex with two underlying Laplacian matrices LA,LH for in-links and out-links.

Graph neural networks (GNNs) are the de facto standard deep learning architectures for machine learning on graphs. This has led to a large body of work analyzing the capabilities and limitations of these models, particularly pertaining to their representation and extrapolation capacity. We offer a novel theoretical perspective on the representation and extrapolation capacity of GNNs, by answering the question: how do GNNs behave as the number of graph nodes become very large? Under mild assumptions, we show that when we draw graphs of increasing size from the Erd os-Rényi model, the probability that such graphs are mapped to a particular output by a class of GNN classifiers tends to either zero or to one. This class includes the popular graph convolutional network architecture. The result establishes'zero-one laws' for these GNNs, and analogously to other convergence laws, entails theoretical limitations on their capacity. We empirically verify our results, observing that the theoretical asymptotic limits are evident already on relatively small graphs.

A.1 Background on graph neural networks Many GNN architectures iteratively update node features following a neighborhood aggregation scheme.