In this section, we discuss the hyperbolic operations used in HNN formulations and set up the meta-learning problem. This particular setup is also known as the N-ways K-shot learning problem. This section provides the theoretical proofs of the theorems presented in our main paper. Note that points in the local tangent space follow Euclidean algebra. The columns present the number of tasks in each batch (# Tasks), HNN update learning rate (), meta update learning rate (), and size of hidden dimensions (d).

Machine learning has been quitesuccessful atgenerativemodeling ofcomplexdomains such asimages, audio, and text.

Recently, contrastiveness-based augmentation surges a new climax in the computer vision domain, where some operations, including rotation, crop, and flip, combined with dedicated algorithms, dramatically increase the model generalization and robustness. Following this trend, some pioneering attempts employ the similar idea to graph data. Nevertheless, unlike images, it is much more difficult to design reasonable augmentations without changing the nature of graphs. Although exciting, the current graph contrastive learning does not achieve as promising performance as visual contrastive learning. We conjecture the current performance of graph contrastive learning might be limited by the violation of the label-invariant augmentation assumption. In light of this, we propose a label-invariant augmentation for graph-structured data to address this challenge. Different from the node/edge modification and subgraph extraction, we conduct the augmentation in the representation space and generate the augmented samples in the most difficult direction while keeping the label of augmented data the same as the original samples. In the semi-supervised scenario, we demonstrate our proposed method outperforms the classical graph neural network based methods and recent graph contrastive learning on eight benchmark graph-structured data, followed by several in-depth experiments to further explore the label-invariant augmentation in several aspects.

Representation learning of graph-structured data is challenging because both graph structure and node features carry important information. Graph Neural Networks (GNNs) provide an expressive way to fuse information from network structure and node features. However, GNNs are prone to adversarial attacks. Here we introduce Graph Information Bottleneck (GIB), an information-theoretic principle that optimally balances expressiveness and robustness of the learned representation of graph-structured data. Inheriting from the general Information Bottleneck (IB), GIB aims to learn the minimal sufficient representation for a given task by maximizing the mutual information between the representation and the target, and simultaneously constraining the mutual information between the representation and the input data.

Graph Neural Networks (GNNs) have emerged as powerful tools to encode graph-structured data. Due to their broad applications, there is an increasing need to develop tools to explain how GNNs make decisions given graph-structured data. Existing learning-based GNN explanation approaches are task-specific in training and hence suffer from crucial drawbacks. Specifically, they are incapable of producing explanations for a multitask prediction model with a single explainer. They are also unable to provide explanations in cases where the GNN is trained in a self-supervised manner, and the resulting representations are used in future downstream tasks. To address these limitations, we propose a Task-Agnostic GNN Explainer (TAGE) that is independent of downstream models and trained under self-supervision with no knowledge of downstream tasks. TAGE enables the explanation of GNN embedding models with unseen downstream tasks and allows efficient explanation of multitask models. Our extensive experiments show that TAGE can significantly speed up the explanation efficiency by using the same model to explain predictions for multiple downstream tasks while achieving explanation quality as good as or even better than current state-of-the-art GNN explanation approaches.

In this section, we discuss the hyperbolic operations used in HNN formulations and set up the meta-learning problem. This particular setup is also known as the N-ways K-shot learning problem. This section provides the theoretical proofs of the theorems presented in our main paper. Note that points in the local tangent space follow Euclidean algebra. The columns present the number of tasks in each batch (# Tasks), HNN update learning rate (), meta update learning rate (), and size of hidden dimensions (d).

We first design four types of graph augmentations to incorporate various priors.

Graph-structured data is ubiquitous in scientific domains, where models often face imbalanced learning settings. In imbalanced regression, domain preferences focus on specific target value ranges that represent the most scientifically valuable cases; however, we observe a significant lack of research regarding this challenge. In this paper, we present Spectral Manifold Harmonization (SMH), a novel approach to address imbalanced regression challenges on graph-structured data by generating synthetic graph samples that preserve topological properties while focusing on the most relevant target distribution regions. Conventional methods fail in this context because they either ignore graph topology in case generation or do not target specific domain ranges, resulting in models biased toward average target values. Experimental results demonstrate the potential of SMH on chemistry and drug discovery benchmark datasets, showing consistent improvements in predictive performance for target domain ranges. Code is available at https://github.com/brendacnogueira/smh-graph-imbalance.git.