Aqueous solubility is a key property in early-stage drug discovery, but most predictive models merge physicochemical descriptors and molecular graph information into a single representation, obscuring whether a prediction is driven by global chemistry, molecular structure, or both. We present an additive deep-learning framework that keeps these two sources of information separate throughout training: physicochemical descriptors are encoded by a multilayer perceptron (the chemical branch) and molecular graph topology by a graph neural network (the structural branch), with the two outputs combined only at the prediction stage through an additive model with an optional multiplicative interaction. This design provides a direct decomposition of chemical and structural components that can be examined separately after training. Furthermore, pretraining on the larger AqSolDB dataset and fine-tuning on the smaller BigSolDB2 dataset substantially improve accuracy and reduce run-to-run variations, indicating generalizability of the learned features from the data-rich settings. We further interpret the fitted model using best linear projections of the branch outputs, molecule-level embedding summaries across solubility classes, and atom-level GNNExplainer masks aggregated over functional groups. These analyses show that the chemical branch aligns with familiar physicochemical descriptors, while the structural branch captures graph-topological and functional-group patterns associated with solubility. Across both datasets, the framework attains competitive predictive performance while making the distinct roles of chemical and structural information more transparent.

Graph Neural Networks (GNNs) have achieved great success but are often considered to be challenged by varying levels of homophily in graphs. Recent empirical studies have surprisingly shown that homophilic GNNs can perform well across datasets of different homophily levels with proper hyperparameter tuning, but the underlying theory and effective architectures remain unclear.

Graph few-shot learning has attracted increasing attention due to its ability to rapidly adapt models to new tasks with only limited labeled nodes. Despite the remarkable progress made by existing graph few-shot learning methods, several key limitations remain. First, most current approaches rely on predefined and unified graph filters (e.g., low-pass or high-pass filters) to globally enhance or suppress node frequency signals. Such fixed spectral operations fail to account for the heterogeneity of local topological structures inherent in real-world graphs. Moreover, these methods often assume that the support and query sets are drawn from the same distribution. However, under few-shot conditions, the limited labeled data in the support set may not sufficiently capture the complex distribution of the query set, leading to suboptimal generalization.

Large language models (LLMs) have been used in many zero-shot learning problems, with their strong generalization ability. Recently, adopting LLMs in textattributed graphs (TAGs) has drawn increasing attention. However, the adoption of LLMs faces two major challenges: limited information on graph structure and unreliable responses. LLMs struggle with text attributes isolated from the graph topology. Worse still, they yield unreliable predictions due to both information insufficiency and the inherent weakness of LLMs (e.g., hallucination). Towards this end, this paper proposes a novel method named Dynamic Text Bundling Supervision (DENSE) that queries LLMs with bundles of texts to obtain bundle-level labels and uses these labels to supervise graph neural networks.

ChebNet, one of the earliest spectral GNNs, has largely been overshadowed by Message Passing Neural Networks (MPNNs), which gained popularity for their simplicity and effectiveness in capturing local graph structure. Despite their success, MPNNs are limited in their ability to capture long-range dependencies between nodes. This has led researchers to adapt MPNNs through rewiring or make use of Graph Transformers, which compromises the computational efficiency that characterized early spatial message-passing architectures, and typically disregards the graph structure. Almost a decade after its original introduction, we revisit ChebNet to shed light on its ability to model distant node interactions. We find that out-of-box, ChebNet already shows competitive advantages relative to classical MPNNs and GTs on long-range benchmarks, while maintaining good scalability properties for high-order polynomials. However, we uncover that this polynomial expansion leads ChebNet to an unstable regime during training. To address this limitation, we cast ChebNet as a stable and non-dissipative dynamical system, which we coin Stable-ChebNet. Our Stable-ChebNetmodel allows for stable information propagation, and has controllable dynamics which do not require the use of eigendecompositions, positional encodings, or graph rewiring.

Graph self-supervised learning aims to learn the intrinsic graph representations from unlabeled data, with broad applicability in areas such as computing networks. Although graph contrastive learning (GCL) has achieved remarkable progress by generating perturbed views via data augmentation and optimizing sample similarity, it performs poorly in heterophilic graph scenarios (where connected nodes are likely to belong to different classes or exhibit dissimilar features). In heterophilic graphs, existing methods typically rely on random or carefully designed augmentation strategies (e.g., edge dropping) for contrastive views. However, such graph structures exhibit intricate edge relationships, where topological perturbations may completely alter the semantics of neighborhoods. Moreover, most methods focus solely on local contrastive signals while neglecting global structural constraints. To address these limitations, inspired by graph coloring, we propose a novel Coloring learning for heterophilic graph Representation framework, CoRep, which: 1) Pioneers a coloring classifier to generate coloring labels, explicitly minimizing the discrepancy between homophilic nodes while maximizing that of heterophilic nodes. A global positive sample set is constructed using multi-hop same-color nodes to capture global semantic consistency.

Graph Neural Networks (GNNs) are powerful models for node classification, but their performance is heavily reliant on manually labeled data, which is often costly and results in insufficient labeling. Recent studies have shown that message-passing neural networks struggle to propagate information in low-degree nodes, negatively affecting overall performance. To address the information bias caused by degree imbalance, we propose a Learnable Enhancement and Label Selection Dynamic Graph Convolutional Network (L2DGCN). L2DGCN consists of a teacher model and a student model. The teacher model employs an improved label propagation mechanism that enables remote label information dissemination among all nodes.

Graph Neural Networks (GNNs) have achieved remarkable success in a wide range of applications. However, when trained on limited or low-diversity datasets, GNNs are prone to overfitting and memorization, which impacts their generalization. To address this, graph data augmentation (GDA) has become a crucial task to enhance the performance and generalization of GNNs. Traditional GDA methods employ simple transformations that result in limited performance gains. Although recent diffusion-based augmentation methods offer improved results, they are sparse, task-specific, and constrained by class labels.

Message Passing Neural Networks (MPNNs) are the building block of graph foundation models, but fundamentally suffer from oversmoothing and oversquashing. There has recently been a surge of interest in fixing both issues. Existing efforts primarily adopt global approaches, which may be beneficial in some regions but detrimental in others, ultimately leading to the suboptimal expressiveness. In this paper, we begin by revisiting oversquashing through a global measure - spectral gap λ- and prove that the increase of λleads to gradient vanishing with respect to the input features, thereby undermining the effectiveness of message passing. Motivated by such theoretical insights, we propose a local approach that adaptively adjusts message passing based on local structures. To achieve this, we connect local Riemannian geometry with MPNNs, and establish a novel nonhomogeneous boundary condition to address both oversquashing and oversmoothing. Building on the Robin condition, we design a GBN network with local bottleneck adjustment, coupled with theoretical guarantees. Extensive experiments on homophilic and heterophilic graphs show the expressiveness of GBN. Furthermore, GBN does not exhibit performance degradation even when the network depth exceeds 256 layers.

Message Passing Neural Networks (MPNNs) are a class of Graph Neural Networks (GNNs) that propagate information across the graph via local neighborhoods. The scheme gives rise to two key challenges: over-smoothing and over-squashing. While several Dropout-style algorithms, such as DropEdge and DropMessage, have successfully addressed over-smoothing, their impact on oversquashing remains largely unexplored. This represents a critical gap in the literature, as failure to mitigate over-squashing would make these methods unsuitable for long-range tasks - the intended use case of deep MPNNs. In this work, we study the aforementioned algorithms, and closely related edge-dropping algorithms - DropNode, DropAgg and DropGNN - in the context of over-squashing.