Graph Representation Learning

Antibodies neutralize foreign antigens by binding to specific surface regions called epitopes. Computational epitope prediction is critical for understanding immune recognition and guiding antibody engineering. However, existing methods face three fundamental challenges: antibody-aware models encode each chain independently and combine them only at a late stage, failing to capture co-dependent structural features that define binding interfaces, whereas severe class imbalance and scarcity of known antibody-antigen complexes render standard training objectives ineffective. We propose EpiFormer, a general encoder-decoder framework that addresses these challenges jointly. Our key design principle is interleaved cross-attention within GNN encoding layers, enabling bidirectional antigen-antibody information flow throughout representation learning rather than only at the output. This early-fusion principle is backbone-agnostic, providing consistent gains across GNN architectures from simple GCNs to equivariant models. We further show that sparsity-aware objectives are effective when paired with early-fusion architectures for the epitope prediction task. EpiFormer improves over the previous best method by over 40% in F1 score on standard benchmarks, demonstrating generalizability and cross-dataset transferability. Notably, EpiFormer discovers known biological principles as emergent behaviors of end-to-end training, where the learned cross-attention gates favor antigen-to-antibody information flow, consistent with the asymmetric roles of the two chains at the binding interface, and the model's preference for geometric over evolutionary features aligns with the established finding that epitope residues are not evolutionarily conserved. The source code is available at: https://github.com/mansoor181/epiformer.git

Graph coloring seeks to assigns colors to a graph's nodes so that adjacent nodes receive different colors, using as few colors as possible. Here, we study approximate $k$-coloring, where the goal is to use at most $k$ colors while minimizing the number of monochromatic edges. This problem is central to graph theory and has applications in areas such as scheduling and resource allocation. Recent unsupervised GNN approaches optimize each instance directly, precluding generalization across graph sizes and distributions. We instead propose a contrastive learning framework that learns transferable coloring geometry where the embeddings of same-color nodes align, while adjacent nodes' representations are pushed toward distinct directions. We analyze the resulting population objective over bounded-size graphs. For unit-norm embeddings, we show that its optima have a line-prototype structure: Representations of nodes of the same color collapse to a shared one-dimensional subspace, and edges connect orthogonal subspaces. This geometry yields stationarity conditions in the supervised setting and is preserved by projected subgradient dynamics under a balanced-coloring assumption. In an unnormalized variant, gradient descent has a max-margin bias governed by a quotient-graph hard-margin problem. Experiments on synthetic and real-world graphs show that contrastive GNN encoders generalize effectively and produce low-conflict colorings, matching and sometimes improving on greedy approaches.

While Virtual Nodes (VNs) are often utilized in Message Passing Neural Networks (MPNNs) to facilitate effective message passing, existing VN-based methods have limitations, such as constraining all nodes to connect to the same number of VNs, fixing the connections before applying MPNNs, and connecting a node to a VN independently of the other nodes that connect to the same VN. We propose MAVN, an end-to-end differentiable MPNN framework that allows non-constrained connections between nodes and VNs and dynamically introduces VNs on demand in response to evolving node representations across layers. Specifically, MAVN learns to adaptively determine when (at which layer) and where (to which nodes) to introduce and connect VNs based on the relative importance of connections. From a pool of candidate VNs, MAVN selects the necessary VNs in each layer, where each selected VN is connected to a nonempty subset of nodes, guided by a dual-perspective scoring mechanism that jointly captures the nodes' preferences for VNs and the VNs' preferences for nodes. We theoretically prove that for any node-VN connectivity pattern, there exists a set of MAVN's parameters that can simulate the pattern. Experiments on nine real-world datasets demonstrate that MAVN consistently improves the performance of backbone MPNNs, achieving up to 46.5% improvement over the backbones and outperforms the baselines.

Graph neural networks (GNNs) are limited to modeling pairwise interactions, while higher-order models based on cell complexes achieve greater expressivity but often suffer from poor scalability. We introduce simplified and factored cellular Weisfeiler Leman tests (sCWL and fCWL), which preserve the expressivity of the CWL test while improving computational efficiency. We further introduce the maximal clique complex, enabling scalable CWNs with reduced time and memory complexity while retaining strong empirical performance. To avoid explicit clique enumeration, we propose CliqueWalk, a biased random walk that samples maximal cliques and scales linearly with graph size. These contributions yield a scalable topological learning framework for higher-order graph representation.

We show that contrary to conventional wisdom in the community, graph neural networks (GNNs) are not continuous with respect to all natural modes of graph convergence. As a result, GNNs may generate substantially different latent representations for graphs that are very similar. In particular they assign vastly different latent embeddings to graphs that represent the same underlying object at different resolution scales. We trace this failure of continuity back to a structural obstruction arising from commonly used information-propagation schemes. Building on this insight we then derive a principled modification to standard GNN architectures which equips models with continuity across scales. The proposed modification enables consistent integration of distinct resolutions and reliable generalization between them. We systematically validate our theoretical findings in a wide range of numerical experiments.

Graph foundation models (GFMs) aim to reuse a single backbone across diverse graph domains, yet their transfer is often uneven and can exhibit negative transfer. While most prior work improves transfer through architectural or adaptation choices, we ask a data-centric question: which properties of two graph domains determine how much a fixed representation model changes its outputs? Using a graphon-based continuous limit for dense graphs, we show that for both set-based and message-passing tokenizations, any Lipschitz backbone admits an explicit decomposition of cross-domain output shift into (i) graph-specific finite-sample approximation terms and (ii) an intrinsic, relabeling-invariant domain discrepancy capturing structural mismatch. A key ingredient is positional-encoding (PE) stability: we establish stability guarantees for spectral PEs and highlight contrasting behaviors of eigenvector- versus subspace-based PEs. Experiments on synthetic and real graphs validate the theory and translate the decomposition into guidance for data curation in GFM transfer.

Representation learning on dynamic graphs requires capturing complex dependencies that evolve across both time and structure. Existing approaches typically adopt fixed temporal decay schemes or predetermined structural propagation depths, limiting their ability to generalize across graphs with diverse interaction frequencies and topological characteristics. We propose Dual-Scale Retentive Dynamics (DSRD), a unified framework that maintains a retentive representation state encoding both temporal memory and structural context. DSRD introduces two key components: (i) a retentive state with dual-scale adaptation that jointly models temporal dynamics and structural propagation within a single recurrent formulation, and (ii) adaptive decay kernels with learnable time-sensitivity parameters that automatically balance short-term responsiveness and long-term retention based on the underlying interaction patterns. We provide theoretical analysis establishing the equivalence between event-wise parallel aggregation and efficient recurrent state updates, as well as stability and boundedness guarantees for the learned dynamics. Extensive experiments on 14 real-world benchmarks demonstrate that DSRD consistently achieves state-of-the-art performance on both link prediction and node classification tasks, with strong generalization across transductive and inductive settings.

Protein structure classification (PSC) uses supervised learning to predict a protein's CATH/SCOP(e) class from the protein's sequence or 3D structural feature(s). We already modeled 3D structures as (static) protein structure networks (PSNs), demonstrating the competitiveness of PSN-based features to sequence or direct (i.e. non-network) 3D structural features in the PSC task. More recently, we demonstrated the power of features extracted from dynamic PSNs over features extracted from static PSNs (and thus by transitivity over sequence and direct 3D structural features) in the same task. That dynamic PSN approach used traditional machine learning (ML), combining manual (pre-engineered) features with an off-the-shelf classifier. Here, we evaluate whether automatic deep learning (DL) from the dynamic PSNs yields improvements. Our evaluation on 72 datasets spanning ~44,000 CATH- or SCOPe-labeled dynamic PSNs reveals that in terms of PSC accuracy, traditional ML and DL are (close to) tied for a large majority of the datasets, while DL is on average 10+ times slower. We are the first to evaluate traditional ML vs. DL in the dynamic PSN-based PSC task.

In recent years, Large Language Models (LLMs) have shown great capability in processing graph tasks such as fraud detection. However, most existing methods rely heavily on rich text attributes, which poses difficulties for this domain due to the lack of textual data. Although some pioneering methods attempt to overcome it, their textualization of graph structures via hard prompts easily leads to feature distortion. Additionally, fraud detection often exhibits multi-relational complexity, where current methods struggle to capture this deep semantic information. To address these challenges, we propose LLM-GNN Soft Prompt Framework (LGSPF). Specifically, LGSPF bridges the graph structure and semantic space using soft prompt to eliminate reliance on text. We further introduce a parallel Graph Neural Network (GNN) encoder to translate multi-relational topologies into graph tokens for fine-grained LLM fraud comprehension. Through end-to-end optimization, LGSPF enhances deep semantic alignment between LLM and GNN. Experiments across diverse fraud detection benchmarks demonstrate our method achieves state-of-the-art performance. Moreover, we further validate the contribution of LGSPF on enhancing the semantic interpretability of fraud behaviors.

Traditional network analysis focuses on single-layer networks, real-world systems often form multilayer networks with multiple relationship types. However, existing methods typically fail to capture complex inter-layer dependencies by treating layers independently or aggregating them. To address this, we propose T-GINEE (Tensor-Based Generalized Multilayer-graph Estimating Equation), a statistical regularization framework combining tensor-based generalized estimating equations with task-specific loss to model cross-network correlations explicitly. Key innovations include: (1) CP tensor decomposition capturing structural dependencies via shared latent factors; (2) a generalized estimating equation framework modeling inter-layer correlations through working covariance matrices; and (3) a flexible link function accommodating characteristics like sparsity. Our theoretical analysis establishes consistency and asymptotic normality under mild conditions. Extensive experiments on synthetic and real-world datasets validate T-GINEE's effectiveness for multilayer network analysis.

Graph clustering is essential in graph analysis for revealing structural patterns and node communities. Despite recent advances in self-supervised contrastive learning that have improved clustering via structural and attribute signals, existing methods still struggle to flexibly capture high-order local structures and often overlook global semantics in complex graphs. These limitations lead to suboptimal node representations, especially in real-world graphs with fragmented structures and ambiguous cluster boundaries. To address these limitations, a contrastive graph clustering framework is proposed to jointly integrate multi-scale local structures with global semantics via attention mechanisms. At the local level, GNN-based topological signals extracted from multiple propagation depths are adaptively fused through attention-based weighting to capture multi-scale neighborhood features. At the global level, semantic prototypes derived from dynamically evolving cluster centers are adaptively aggregated through attention to guide node representations and enhance inter-cluster separability. The model is trained under a dual-view contrastive learning paradigm with a hybrid objective that combines instance-level and structure-aware losses to improve representation robustness and discrimination. Experiments on eight real-world graph datasets demonstrate that our method achieves competitive clustering performance. Code is available at https://github.com/vege12138/w2.

International Classification of Diseases (ICD) is a globally recognized coding system that records diagnostic events during each patient encounter, providing a standardized data foundation for various clinical tasks. However, the irregular and hierarchical nature of ICD code sequences poses challenges for N-D lattice-based sequential modeling methods, leading to overly complex model designs. In this paper, we propose GraD-IBD, a graph diagnosis model that reformulates longitudinal ICD trajectories as visit-bucketized, temporally directed graphs to detect the risk of inflammatory bowel disease (IBD). A novel context-aware, time-decay message passing mechanism was developed to capture temporal dependencies while reducing model complexity. The experimental results using a real-world clinical dataset demonstrated consistent and robust improvements in IBD detection over state-of-the-art methods, with significant reductions in computational complexity compared to sequential models. These findings highlight the potential of graph representation learning to enable efficient, scalable, and accurate disease risk prediction from longitudinal ICD diagnosis codes.

Graph neural networks for node classification are typically trained by gradient descent over hundreds or thousands of epochs. Recent work has shown that, when properly tuned, classic GCN/SAGE/GAT architectures can match graph transformers on many node-classification benchmarks. We ask a complementary question: how much of this performance can be recovered by deterministic closed-form solvers, and what guarantees does this enable? We introduce a routed closed-form framework selected by adjusted homophily. For assortative graphs, we use SGC-style propagation followed by Ridge regression; for heterophilous graphs, we introduce LCF-Net, a layer-wise closed-form graph feature-refinement network whose per-layer Ridge solves are capped by a Gaussian kernel-Ridge head. Across 14 benchmarks, including ogbn-arxiv and ogbn-proteins, our closed-form predictors match or beat the best vanilla 2-layer GCN/SAGE/GAT on 9 of 9 measured datasets, tie tuned deep recipes within one standard deviation on 9 of 12 small benchmarks, and exceed the OGB-leaderboard plain GCN on both large graphs. The remaining heterophilous gap closely tracks the gain from vanilla 2-layer to deep SAGE, suggesting that the residual difference is primarily architectural. Because our predictors are explicit solutions of deterministic linear systems, modified graph inputs can be re-solved to obtain retrain-equivalent parameters. We formalize exact graph-object unlearning for label, feature, edge, node, and subgraph modifications, prove K-hop locality for Ridge components, and verify exactness across 109 configurations. On ogbn-arxiv, localized updates give $21$--$45\times$ speedups over full re-solving and roughly $10^{6}\times$ speedups over gradient retraining. Structural-inversion experiments further quantify the privacy floor of exact retraining and the additional leakage of approximate graph-unlearning methods.

Dynamic graph neural networks (DGNNs) that operate on snapshot sequences typically fall into one of two categories. Temporal-first approaches build per-node temporal embeddings and only afterward perform spatial aggregation, whereas Spatial-first approaches invert this order, feeding the output of a graph convolution into a downstream temporal module. In either case, the rigid sequencing forces the second stage to consume an already-compressed summary produced by the first, ruling out joint reasoning over topology and evolution; effectively, the message-passing operator never gets to weight a neighbor's contribution by that neighbor's past trajectory. This paper introduces SiST-GNN (Simultaneous Spatial-Temporal GNN), which fuses the two signals inside a single message-passing operation rather than chaining them. At each snapshot, we maintain a recurrent hidden state per node that summarises its history, pairs it with the node's current feature vector, and treats the pair as two nodes joined by a cross-time edge; running a standard graph convolution on this temporally augmented graph yields the updated representation. We compare against fourteen link-prediction baselines under both the fixed-split and live-update evaluation regimes, and eleven baselines on node classification. Across the public benchmarks, SiST-GNN improves on the strongest prior method in link prediction by 1-18% in the fixed-split setting, and is the leading learned method on five of six datasets in the live-update setting, improving on the strongest prior method by 1-158% there. We additionally derive three dynamic node-classification tasks by discretizing the underlying continuous-time event streams; here SiST-GNN beats the leading discrete-time (DTDG) baseline by 7-23% and matches continuous-time (CTDG) methods that consume the raw events directly.

Chain-of-Thought (CoT) prompting has shown promise in enhancing the reasoning capabilities of large language models (LLMs) on text-attributed graphs (TAGs). This work reframes CoT-based graph learning through the principle of clustering as reasoning, offering a $k$-means interpretation of how iterative reasoning operates over graph-structured data. We observe that existing graph CoT methods rely on disjoint architectures and fixed graph representations, limiting step-by-step semantic-topological interaction and interpretability. To overcome this limitation, we propose a unified framework named KCoT that integrates CoT reasoning with graph representation learning. Our key theoretical result reveals a formal mathematical correspondence between a Transformer block and the $k$-means algorithm, allowing reasoning to be interpreted as iterative assignment and update steps. Based on this insight, we introduce a Semantic Discriminating Prompt that explicitly formulates these steps as structured CoT reasoning, together with a structure-grounded alignment strategy to fuse topological priors with evolving thought-conditioned representations. Experiments on standard benchmarks demonstrate consistent improvements over state-of-the-art methods, validating clustering as a principled mechanism for CoT-based graph learning.

Biological systems are governed by structured molecular interactions, where pathways, regulatory circuits, and functional gene relationships shape cellular behavior and disease progression. Much of this knowledge is naturally represented as graphs. However, most biomedical AI models cannot directly use graph-encoded biological knowledge and instead require compressed low-dimensional representations, which can lose important structure and reduce performance, especially in limited-sample clinical studies. Here, we introduce Graph-in-Graph (GiG), a knowledge graph-modulated deep learning framework for data-efficient clinical prediction. GiG represents each patient as a standalone modular graph, in which curated biological knowledge graphs define edges and patient-specific measurements, such as gene expression, define node features. This design allows multiple biological knowledge graphs to be integrated while preserving gene-gene interactions and pathway topology during patient-level representation learning. Across cohorts comprising nearly 9,700 patients and five clinical tasks, including liquid biopsy cancer detection, prostate cancer diagnosis, and 32-class pan-cancer classification, GiG consistently outperforms traditional and state-of-the-art methods, with the largest gains in limited-sample settings. On the challenging prostate cancer diagnosis task, GiG improves macro-F1 by up to 49 percentage points relative to competing methods. Control experiments replacing real pathway graphs with random topologies confirm that these gains arise from biologically grounded knowledge graph structure rather than graph modeling alone. These findings show that knowledge graph-modulated deep learning can improve robustness, interpretability, and sample efficiency in clinical data analysis, and provide a principled framework for integrating biological knowledge graphs into predictive modeling.

Message-passing neural networks (MPNNs) often suffer from an information bottleneck when capturing long-range dependencies, leading to the oversquashing (OSQ) phenomenon. Alongside spatial connectivity enrichment (e.g., rewiring), recent studies have shown that spectral filtering can yield strong long-range learning outcomes, as spectral operators enable global information mixing that alleviates OSQ. These approaches achieve this either by stabilizing the Jacobian energies in deep propagation or by guaranteeing OSQ mitigation under strong theoretical assumptions. We revisit these conclusions and show that the associated Jacobian sensitivity lower bound is generally difficult to achieve in practice. We then propose S$^3$GNN, which mitigates OSQ without such restrictive assumptions by lightweightly reintroducing omitted components with substantially lower computational complexity, while standard stability constraints on feature transformations remain effective under our new dynamics. Extensive experiments across diverse domains (e.g., long-range benchmarks, KGQA, and mesh-based fluid dynamics) demonstrate that S$^3$GNN achieves up to an order-of-magnitude error reduction with up to 50% fewer parameters. Our code can be found in https://github.com/EEthanShi/S3-GNN.git.

Hyper-relational knowledge graphs (HKGs) effectively represent complex facts. While inferring new knowledge in HKGs is a critical problem, current methods cast it as a simple link prediction, assuming that nearly all entities and relations within a fact are known, leaving only a single blank to be filled. However, this restricted assumption may not hold in real-world scenarios in which multiple, or even all, constituent components of a fact may be missing simultaneously. To bridge this gap, we introduce a task called fact generation: generating a valid hyper-relational fact from an arbitrarily masked query, i.e., completing a partially observed fact or generating a fact from scratch. We propose KREPE, the first generative representation learning method for HKGs that learns to model the probability distributions of missing components conditioned on the local fact components and global structure of HKGs via a masked discrete diffusion. KREPE models both the intra-fact dependencies by contextual message passing and inter-fact correlations by aggregating stochastically sampled contexts. KREPE seamlessly unifies link prediction and fact generation within a single training framework, achieving state-of-the-art performance on standard HKG link prediction benchmarks and outperforming LLM-based baselines in generating novel and correct facts.

Transformers have become a central architecture for graph learning, but their application to graphs requires first choosing a tokenization: a graph-to-token map that determines which structural information is exposed at the input. In this work, we show that this choice is a fundamental component of transformer expressivity. We examine three tokenizations that serve as building blocks for many existing graph tokenizations: spectral, random-walk, and adjacency tokenizations. We prove that different tokenizations induce distinct depth regimes: the same graph computation may be realizable by a shallow transformer under one tokenization, while requiring substantially larger depth under another. For example, we prove that random-walk tokenization is lossy for any walk length, making it impossible in general to recover the graph from it, and that while spectral tokenization is lossless, it is ill-conditioned for local tasks. We further show that although both random-walk and spectral tokenizations are derived from adjacency information, it is impossible for a limited-depth transformer to convert between tokenization families in general. In particular, we establish lower bounds and impossibility results showing that unfavorable tokenizations may preclude the efficient recovery of more suitable structural representations. Finally, we complement our theory with controlled experiments on synthetic and real-world tasks, validating the predicted separations and showing that different tasks favor different structural views, and combining complementary tokenizations allows the transformer to leverage distinct signals from each representation.

We introduce Contrastive FUSE, a fast and unified framework for scalable node representation learning in graphs with partially available pairwise node labels and no available node features. Unlike existing methods, we directly optimize a spectral contrastive objective that integrates community-aware structural signals with signed pairwise constraints. To support large-scale training, we replace the expensive modularity gradient with a lightweight approximation, which preserves the structure-seeking behavior of modularity while reducing the computational cost significantly. This yields an efficient optimization scheme with a natural gradient decomposition and adaptive learning-rate scaling, enabling fast iterative updates even on million-edge graphs. Extensive experiments on benchmark citation networks, large co-purchase graphs, and OGB datasets show that Contrastive FUSE achieves competitive or superior contrastive classification performance without relying on node features, while offering substantial runtime gains over existing baselines. These results highlight the effectiveness of coupling modularity-inspired structural learning with contrastive supervision for efficient and scalable contrastive node representation learning.

Graph Anomaly Detection (GAD) aims to identify atypical graph entities, such as nodes, edges, or substructures, that deviate significantly from the majority. While existing text-rich approaches typically integrate structural context into the data representation pipeline using raw textual features, they often neglect the structural context of nodes. This limitation hinders their ability to detect sophisticated anomalies arising from inconsistencies between a node's inherent content and its topological role. To bridge this gap, we propose TERGAD (Structure-aware Text-enhanced Representations for Graph Anomaly Detection), A novel data augmentation framework that enriches structural semantics for GAD via the semantic reasoning capabilities of Large Language Models (LLMs). Specifically, TERGAD translates node-level topological properties into descriptive natural language narratives, which are subsequently processed by an LLM to derive high-level semantic embeddings. These embeddings are then adaptively fused with original node attributes through a gated dual-branch autoencoder to jointly reconstruct both graph structure and node features. The anomaly score is computed based on the integrated reconstruction error, effectively capturing deviations in both observable attributes and LLM-informed semantic expectations. Extensive experiments on six real-world datasets demonstrate that TERGAD consistently outperforms state-of-the-art baselines. Furthermore, our ablation studies validate the indispensable role of structural semantic guidance and the efficacy of the gated fusion mechanism. Code is available at https://github.com/Kantorakitty/TERGAD-main.

Knowledge Graphs (KGs) are a powerful representation of linked data, offering flexibility, semantic richness, and support for knowledge enrichment and reasoning. They help data owners organize and exploit heterogeneous data to provide insightful services (e.g., recommendations), yet real-world KGs are often incomplete, hiding true facts or missing valuable insights. Knowledge graph embedding techniques are commonly used to infer valuable missing information. However, reasoning over KGs can inadvertently expose sensitive user information, even when such data is not explicitly stored. In this work, we investigate the privacy risks associated with KGE-based reasoning, focusing on attribute inference attacks where adversaries attempt to deduce sensitive user attributes from seemingly non-sensitive outputs. We propose and evaluate a framework that mitigates these privacy risks by applying post processing sanitization techniques to KGE outputs. Preliminary results demonstrate the effectiveness of these attacks on the outputs of KGE models, and explore the trade-off between recommendation quality and privacy protection when applying randomization based approaches, highlighting the need to experiment with more advanced techniques in future work to address this issue.

Graph Neural Networks and Graph Transformers have become central to graph learning, combining expressive representation learning with sample-efficient inductive biases. Yet they remain fundamentally limited when predictions depend on correlations between distant graph regions. We address this limitation with Graph Hierarchical Recurrence (GHR), a novel framework that jointly operates on the input graph and a pooled hierarchical abstraction. We also show that existing models degrade more sharply under out-of-range generalization, where test instances require interactions across distances exceeding those observed during training. Despite its minimal design, GHR consistently strengthens every tested message-passing backbone, yielding robust performance on long-range dependencies and particularly pronounced gains in out-of-range regimes. Across a broad suite of long-range benchmarks, GHR achieves state-of-the-art or competitive results on multiple tasks, establishing hierarchical recurrence as an effective mechanism for extending graph models beyond their observed interaction range.

Conventional approaches to learning on graphs involve message passing along existing (i.e., positive) edges to update node features. However, these approaches often disregard the potentially valuable information contained in the absence (i.e., negative) of edges. Here, we theoretically analyze the value of negative edges in graph representations and prove that in settings of low label rates, high homophily, and high edge density, access to negative edges provides significant information gain over using only positive edges. Motivated by this insight, we introduce Contrastive Message Passing (CMP), a general message passing architecture that enable graph neural network layers to reason over positive and negative edges. By imposing soft positive semidefinite constraints on the learnable weights, our approach differentially applies similarity-preserving transformations to positively connected nodes and dissimilarity-inducing transformations to negatively connected nodes. Over simulated and real datasets in varying data regimes, CMP consistently outperforms baselines in low-label settings when negative edges are informative.

Graph Neural Networks (GNNs) are powerful tools for learning from graph-structured data, but their scalability is increasingly strained by the size of real-world graphs in domains like recommender systems, fraud detection, and molecular biology. Graph condensation -- the task of generating a smaller synthetic graph that retains the performance of models trained on the original -- has emerged as a promising solution. However, the dominant approach of gradient matching introduces a fundamental contradiction: it requires training on the full dataset to create the compressed version, thereby undermining the goal of efficiency. Worse still, these methods suffer from high computational overhead, poor generalization across GNN architectures, and brittle reliance on specific model configurations. Equally concerning is the community's reliance on misleading evaluation protocols such as node compression ratios, which fail to reflect true resource savings, condensation overhead, and illusory application to neural architecture search. These shortcomings are not incidental -- they are systemic, and they obstruct meaningful progress. In this position paper, we argue that graph condensation, in its current form, needs a reset. We call for moving beyond full-dataset training and model-dependent design, and instead advocate for methods that are lightweight, architecture-agnostic, and practically deployable. By identifying key methodological flaws and outlining concrete research directions, we aim to reorient the field toward approaches that deliver on the true promise of condensation: efficient, generalizable, and usable GNN training at scale.

Understanding how objects relate to each other in space is fundamental to scene understanding, yet most contrastive pre-training approaches only model pairwise relationships, leaving richer compositional and multi-hop interactions largely unexplored. We introduce Multi-Hop Relational Contrastive Learning (MRCL), a framework that extends spatial contrastive learning to graph-structured scene representations. By tracing k-hop paths through scene graphs built from detected objects, MRCL captures implicit spatial dependencies that go well beyond what direct object pairs can express. We define a multi-level contrastive objective spanning nodes, edges, and multi-hop paths, encouraging embeddings that remain stable across object semantics while staying responsive to spatial layout. On a GQA subset, MRCL produces spatially-aware representations that improve content-based graph retrieval (NDCG@5 = 0.748) and consistently benefit downstream tasks, including spatial relationship recognition and graph-based question answering. Together, these results suggest that multi-hop relational supervision offers substantially richer structural guidance than pairwise-only methods, leading to visual representations that are more robust, compositional, and geometry-aware.

Relational graph learning enables predictive modeling over relational databases by directly capturing dependencies across interconnected tables. While relational graph Transformers extend the receptive field beyond local message passing, a larger receptive field does not necessarily provide more useful information: sampling must preserve relational structure without introducing excessive semantically irrelevant nodes, while attention must account for the temporal relevance of the retained information. We propose GelGT, a Gaussian relational graph transformer that explicitly addresses these challenges. GelGT introduces a structure-semantic collaborative sampling strategy to preserve structural connectivity while filtering irrelevant semantic information, and incorporates a Gaussian graph attention mechanism with a learnable Gaussian bias on the sampled subgraphs to dynamically encode temporal dependencies. We provide theoretical analysis characterizing the structural preservation, semantic refinement, and temporal discrimination of these mechanisms. Experiments on 7 real-world relational datasets covering 21 prediction tasks show that GelGT consistently outperforms existing relational graph learning methods, with improvements of up to 13.8%.

Graph Neural Networks (GNNs) have become the dominant framework for inductive graph-level learning. Yet most benchmarks focus on the regime $n \gg p$, where the number of graphs $n$ greatly exceeds the number of nodes per graph $p$. This overlooks biological domains such as omics, which operate in the opposite $n \ll p$ regime, characterized by large graphs of genes, transcripts, or proteins across few patient samples. This raises the question: how do GNNs perform in this low-sample, high-node omics setting? We introduce OgBench (Omics-Graph Bench), the first benchmarking platform for graph-level prediction in the $n \ll p$ regime characteristic of omics data. We provide a standardized, end-to-end modular infrastructure from raw omics data to families of featured graphs with varied structural properties. We benchmark classical GNNs, as well as GNNs designed for large graphs and omics applications, alongside MLPs and machine learning baselines to establish reference performances. Our results show that widely used GNNs often do not outperform simple MLPs and classical baselines. These findings challenge the prevailing assumption that graph structure inherently adds value in this domain, fostering a critical reassessment of current learning paradigms. Ultimately, by exposing these limitations, OgBench provides the open-source ecosystem necessary for the community to develop and validate novel architectures explicitly tailored for biological graphs. The code is available at https://github.com/geometric-intelligence/ogbench.

We introduce an empowered transposed Fully Connected Weighted (t-FCW) graph representation to embed point clouds into a metric space. While original t-FCW has shown promising results for point cloud classification, the reasons behind its effectiveness and its broader applicability remained unclear. In this work, we analyze the properties that make the empowered and original t-FCW effective and design a network that uses the empowered t-FCW exclusively as feature extractors. From an interpretability perspective, we build memory banks for classification, part segmentation, and semantic segmentation using the empowered t-FCW. Our analysis reveals that the empowered t-FCW inherits robustness from surface descriptors, provides interpretability through dimension-wise relations. These properties enable a highly efficient and interpretable network, which processes the ModelNet40 classification problem in approximately 7 seconds on an NVIDIA RTX A5000 GPU. Importantly, empowered t-FCW can function both as a lightweight standalone baseline and as a complementary plug-in to existing deep models.

Graph convolutional networks (GCNs) are widely used for 3D hand pose estimation, where the hand skeleton is encoded as a fixed adjacency graph. We revisit whether this is the most effective way to incorporate hand topology in 2D-to-3D lifting. In this paper, we perform controlled, parameter-matched ablations on the FPHA benchmark and show that standard multi-head self-attention consistently outperforms GCN baselines. Even when the GCN is strengthened with multi-hop adjacency and matched parameter count, self-attention reduces MPJPE from 12.36 mm to 10.09 mm. A skeleton-constrained graph attention network recovers most of this gap, indicating that input-dependent aggregation is a major source of improvement, while fully connected attention yields additional gains. We further show that hand topology is most effective when introduced as a soft structural prior through graph-distance positional encoding, rather than as a hard adjacency constraint. These results suggest that, for hand pose lifting, adaptive spatial attention is a more effective inductive bias than fixed graph convolution.