ICLR 2026 Papers

Graph Neural Networks (GNNs) are powerful tools for learning on structured data, yet the relationship between their expressivity and predictive performance remains unclear. We introduce a family of pseudometrics that capture different degrees of structural similarity between graphs and relate these similarities to generalization, and consequently, the performance of expressive GNNs. By considering a setting where graph labels are correlated with structural features, we derive generalization bounds that depend on the distance between training and test graphs, model complexity, and training set size. These bounds reveal that more expressive GNNs may generalize worse unless their increased complexity is balanced by a sufficiently large training set or reduced distance between training and test graphs. Our findings relate expressivity and generalization, offering theoretical insights supported by empirical results.

This paper studies a novel problem of out-of-distribution graph models merging, which aims to construct a generalized model from multiple graph models pre-trained on different domains with distribution discrepancy. This problem is challenging because of the difficulty in learning domain-invariant knowledge implicitly in model parameters and consolidating expertise from potentially heterogeneous GNN backbones. In this work, we propose a graph generation strategy that instantiates the mixture distribution of multiple domains. Then, we merge and fine-tune the pre-trained graph models via a MoE module and a masking mechanism for generalized adaptation. Our framework is architecture-agnostic and can operate without any source/target domain data. Both theoretical analysis and experimental results demonstrate the effectiveness of our approach in addressing the model generalization problem.

Graph Neural Networks (GNNs) have demonstrated remarkable success in various domains such as social networks, molecular chemistry, and more. A crucial component of GNNs is the pooling procedure, in which the node features calculated by the model are combined to form an informative final descriptor to be used for the downstream task. However, previous graph pooling schemes rely on the last GNN layer features as an input to the pooling or classifier layers, potentially under-utilizing important activations of previous layers produced during the forward pass of the model, which we regard as \emph{historical graph activations}. This gap is particularly pronounced in cases where a node’s representation can shift significantly over the course of many graph neural layers, and worsen by graph-specific challenges such as over-smoothing in deep architectures. To bridge this gap, we introduce HistoGraph, a novel two‑stage attention‑based final aggregation layer that first applies a unified layer-wise attention over intermediate activations, followed by node-wise attention. By modeling the evolution of node representations across layers, our HistoGraph leverages both the activation history of nodes and the graph structure to refine features used for final prediction. Empirical results on multiple graph classification benchmarks demonstrate that HistoGraph offers strong performance that consistently improves traditional techniques, with particularly strong robustness in deep GNNs.

We study multi-user contextual bandits where users are related by a graph and their reward functions exhibit both non-linear behavior and graph homophily. We introduce a principled joint penalty for the collection of user reward functions $\\{f_u\\}$, combining a graph smoothness term based on RKHS distances with an individual roughness penalty. Our central contribution is proving that this penalty is equivalent to the squared norm within a single, unified _multi-user RKHS_. We explicitly derive its reproducing kernel, which elegantly fuses the graph Laplacian with the base arm kernel. This unification allows us to reframe the problem as learning a single "lifted" function, enabling the design of principled algorithms, LK-GP-UCB and LK-GP-TS, that leverage Gaussian Process posteriors over this new kernel for exploration. We provide high-probability regret bounds that scale with an _effective dimension_ of the multi-user kernel, replacing dependencies on user count or ambient dimension. Empirically, our methods outperform strong linear and non-graph-aware baselines in non-linear settings and remain competitive even when the true rewards are linear. Our work delivers a unified, theoretically grounded, and practical framework that bridges Laplacian regularization with kernelized bandits for structured exploration.

Existing Graph Neural Networks usually learn long-distance knowledge via stacked layers or global attention, but struggle to balance cost-effectiveness and global receptive field. In this work, we break the dilemma by proposing a novel forest-based graph learning (FGL) paradigm that enables efficient long-range information propagation. Our key insight is to reinterpret message passing on a graph as transportation over spanning trees that naturally facilitates long-range knowledge aggregation, where several trees--a forest--can capture complementary topological pathways. Theoretically, we demonstrate that as edge-homophily estimates improve, the induced distribution biases towards higher-homophily trees, which enables generating a high-quality forest by refining a homophily estimator. Furthermore, we propose a linear-time tree aggregator that realizes quadratic node-pair interactions. Empirically, our framework achieves comparable results against state-of-the-art counterparts on semi-supervised node classification tasks while remaining efficient. Codes are available at \url{https://anonymous.4open.science/r/FGL/}.

Predictive modeling over relational databases (RDBs) powers applications in various domains, yet remains challenging due to the need to capture both cross-table dependencies and complex feature interactions. Recent Relational Deep Learning (RDL) methods automate feature engineering via message passing, while classical approaches like Deep Feature Synthesis (DFS) rely on predefined non-parametric aggregators. Despite promising performance gains, the comparative advantages of RDL over DFS and the design principles for selecting effective architectures remain poorly understood. We present a comprehensive study that unifies RDL and DFS in a shared design space and conducts large-scale architecture-centric searches across diverse RDB tasks. Our analysis yields three key findings: (1) RDL does not consistently outperform DFS, with performance being highly task-dependent; (2) no single architecture dominates across tasks, underscoring the need for task-aware model selection; and (3) validation accuracy is an unreliable guide for architecture choice. This search yields a curated model performance bank that links model architecture configurations to their performance; leveraging this bank, we analyze the drivers of the RDL–DFS performance gap and introduce two task signals—RDB task homophily and an affinity embedding that captures path, feature, and temporal structure—whose correlation with the gap enables principled routing. Guided by these signals, we propose Relatron, a task embedding-based meta-selector that first chooses between RDL and DFS and then prunes the within-family search to deliver strong performance. Lightweight loss-landscape metrics further guard against brittle checkpoints by preferring flatter optima. In experiments, Relatron resolves the “**more tuning, worse performance**” effect and, in joint hyperparameter–architecture optimization, achieves up to 18.5\% improvement over strong baselines with $10\times$ lower computational cost than Fisher information–based alternatives.

Molecular representations that fully capture geometric parameters such as bond angles and torsion angles are crucial for accurately predicting important molecular properties including enzyme catalytic activity, drug bioactivity, and molecular spectral characteristics, as demonstrated by extensive studies. However, current molecular graph representation learning approaches represent molecular geometric parameters only indirectly through combinations of atoms and bonds, neglecting the spatial relationships and interactions between these higher-order geometric structures. In this paper, we propose \textbf{TetraGT} (\textbf{Tetra}hedral \textbf{G}eometry-Driven Explicit \textbf{T}oken Interactions with Graph Transformer), a novel architecture that directly models molecular geometric parameters. Based on the spatial solid geometry theory of face angle and dihedral angle inequality, TetraGT explicitly represents bond angles and torsion angles as structured tokens for the first time, directly reflecting their intrinsic role in determining the molecular conformational stability and properties. Through our designed spatial tetrahedral attention mechanism, TetraGT achieves highly selective direct communication between structural tokens. Experimental results demonstrate that TetraGT achieves superior performance on the PCQM4Mv2 and OC20 IS2RE benchmarks. We also apply our pre-trained TetraGT model to downstream tasks including QM9, PDBBind, Peptides and LIT-PCBA, demonstrating that TetraGT delivers excellent results in transfer learning scenarios and shows scalability with increasing molecular size.

Relational Deep Learning (RDL) is a promising approach for building state-of-the-art predictive models on multi-table relational data by representing it as a heterogeneous temporal graph. However, commonly used Graph Neural Network models suffer from fundamental limitations in capturing complex structural patterns and long-range dependencies that are inherent in relational data. While Graph Transformers have emerged as powerful alternatives to GNNs on general graphs, applying them to relational entity graphs presents unique challenges: (i) Traditional positional encodings fail to generalize to massive, heterogeneous graphs; (ii) existing architectures cannot model the temporal dynamics and schema constraints of relational data; (iii) existing tokenization schemes lose critical structural information. Here we introduce the Relational Graph Transformer (RelGT), the first graph transformer architecture designed specifically for relational tables. RelGT employs a novel multi-element tokenization strategy that decomposes each node into five components (features, type, hop distance, time, and local structure), enabling efficient encoding of heterogeneity, temporality, and topology without expensive precomputation. Our architecture combines local attention over sampled subgraphs with global attention to learnable centroids, incorporating both local and database-wide representations. Across 21 tasks from the RelBench benchmark, RelGT consistently matches or outperforms GNN baselines by up to 18%, establishing Graph Transformers as a powerful architecture for Relational Deep Learning.

Learning dynamical systems that respect physical symmetries and constraints remains a fundamental challenge in data-driven modeling. Integrating physical laws with graph neural networks facilitates principled modeling of complex N-body dynamics and yields accurate and permutation-invariant models. However, training graph neural networks with iterative, gradient-descent-based optimization algorithms (e.g., Adam, RMSProp, LBFGS) often leads to slow training, especially for large, complex systems. In comparison to 15 different optimizers, we demonstrate that Hamiltonian Graph Networks (HGN) can be trained 150-600× faster - but with comparable accuracy - by replacing iterative optimization with random feature-based parameter construction. We show robust performance in diverse simulations, including N-body mass-spring and molecular dynamics systems in up to $3$ dimensions and 10,000 particles with different geometries, while retaining essential physical invariances with respect to permutation, rotation, and translation. Our proposed approach is benchmarked using a NeurIPS 2022 Datasets and Benchmarks Track publication to further demonstrate its versatility. We reveal that even when trained on minimal 8-node systems, the model can generalize in a zero-shot manner to systems as large as 4096 nodes without retraining. Our work challenges the dominance of iterative gradient-descent-based optimization algorithms for training neural network models for physical systems.

We study the problem of zero-shot link prediction on knowledge graphs (KGs), which requires models to generalize to novel entities and novel relations. Knowledge graph foundation models (KGFMs) address this task by enforcing equivariance over both nodes and relations, which enables them to learn structural properties of nodes and relations that transfer to novel KGs with similar structure. However, the conventional notion of deterministic equivariance inherently limits the expressive power of KGFMs, as it prevents them from distinguishing relations that are structurally similar but semantically distinct. To overcome this limitation, we propose to leverage probabilistic node-relation equivariance, which preserves equivariance in distribution while using structured randomness to break symmetries at inference time. Building on this principle, we present Flock, a KGFM that iteratively samples random walks, encodes them into sequences, embeds them with a sequence model, and aggregates node and relation representations through learned pooling. Flock respects probabilistic node-relation equivariance and, crucially, is a universal approximator for isomorphism-invariant link-level functions over KGs. Empirically, Flock perfectly solves our new diagnostic dataset Petals on which current KGFMs fail, and achieves state-of-the-art performance on entity and relation prediction tasks across 54 KGs from diverse domains. Code is available at https://github.com/jw9730/flock.

Real-world temporal data often consists of multiple signal types recorded at irregular, asynchronous intervals. For instance, in the medical domain, different types of blood tests can be measured at different times and frequencies, resulting in fragmented and unevenly scattered temporal data. Similar issues of irregular sampling occur in other domains, such as the monitoring of large systems using event log files. Effectively learning from such data requires handling sets of temporally sparse and heterogeneous signals. In this work, we propose Graph Mixing Additive Networks (GMAN), a novel and interpretable-by-design framework for learning directly from sets of graphs that represent such signals. GMAN provides diverse interpretability capabilities, including node-level, graph-level, and subset-level importance, and enables practitioners to trade finer-grained interpretability for greater expressivity when domain priors are available. GMAN achieves state-of-the-art performance in real-world high-stakes tasks, including predicting Crohn’s disease onset and hospital length of stay from routine blood test measurements and detecting fake news. Furthermore, we demonstrate how GMAN’s interpretability properties assist in revealing disease development phase transitions and provide crucial insights in the healthcare domain.