A systematic approach maps any-dimensional invariant functions to a unique function on an infinite-dimensional limit space admitting a topology with compact sets where universality holds, with examples of non-universal architectures and fixes.
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How Powerful are Graph Neural Networks?
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abstract
Graph Neural Networks (GNNs) are an effective framework for representation learning of graphs. GNNs follow a neighborhood aggregation scheme, where the representation vector of a node is computed by recursively aggregating and transforming representation vectors of its neighboring nodes. Many GNN variants have been proposed and have achieved state-of-the-art results on both node and graph classification tasks. However, despite GNNs revolutionizing graph representation learning, there is limited understanding of their representational properties and limitations. Here, we present a theoretical framework for analyzing the expressive power of GNNs to capture different graph structures. Our results characterize the discriminative power of popular GNN variants, such as Graph Convolutional Networks and GraphSAGE, and show that they cannot learn to distinguish certain simple graph structures. We then develop a simple architecture that is provably the most expressive among the class of GNNs and is as powerful as the Weisfeiler-Lehman graph isomorphism test. We empirically validate our theoretical findings on a number of graph classification benchmarks, and demonstrate that our model achieves state-of-the-art performance.
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- abstract Graph Neural Networks (GNNs) are an effective framework for representation learning of graphs. GNNs follow a neighborhood aggregation scheme, where the representation vector of a node is computed by recursively aggregating and transforming representation vectors of its neighboring nodes. Many GNN variants have been proposed and have achieved state-of-the-art results on both node and graph classification tasks. However, despite GNNs revolutionizing graph representation learning, there is limited understanding of their representational properties and limitations. Here, we present a theoretical f
co-cited works
representative citing papers
Gauge-equivariant graph neural networks embed non-Abelian local symmetries directly into message passing for lattice gauge theories, enabling learning of nonlocal observables from local operations.
BadImplant is the first multi-targeted backdoor attack on GNN graph classification that uses subgraph injection to achieve high success rates on multiple target labels with minimal clean accuracy loss.
Characterizes constituents of n-qubit graph quantum ML models and supplies a toolbox enabling integration with classical models, generalization of prior GQML approaches, and classical pre-training.
PromptGNN-sim uses GAT-based semantically aware neighborhood selection and structure-aware LLM prompts with bi-directional contrastive alignment to outperform prior GNN, LLM, and fusion methods on text-attributed graph datasets.
GILP trains a parameterized backbone for valid actions and state predictions, then uses a consistency gate with LLM drafts to reduce hallucinated-state rate from 0.176 to 0.035 on GPT-4o-mini while raising success from 0.668 to 0.838.
DS-HGNN achieves lower RMSE for stress and displacement prediction on stiffened panels than six benchmark GNN models and matches top accuracy with 19-38% fewer training samples.
AGDN is a new GNN framework using a MixScore matrix and anisotropic graph diffusion to outperform prior methods on TSP instances across sizes and distributions.
mHIP-NN extends hierarchical message-passing networks to model electron-mediated spin dynamics in disordered itinerant magnets while preserving rotational symmetry.
EpiFormer improves epitope prediction F1 score by over 40% via early-fusion cross-attention in GNN layers and sparsity-aware objectives, while recovering known biology as emergent behavior.
AbstainGNN is a framework that jointly models prediction and abstention in GNNs for graph classification, using a PAC-Bayesian-derived unified objective and two-stage training to achieve better accuracy at given rejection rates than prior abstention methods.
k-WL is incomplete on simple spectrum graphs; PRiSM is the first provably complete canonicalization for their eigendecompositions.
ConTact introduces a contact-then-act architecture with distance-biased cross-attention and contact-weighted loss for antibody CDR design, reporting 5-6% better backbone RMSD and superior contact metrics on CHIMERA-Bench splits.
Introduces the 1GC-7RC benchmark to evaluate AI coding agents on seven diverse ML tasks under single-GPU time and access constraints.
MSRL represents trajectory segments as PSD matrices to prove additive composition properties and bootstrap value functions for better transfer, reaching 0.73 AUC versus 0.57-0.65 baselines.
scShapeBench supplies synthetic and real annotated single-cell datasets across four shape categories, with scReebTower outperforming PAGA and Mapper on topology-aware metrics.
TopoU-Net is a rank-path U-Net for combinatorial complexes that encodes by lifting cochains upward along incidences, decodes by transporting downward, and merges via skip connections at matched ranks.
CTQWformer fuses continuous-time quantum walks into a graph transformer and recurrent module to outperform standard GNNs and graph kernels on classification benchmarks.
SoftBlobGIN combines ESM-2 representations with protein contact graphs via a lightweight GNN and differentiable substructure pooling to achieve 92.8% accuracy on enzyme classification, raise binding-site AUROC to 0.983, and generate auditable structural explanations without retraining the language模型
A gauge-invariant GNN using Wilson loops as inputs accurately predicts observables and simulates dynamics in Z2 and U(1) lattice gauge models.
LUMINA-Bench is a standardized evaluation framework for ACOPF surrogate models that tests generalization across multiple grid topologies using accuracy and physics-constraint metrics.
Hyperdimensional fingerprints use algebraic vector operations to create training-free molecular representations that outperform conventional fingerprints on similarity preservation and property prediction at low dimensions.
PiGGO integrates a learned graph neural ODE as the continuous-time dynamics model within an extended Kalman filter to enable online virtual sensing and uncertainty-aware state estimation for nonlinear dynamic systems with unknown model form and sparse sensing.
TF-LLMER resolves optimization barriers in LLM-enhanced recommenders through embedding normalization and Rec-PCA that aligns semantic representations with collaborative co-occurrence graphs.
citing papers explorer
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Any-Dimensional Invariant Universality
A systematic approach maps any-dimensional invariant functions to a unique function on an infinite-dimensional limit space admitting a topology with compact sets where universality holds, with examples of non-universal architectures and fixes.
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Gauge-Equivariant Graph Neural Networks for Lattice Gauge Theories
Gauge-equivariant graph neural networks embed non-Abelian local symmetries directly into message passing for lattice gauge theories, enabling learning of nonlocal observables from local operations.
-
BadImplant: Injection-based Multi-Targeted Graph Backdoor Attack
BadImplant is the first multi-targeted backdoor attack on GNN graph classification that uses subgraph injection to achieve high success rates on multiple target labels with minimal clean accuracy loss.
-
Quantum machine learning models for graphs
Characterizes constituents of n-qubit graph quantum ML models and supplies a toolbox enabling integration with classical models, generalization of prior GQML approaches, and classical pre-training.
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PromptGNN-sim: Deep Fusion and Alignment of GNN and LLMs for Text-Attributed Graph Learning
PromptGNN-sim uses GAT-based semantically aware neighborhood selection and structure-aware LLM prompts with bi-directional contrastive alignment to outperform prior GNN, LLM, and fusion methods on text-attributed graph datasets.
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Grounded Iterative Language Planning: How Parameterized World Models Reduce Hallucination Propagation in LLM Agents
GILP trains a parameterized backbone for valid actions and state predictions, then uses a consistency gate with LLM drafts to reduce hallucinated-state rate from 0.176 to 0.035 on GPT-4o-mini while raising success from 0.668 to 0.838.
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Physics-Guided Dual-Stream Heterogeneous Graph Neural Network for Predicting Full-Field Structural Response of Stiffened Panels
DS-HGNN achieves lower RMSE for stress and displacement prediction on stiffened panels than six benchmark GNN models and matches top accuracy with 19-38% fewer training samples.
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AGDN: Learning to Solve Traveling Salesman Problem with Anisotropic Graph Diffusion Network
AGDN is a new GNN framework using a MixScore matrix and anisotropic graph diffusion to outperform prior methods on TSP instances across sizes and distributions.
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Magnetic HIP-NN for spin dynamics in disordered itinerant magnets
mHIP-NN extends hierarchical message-passing networks to model electron-mediated spin dynamics in disordered itinerant magnets while preserving rotational symmetry.
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EpiFormer: Learning Antigen-Antibody Interactions for Epitope Prediction via Geometric Deep Learning
EpiFormer improves epitope prediction F1 score by over 40% via early-fusion cross-attention in GNN layers and sparsity-aware objectives, while recovering known biology as emergent behavior.
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AbstainGNN: Teaching Graph Neural Networks to Abstain for Graph Classification
AbstainGNN is a framework that jointly models prediction and abstention in GNNs for graph classification, using a PAC-Bayesian-derived unified objective and two-stage training to achieve better accuracy at given rejection rates than prior abstention methods.
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Weisfeiler-Leman Is Incomplete on Simple Spectrum Graphs, so Canonicalize Them
k-WL is incomplete on simple spectrum graphs; PRiSM is the first provably complete canonicalization for their eigendecompositions.
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ConTact: Contact-First Antibody CDR Design via Explicit Interface Reasoning
ConTact introduces a contact-then-act architecture with distance-biased cross-attention and contact-weighted loss for antibody CDR design, reporting 5-6% better backbone RMSD and superior contact metrics on CHIMERA-Bench splits.
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1GC-7RC: One Graphic Card -- Seven Research Challenges! How Good Are AI Agents at Doing Your Job?
Introduces the 1GC-7RC benchmark to evaluate AI coding agents on seven diverse ML tasks under single-GPU time and access constraints.
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Matrix-Space Reinforcement Learning for Reusing Local Transition Geometry
MSRL represents trajectory segments as PSD matrices to prove additive composition properties and bootstrap value functions for better transfer, reaching 0.73 AUC versus 0.57-0.65 baselines.
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scShapeBench: Discovering geometry from high dimensional scRNAseq data
scShapeBench supplies synthetic and real annotated single-cell datasets across four shape categories, with scReebTower outperforming PAGA and Mapper on topology-aware metrics.
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TopoU-Net: a U-Net architecture for topological domains
TopoU-Net is a rank-path U-Net for combinatorial complexes that encodes by lifting cochains upward along incidences, decodes by transporting downward, and merges via skip connections at matched ranks.
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CTQWformer: A CTQW-based Transformer for Graph Classification
CTQWformer fuses continuous-time quantum walks into a graph transformer and recurrent module to outperform standard GNNs and graph kernels on classification benchmarks.
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Structural Interpretations of Protein Language Model Representations via Differentiable Graph Partitioning
SoftBlobGIN combines ESM-2 representations with protein contact graphs via a lightweight GNN and differentiable substructure pooling to achieve 92.8% accuracy on enzyme classification, raise binding-site AUROC to 0.983, and generate auditable structural explanations without retraining the language模型
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Graph Neural Networks in the Wilson Loop Representation of Abelian Lattice Gauge Theories
A gauge-invariant GNN using Wilson loops as inputs accurately predicts observables and simulates dynamics in Z2 and U(1) lattice gauge models.
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LUMINA: A Grid Foundation Model for Benchmarking AC Optimal Power Flow Surrogate Learning
LUMINA-Bench is a standardized evaluation framework for ACOPF surrogate models that tests generalization across multiple grid topologies using accuracy and physics-constraint metrics.
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Hyper-Dimensional Fingerprints as Molecular Representations
Hyperdimensional fingerprints use algebraic vector operations to create training-free molecular representations that outperform conventional fingerprints on similarity preservation and property prediction at low dimensions.
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PiGGO: Physics-Guided Learnable Graph Kalman Filters for Virtual Sensing of Nonlinear Dynamic Structures under Uncertainty
PiGGO integrates a learned graph neural ODE as the continuous-time dynamics model within an extended Kalman filter to enable online virtual sensing and uncertainty-aware state estimation for nonlinear dynamic systems with unknown model form and sparse sensing.
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Break the Optimization Barrier of LLM-Enhanced Recommenders: A Theoretical Analysis and Practical Framework
TF-LLMER resolves optimization barriers in LLM-enhanced recommenders through embedding normalization and Rec-PCA that aligns semantic representations with collaborative co-occurrence graphs.
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Concept Graph Convolutions: Message Passing in the Concept Space
Concept Graph Convolutions perform message passing on node concepts to increase interpretability of graph neural networks without losing task performance.
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Modeling Higher-Order Brain Interactions via a Multi-View Information Bottleneck Framework for fMRI-based Psychiatric Diagnosis
A tri-view information-bottleneck model that fuses pairwise, triadic and tetradic O-information outperforms eleven baselines on four fMRI psychiatric datasets while revealing region-level synergy-redundancy patterns.
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Beyond Nodes vs. Edges: A Multi-View Fusion Framework for Provenance-Based Intrusion Detection
PROVFUSION fuses three complementary views of provenance data with lightweight schemes and voting to achieve higher detection accuracy and lower false positives than node- or edge-only baselines on nine benchmarks.
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R2G: A Multi-View Circuit Graph Benchmark Suite from RTL to GDSII
R2G is a multi-view circuit graph benchmark showing that representation choice affects GNN accuracy more than model architecture, with node-centric views and deeper decoders performing best.
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Graph Topology Information Enhanced Heterogeneous Graph Representation Learning
ToGRL learns high-quality graph structures from raw heterogeneous graphs via a two-stage topology extraction process and prompt tuning, outperforming prior methods on five datasets.
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DSBD: Dual-Aligned Structural Basis Distillation for Graph Domain Adaptation
DSBD distills a dual-aligned structural basis to adapt GNNs across graphs with structural distribution shifts, outperforming prior methods on benchmarks.
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Complex-Valued GNNs for Distributed Basis-Invariant Control of Planar Systems
Complex-valued GNNs using phase-equivariant activations achieve global basis invariance for distributed planar control, outperforming real-valued baselines in data efficiency, tracking, and generalization on flocking.
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GraphScout: Empowering Large Language Models with Intrinsic Exploration Ability for Agentic Graph Reasoning
GraphScout trains LLMs to autonomously synthesize structured training data from knowledge graphs via flexible exploration tools, enabling a 4B model to outperform larger LLMs by 16.7% on average with fewer inference tokens and strong cross-domain transfer.
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Graph Property Inference in Small Language Models: Effects of Representation and Reasoning Strategy
Small instruction-tuned language models cannot reliably estimate graph-theoretic properties from textual encodings, though adjacency-list formats and multi-branch reasoning reduce errors relative to edge lists and single-path inference.
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DisRFM: Polar Riemannian Flow Matching for Structure-Preserving Graph Domain Adaptation
DisRFM uses polar Riemannian flow matching on constant-curvature manifolds to align graph domains while preserving label-relevant topology via radial Wasserstein and angular confidence matching.
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Cross-Paradigm Graph Backdoor Attacks with Promptable Subgraph Triggers
CP-GBA distills a queryable repository of promptable subgraph triggers via graph prompt learning to achieve transferable backdoor attacks on GNNs with state-of-the-art success rates across paradigms and defenses.
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Estimation--Prediction Tradeoff in Causal Probabilistic Temporal Graphs
Characterizes an estimation-prediction tradeoff in binary logistic models for causal probabilistic temporal graphs and proposes a framework to jointly evaluate temporal link prediction with causal parameter recovery via Cramér-Rao bounds.
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hia-gat: A Heterogeneous Interaction-Aware Graph Attention Network For Frame-Level Traffic Conflict Risk Prediction On Freeways
HIA-GAT, a heterogeneous graph attention network with conflict-type-aware gating, reports the highest AUC for frame-level risk prediction on NGSIM I-80 and US-101 datasets, with largest gains on lateral (PET) conflicts.
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Scalable Message-Passing Quantum Graph Neural Networks in the Weisfeiler-Leman Hierarchy
The work constructs a permutation-equivariant quantum GNN that implements message passing at selectable Weisfeiler-Leman levels, supports pre-training on small graphs, and demonstrates readout scalability with simulations up to 56 qubits on synthetic, molecular, and TSP datasets.
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MMGNN: Multi-level, multi-color graph neural networks for molecular property prediction
MMGNN decomposes molecular graphs into multi-color subgraphs by atom-type pairs and applies shared message-passing per subgraph, achieving top macro AUC-ROC of 0.838 on classification and best RMSE on ESOL and FreeSolv among tested models.
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Temporal Motif Signatures for Temporal Graph Neural Networks
A 13-coordinate leakage-safe motif feature map derived from three empirical axes of temporal motif activity improves TGNN performance on link prediction and edge classification across multiple real and synthetic datasets.
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T-GINEE: A Tensor-Based Multilayer Graph Representation Learning
T-GINEE combines CP tensor decomposition with a generalized estimating equation framework and task-specific loss to explicitly model inter-layer correlations in multilayer graphs while providing consistency and asymptotic normality guarantees under mild conditions.
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Provably Communication-Efficient and Privacy-Preserving Federated Graph Neural Networks
CE-FedGNN enables federated GNN training on coupled distributed graphs via infrequent aggregated representation exchange, moving-average estimation for staleness, and metric-DP, with O(1/sqrt(T)) convergence and O(T^{3/4}) communication.
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fMRI-Diffusion: Generating fMRI Time Series Via a Temporal Transformer Diffusion Model for Major Depressive Disorder Diagnosis
fMRI-Diffusion generates synthetic ROI-level fMRI time series via a temporal transformer diffusion model with supervised pretraining, improving MDD diagnostic accuracy by up to 3.7 percentage points over prior FC-matrix synthesis methods on the REST-meta-MDD dataset.
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AgForce Enables Antigen-conditioned Generative Antibody Design
AgForce improves antigen-conditioned antibody design by using framework dropout, gated bottlenecks, hyperbolic cross attention, MDN sequence head with Potts-like coupling, annealed MCL, and antigen cycle consistency to achieve 8% better amino acid recovery and superior binding metrics on CHIMERA-BEN
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EvoStruct: Bridging Evolutionary and Structural Priors for Antibody CDR Design via Protein Language Model Adaptation
EvoStruct integrates evolutionary priors from a protein language model with structural priors from an E(3)-equivariant GNN to raise amino acid recovery by 16% and diversity by 2.3x on CHIMERA-Bench while cutting perplexity 43%.
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Multi-level Self-supervised Pretraining on Compositional Hierarchical Graph for Molecular Property Prediction
MolCHG uses a multi-level compositional hierarchical graph with atom-bond cross-view contrastive learning, functional group prediction, and structure tasks to achieve top results on seven of nine MoleculeNet benchmarks.
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Rethinking Efficient Graph Coarsening via a Non-Selfishness Principle
NOPE coarsens graphs via neighborhood interference rather than selfish pairwise matching to reach linear memory and near-linear time, with NOPE* variant delivering 1.8-10x speedups and comparable or better learning results than full graphs or LLM reasoning.
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Learning the Interaction Prior for Protein-Protein Interaction Prediction: A Model-Agnostic Approach
L3-PPI reformulates PPI pair classification as graph classification over a prompt graph with controlled virtual L3 paths to inject the biological interaction prior and boost performance on existing models.
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Fairness of Explanations in Artificial Intelligence (AI): A Unifying Framework, Axioms, and Future Direction toward Responsible AI
A conditional invariance framework defines explanation fairness as explanations being statistically independent of protected attributes given task-relevant features, unifying existing metrics and enabling procedural bias audits.
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Quantum Injection Pathways for Implicit Graph Neural Networks
Independent quantum signal injection into graph DEQs yields higher test accuracy and fewer solver iterations than state-dependent or backbone-dependent injection and classical equilibrium models on NCI1, PROTEINS, and MUTAG benchmarks.