Graph Neural Networks

Also known as GNN

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Graph Neural Networks (GNNs) study how to learn from data whose entities and relationships form a graph, supporting tasks such as node classification, link prediction, and graph or molecular property prediction. Common approaches include message-passing networks such as GCN, GraphSAGE, and GIN, attention-based Graph Transformers, and spectral, geometric, or higher-order methods that encode richer structure. They are used on benchmarks such as Cora and ogbn-arxiv, as well as in molecular modeling, recommender systems, scientific simulation, and network control. Key open challenges include handling heterophilic graphs, preserving useful information in deep networks without oversmoothing or oversquashing, and achieving reliable generalization, robustness, and efficiency on large or shifting graphs.

Latest papers

751 papers73 papers in the last four weeks, down 13% on the four weeks before. 0.5% of all new papers.

Feb 19, 2026

COMBA: Cross Batch Aggregation for Learning Large Graphs with Context Gating State Space Models

State space models (SSMs) have recently emerged for modeling long-range dependency in sequence data, with much simplified computational costs than modern alternatives, such as transformers. Advancing SMMs to graph structured data, especially for large graphs, is a significant challenge because SSMs are sequence models and the shear graph volumes make it very expensive to convert graphs as sequences for effective learning. In this paper, we propose COMBA to tackle large graph learning using state space models, with two key innovations: graph context gating and cross batch aggregation. Graph context refers to different hops of neighborhood for each node, and graph context gating allows COMBA to use such context to learn best control of neighbor aggregation. For each graph context, COMBA samples nodes as batches, and train a graph neural network (GNN), with information being aggregated cross batches, allowing COMBA to scale to large graphs. Our theoretical study asserts that cross-batch aggregation guarantees lower error than training GNN without aggregation. Experiments on benchmark networks demonstrate significant performance gains compared to baseline approaches. Code and benchmark datasets will be released for public access.

Jiajun Shen, Yufei Jin, Yi He +1

Florida Atlantic University · William & Mary

Graph Representation Learning Graph Neural Networks State Space Models

Feb 19, 2026

A Benchmark Analysis of Graph and Non-Graph Methods for Caenorhabditis Elegans Neuron Classification

This study establishes a benchmark for Caenorhabditis elegans neuron classification, comparing four graph methods (GCN, GraphSAGE, GAT, GraphTransformer) against four non-graph methods (Logistic Regression, MLP, LOLCAT, NeuPRINT). Using the functional connectome, we classified Sensory, Interneuron, and Motor neurons based on Spatial, Connection, and Neuronal Activity features. Results show that attention-based GNNs significantly outperform baselines on the Spatial and Connection features. The Neuronal Activity features yielded poor performance, likely due to the low temporal resolution of the underlying neuronal activity data. Our benchmark validates the use of GNNs and highlights that Spatial and Connection features are key predictors for Caenorhabditis elegans neuron classes. Code is available at: https://github.com/JingqiLuu/neuronclf-gnn-benchmark.

Jingqi Lu, Keqi Han, Yun Wang +2

Department of Computer Science, Emory University, USA · Department of Biomedical Informatics, Emory University, USA · College of AI, Tsinghua University, China

Classification Node Classification Graph Neural Networks Graph Attention Networks

Feb 19, 2026

Semi-Supervised Learning on Graphs using Graph Neural Networks

Graph neural networks (GNNs) work remarkably well in semi-supervised node regression, yet a rigorous theory explaining when and why they succeed remains lacking. To address this gap, we study an aggregate-and-readout model that encompasses several common message passing architectures: node features are first propagated over the graph then mapped to responses via a nonlinear function. For least-squares estimation over GNNs with linear graph convolutions and a deep ReLU readout, we prove a sharp non-asymptotic risk bound that separates approximation, stochastic, and optimization errors. The bound makes explicit how performance scales with the fraction of labeled nodes and graph-induced dependence. Approximation guarantees are further derived for graph-smoothing followed by smooth nonlinear readouts, yielding convergence rates that recover classical nonparametric behavior under full supervision while characterizing performance when labels are scarce. Numerical experiments validate our theory, providing a systematic framework for understanding GNN performance and limitations.

Juntong Chen, Claire Donnat, Olga Klopp +1

School of Mathematical Sciences, Xiamen University · Department of Statistics, University of Chicago · ESSEC Business School +1

Graph Neural Networks Graph-Based Semi-Supervised Learning Statistical Learning Theory

Feb 19, 2026

A Locality Radius Framework for Understanding Relational Inductive Bias in Database Learning

Foreign key discovery and related schema-level prediction tasks are often modeled using graph neural networks (GNNs), implicitly assuming that relational inductive bias improves performance. However, it remains unclear when multi-hop structural reasoning is actually necessary. In this work, we introduce locality radius, a formal measure of the minimum structural neighborhood required to determine a prediction in relational schemas. We hypothesize that model performance depends critically on alignment between task locality radius and architectural aggregation depth. We conduct a controlled empirical study across foreign key prediction, join cost estimation, blast radius regression, cascade impact classification, and additional graph-derived schema tasks. Our evaluation includes multi-seed experiments, capacity-matched comparisons, statistical significance testing, scaling analysis, and synthetic radius-controlled benchmarks. Results reveal a consistent bias-radius alignment effect.

Aadi Joshi, Kavya Bhand

Dept. of Computer Engineering, Vishwakarma Institute of Technology, Pune, India.

Relational Deep Learning Graph Neural Networks

Feb 19, 2026

AdvSynGNN: Structure-Adaptive Graph Neural Nets via Adversarial Synthesis and Self-Corrective Propagation

Graph neural networks frequently encounter significant performance degradation when confronted with structural noise or non-homophilous topologies. To address these systemic vulnerabilities, we present AdvSynGNN, a comprehensive architecture designed for resilient node-level representation learning. The proposed framework orchestrates multi-resolution structural synthesis alongside contrastive objectives to establish geometry-sensitive initializations. We develop a transformer backbone that adaptively accommodates heterophily by modulating attention mechanisms through learned topological signals. Central to our contribution is an integrated adversarial propagation engine, where a generative component identifies potential connectivity alterations while a discriminator enforces global coherence. Furthermore, label refinement is achieved through a residual correction scheme guided by per-node confidence metrics, which facilitates precise control over iterative stability. Empirical evaluations demonstrate that this synergistic approach effectively optimizes predictive accuracy across diverse graph distributions while maintaining computational efficiency. The study concludes with practical implementation protocols to ensure the robust deployment of the AdvSynGNN system in large-scale environments.

Rong Fu, Chunlei Meng, Shuo Yin +2

Independent Researcher

Graph Neural Networks Graph Structure Learning Graph Transformer

Feb 18, 2026

Hardware-accelerated graph neural networks: an alternative approach for neuromorphic event-based audio classification and keyword spotting on SoC FPGA

As the volume of data recorded by embedded edge sensors increases, particularly from neuromorphic devices producing discrete event streams, there is a growing need for hardware-aware neural architectures that enable efficient, low-latency, and energy-conscious local processing. We present an FPGA implementation of event-graph neural networks for audio processing. We utilise an artificial cochlea that converts time-series signals into sparse event data, reducing memory and computation costs. Our architecture was implemented on a SoC FPGA and evaluated on two open-source datasets. For classification task, our baseline floating-point model achieves 92.7% accuracy on SHD dataset - only 2.4% below the state of the art - while requiring over 10x and 67x fewer parameters. On SSC, our models achieve 66.9-71.0% accuracy. Compared to FPGA-based spiking neural networks, our quantised model reaches 92.3% accuracy, outperforming them by up to 19.3% while reducing resource usage and latency. For SSC, we report the first hardware-accelerated evaluation. We further demonstrate the first end-to-end FPGA implementation of event-audio keyword spotting, combining graph convolutional layers with recurrent sequence modelling. The system achieves up to 95% word-end detection accuracy, with only 10.53 microsecond latency and 1.18 W power consumption, establishing a strong benchmark for energy-efficient event-driven KWS.

Kamil Jeziorek, Piotr Wzorek, Krzysztof Blachut +6

The AGH University of Krakow, Poland · Graduate School of Science and Technology, Keio University, Japan · CEA-List, Université Grenoble Alpes, France

Audio Classification Keyword Spotting Graph Neural Networks FPGA-Based Neural Network Acceleration Neuromorphic Computing

Feb 18, 2026

Graph neural network for colliding particles with an application to sea ice floe modeling

This paper introduces a novel approach to sea ice modeling using Graph Neural Networks (GNNs), utilizing the natural graph structure of sea ice, where nodes represent individual ice pieces, and edges model the physical interactions, including collisions. This concept is developed within a one-dimensional framework as a foundational step. Traditional numerical methods, while effective, are computationally intensive and less scalable. By utilizing GNNs, the proposed model, termed the Collision-captured Network (CN), integrates data assimilation (DA) techniques to effectively learn and predict sea ice dynamics under various conditions. The approach was validated using synthetic data, both with and without observed data points, and it was found that the model accelerates the simulation of trajectories without compromising accuracy. This advancement offers a more efficient tool for forecasting in marginal ice zones (MIZ) and highlights the potential of combining machine learning with data assimilation for more effective and efficient modeling.

Ruibiao Zhu

College of Systems and Society, The Australian National University, ACT, 2600, Australia.

Graph Neural Networks Physics-Based Simulation

Feb 18, 2026

Investigating GNN Convergence on Large Randomly Generated Graphs with Realistic Node Feature Correlations

There are a number of existing studies analysing the convergence behaviour of graph neural networks on large random graphs. Unfortunately, the majority of these studies do not model correlations between node features, which would naturally exist in a variety of real-life networks. Consequently, the derived limitations of GNNs, resulting from such convergence behaviour, is not truly reflective of the expressive power of GNNs when applied to realistic graphs. In this paper, we will introduce a novel method to generate random graphs that have correlated node features. The node features will be sampled in such a manner to ensure correlation between neighbouring nodes. As motivation for our choice of sampling scheme, we will appeal to properties exhibited by real-life graphs, particularly properties that are captured by the Barabási-Albert model. A theoretical analysis will strongly indicate that convergence can be avoided in some cases, which we will empirically validate on large random graphs generated using our novel method. The observed divergent behaviour provides evidence that GNNs may be more expressive than initial studies would suggest, especially on realistic graphs.

Mohammed Zain Ali Ahmed

Graph Neural Networks GNN Expressivity Graph Generation

Feb 17, 2026

Beyond ReLU: Bifurcation, Oversmoothing, and Topological Priors

Graph Neural Networks (GNNs) learn node representations through iterative network-based message-passing. While powerful, deep GNNs suffer from oversmoothing, where node features converge to a homogeneous, non-informative state. We re-frame this problem of representational collapse from a bifurcation theory perspective, characterizing oversmoothing as convergence to a stable ``homogeneous fixed point.'' Our central contribution is the theoretical discovery that this undesired stability can be broken by replacing standard monotone activations (e.g., ReLU) with a class of functions. Using Lyapunov-Schmidt reduction, we analytically prove that this substitution induces a bifurcation that destabilizes the homogeneous state and creates a new pair of stable, non-homogeneous patterns that provably resist oversmoothing. Our theory predicts a precise, nontrivial scaling law for the amplitude of these emergent patterns, which we quantitatively validate in experiments. Finally, we demonstrate the practical utility of our theory by deriving a closed-form, bifurcation-aware initialization and showing its utility in real benchmark experiments.

Erkan Turan, Gaspard Abel, Maysam Behmanesh +2

LIX, Ecole Polytechnique, IP Paris · Université Paris Saclay, Université Paris Cité, ENS Paris Saclay, CNRS, SSA, INSERM, Centre Borelli, F-91190, Gif-sur-Yvette, France · Centre d’Analyse et de Mathématique Sociales, EHESS, CNRS, 75006 Paris, France..

GNN Oversmoothing Graph Neural Networks Over-Smoothing in GNNs Neural Network Activation Functions

Feb 17, 2026

On the Geometric Coherence of Global Aggregation in Federated Graph Neural Networks

Federated learning over graph-structured data exposes a fundamental mismatch between standard aggregation mechanisms and the operator nature of graph neural networks (GNNs). While federated optimization treats model parameters as elements of a shared Euclidean space, GNN parameters induce graph-dependent message-passing operators whose semantics depend on underlying topology. Under structurally and distributionally heterogeneous client graph distributions, local updates correspond to perturbations of distinct operator manifolds. Linear aggregation of such updates mixes geometrically incompatible directions, producing global models that converge numerically yet exhibit degraded relational behavior. We formalize this phenomenon as a geometric failure of global aggregation in cross-domain federated GNNs, characterized by destructive interference between operator perturbations and loss of coherence in message-passing dynamics. This degradation is not captured by conventional metrics such as loss or accuracy, as models may retain predictive performance while losing structural sensitivity. To address this, we propose GGRS (Global Geometric Reference Structure), a server-side aggregation framework operating on a data-free proxy of operator perturbations. GGRS enforces geometric admissibility via directional alignment, subspace compatibility, and sensitivity control, preserving the structure of the induced message-passing operator.

Chethana Prasad Kabgere, Shylaja SS

Department of Computer Science and Engineering, PES University, Bengaluru, Karnataka, 560085, India

Federated Graph Learning Federated Learning Aggregation Graph Neural Networks Heterogeneous Federated Learning

Feb 13, 2026

Learning to Approximate Uniform Facility Location via Graph Neural Networks

Neural networks, particularly message-passing neural networks (MPNNs), are increasingly used as heuristics for hard combinatorial optimization problems. Yet many learning-based methods rely on supervision, reinforcement learning, or gradient estimators, causing high computational cost, unstable training, or limited guarantees. Classical approximation algorithms provide worst-case guarantees but are non-differentiable and cannot adapt to structure in natural input distributions. We study this tradeoff through Uniform Facility Location (UniFL), a problem with applications in clustering, summarization, logistics, and supply chains. We propose a fully differentiable MPNN that incorporates approximation-algorithmic principles without solver supervision or discrete relaxations. The model has provable approximation guarantees and empirically improves on standard approximation algorithms, narrowing the gap to integer linear programming.

Chendi Qian, Christopher Morris, Stefanie Jegelka +1

RWTH Aachen University, Germany · Technical University of Munich, Germany · Massachusetts Institute of Technology, USA +1

Graph Neural Networks Combinatorial Optimization Message Passing Neural Networks Approximation Algorithms Neural Combinatorial Optimization

Feb 5, 2026

Smoothness Errors in Dynamics Models and How to Avoid Them

Modern neural networks have shown promise for solving partial differential equations over surfaces, often by discretizing the surface as a mesh and learning with a mesh-aware graph neural network. However, graph neural networks suffer from oversmoothing, where a node's features become increasingly similar to those of its neighbors. Unitary graph convolutions, which are mathematically constrained to preserve smoothness, have been proposed to address this issue. Despite this, in many physical systems, such as diffusion processes, smoothness naturally increases and unitarity may be overconstraining. In this paper, we systematically study the smoothing effects of different GNNs for dynamics modeling and prove that unitary convolutions hurt performance for such tasks. We propose relaxed unitary convolutions that balance smoothness preservation with the natural smoothing required for physical systems. We also generalize unitary and relaxed unitary convolutions from graphs to meshes. In experiments on PDEs such as the heat and wave equations over complex meshes and on weather forecasting, we find that our method outperforms several strong baselines, including mesh-aware transformers and equivariant neural networks.

Edward Berman, Luisa Li, Jung Yeon Park +1

Geometric Learning Lab, Northeastern University.

Graph Neural Networks Over-Smoothing in GNNs PDE Solving

Jan 29, 2026

Breaking the Reasoning Horizon in Entity Alignment Foundation Models

Entity alignment (EA) is critical for knowledge graph (KG) fusion. Existing EA models lack transferability and are incapable of aligning unseen KGs without retraining. While using graph foundation models (GFMs) offer a solution, we find that directly adapting GFMs to EA remains largely ineffective. This stems from a critical "reasoning horizon gap": unlike link prediction in GFMs, EA necessitates capturing long-range dependencies across sparse and heterogeneous KG structuresTo address this challenge, we propose a EA foundation model driven by a parallel encoding strategy. We utilize seed EA pairs as local anchors to guide the information flow, initializing and encoding two parallel streams simultaneously. This facilitates anchor-conditioned message passing and significantly shortens the inference trajectory by leveraging local structural proximity instead of global search. Additionally, we incorporate a merged relation graph to model global dependencies and a learnable interaction module for precise matching. Extensive experiments verify the effectiveness of our framework, highlighting its strong generalizability to unseen KGs.

Yuanning Cui, Zequn Sun, Wei Hu +2

1Nanjing University of Information Science and Technology · 2State Key Laboratory for Novel Software Technology, Nanjing University · 3National Institute of Healthcare Data Science, Nanjing University, Nanjing +2

Graph Neural Networks Graph Foundation Models KG Entity Alignment

Jan 27, 2026

FloydNet: A Learning Paradigm for Global Relational Reasoning

Learning algorithmic computation often requires explicit relational intermediate states, yet many graph processors maintain their primary states on individual entities. We introduce \fnet and Pivotal Attention (PA), which maintain ordered pair states and update a target relation

(i,k)

by attending over candidates formed from

(i,j)

and

(j,k)

for every pivot

j

. Motivated by the pair-and-pivot structure of Floyd--Warshall, PA learns relation composition and pivot weighting in parallel rather than executing its ordered min-plus recurrence. The \kfnet{k} framework extends this operation to ordered

k

-tuples, with Self-Attention and PA as its

k=1

and

k=2

cases at the attention-operation level. Under atomic tuple initialization and invariant readout, we show that \kfnet{k} is no more graph-discriminative than k-FWL; on BREC, each evaluated variant matches the success set of its corresponding WL reference. \fnet further achieves 96.64% mean accuracy under the reported CLRS-30 protocol and a 99.8% optimality rate with 10 samples on held-out non-metric TSP instances.

Jingcheng Yu, Mingliang Zeng, Qiwei Ye

Beijing Academy of Artificial Intelligence

Graph Neural Networks Relational Reasoning Relational Deep Learning Higher-Order GNNs Algorithmic Reasoning

Jan 19, 2026

Graph Neural Networks are Heuristics

Graph neural networks are usually treated as auxiliaries for combinatorial optimization: they imitate algorithms, guide search, or supply scores to classical procedures. We show that this auxiliary role is not intrinsic. A GNN can itself be a heuristic. For the Euclidean Travelling Salesman Problem, we train a non-autoregressive GNN with no labels, rewards, sequential decoding, search, or local improvement. A differentiable Hamiltonian-cycle objective is the only supervision. The trained model produces a complete tour in one forward pass, while dropout and snapshots from a single training trajectory provide solution diversity without engineered moves. The heuristic is therefore learned, not programmed. It is also fast: batched inference remains in the millisecond regime on GPUs. Experiments on TSP100, TSP200, and TSP500 show that the model consistently improves over nearest-neighbor greedy baselines. These results identify unsupervised GNNs as a class of fast learned heuristics for combinatorial optimization.

Yimeng Min, Carla P. Gomes

Department of Computer Science Cornell University Ithaca, NY, USA

Traveling Salesperson Problem Graph Neural Networks Combinatorial Optimization Neural Combinatorial Optimization

Jan 8, 2026

A General Neural Backbone for Mixed-Integer Linear Optimization via Dual Attention

Mixed-integer linear programming (MILP) is a foundational framework for combinatorial optimization across science and engineering, but remains hard to solve at scale due to NP-hardness. Recent learning-based methods typically model MILP instances as variable-constraint bipartite graphs and use Graph Neural Networks (GNNs) for representation learning, yet their locality limits representation power. We propose an attention-driven neural backbone that adopts an element-centric view of variables and constraints, with dual attention performing parallel intra-type self-attention and inter-type cross-attention. Across three representative tasks at the instance, element, and solving-state levels, our model consistently outperforms conventional GNN-based architectures, highlighting attention-based, element-centric modeling as a powerful foundation for learning-enhanced combinatorial optimization.

Peixin Huang, Yaoxin Wu, Yining Ma +3

Shenzhen Research Institute, Shandong University, China

Graph Neural Networks Mixed-Integer Linear Programming Linear Programming Neural Combinatorial Optimization Integer Linear Programming

Dec 20, 2025

Through the PRISm: Importance-Aware Scene Graphs for Semantic Image Retrieval

Web-based visual search increasingly handles queries driven by semantic intent, focusing on what is happening in an image rather than merely what it looks like. While global embeddings from vision-language models capture overall appearance, they often blur fine-grained relational structure. Conversely, scene graphs make these relationships explicit, but generating them automatically for unannotated web images produces dense, noisy graphs that retain every detected entity and relation regardless of relevance. To address this, we introduce PRISm (Pruning-based Image Retrieval via Importance Prediction on Semantic Graphs), an image-to-image retrieval framework that learns to focus on what matters in a scene. PRISm employs an Importance Prediction Module, supervised by caption-derived relevance strictly during training, to score and prune non-essential objects and <subject, relation, object> triplets. An Edge-Aware Contextual GNN then aggregates relation conditioned neighbor messages, fusing the refined graph with global visual features into a single, index-ready embedding per image. On PSG, PRISm outperforms the strongest baseline by points in MAP@1. Furthermore, on Flickr with machine-generated scene graphs and captions, PRISm remains best on top-1 metrics, while adding only 33,ms per query beyond scene graph generation.

Dimitrios Georgoulopoulos, Nikolaos Chaidos, Angeliki Dimitriou +1

National Technical University of Athens Athens, Greece

Image Retrieval Graph-Based Retrieval Graph Representation Learning Graph Neural Networks

Nov 17, 2025

FuseSampleAgg: One-Pass Neighborhood Estimation for Budgeted Knowledge-Graph Refresh and Validation

Operational knowledge-graph (KG) pipelines in networking and cybersecurity increasingly need to refresh embeddings under strict time, memory, and audit budgets, especially as curated feeds and LLM-assisted extraction accelerate KG updates. A recurring per-step cost in mini-batch KG learning is neighborhood-context estimation: uniform neighbor sampling without replacement followed by mean aggregation. Common frameworks implement this estimator through sampled-subgraph materialization and intermediate feature gathers, adding kernel launches, allocator pressure, and transient memory spikes. We present One-Pass Neighborhood Estimation, a fused PyTorch CUDA operator that samples neighbors and directly emits the sampled-neighborhood mean, avoiding explicit block construction while preserving GraphSAGE-mean semantics for the same sampled neighbor IDs. It supports seed-controlled sampling and optional saved-index replay for reproducible validation and regression testing. Across large-graph mini-batch workloads, it improves FP32 end-to-end step latency by 2.24x-3.48x over tuned DGL baselines and reduces transient GPU memory by up to 160x in our measurements. On OGB KG completion benchmarks such as WikiKG2 and BioKG, it reduces step time and peak VRAM while matching ranking quality within seed variability, improving time-to-quality for budgeted KG refresh.

Aleksandar Stanković, Haoran Du, Xinming Wang

University of Novi Sad, Novi Sad, Serbia · Shanghai Key Lab of Intelligent Information Processing,2026 College of Computer Science and Artificial Intelligence, Fudan University, China · Institute of Automation, Chinese Academy of Sciences, China

Graph Neural Networks GPU Kernel Optimization

Nov 14, 2025

Enhancing Graph Representations with Neighborhood-Contextualized Message-Passing

Graph neural networks (GNNs) have become an indispensable tool for analyzing relational data. Classical GNNs are broadly classified into three variants: convolutional, attentional, and message-passing. While the standard message-passing variant is expressive, its typical pair-wise messages only consider the features of the center node and each neighboring node individually. This design fails to incorporate contextual information contained within the broader local neighborhood, potentially hindering its ability to learn meaningful relationships within the entire set of neighboring nodes. To address this, the paper first refines the concept of neighborhood-contextualization within GNNs, leveraging ideas from set-based aggregation methods and a key property of the attentional variant. This then serves as the basis for generalizing the message-passing variant to the proposed neighborhood-contextualized message-passing (NCMP) framework. To demonstrate its utility, a simple, mathematically grounded method to parametrize and operationalize NCMP is presented, leading to the development of the proposed Soft-Isomorphic Neighborhood-Contextualized Graph Convolution Network (SINC-GCN). Across a diverse set of synthetic and benchmark datasets, SINC-GCN strikes a highly favorable balance between expressivity and efficiency. Notably, while more complex models incur significant computational overhead, SINC-GCN delivers substantial performance gains with considerable effect sizes over baseline GNN models while maintaining a highly efficient asymptotic runtime complexity, further underscoring the distinctive utility of neighborhood-contextualization. Overall, by integrating multiset neighborhood context, the proposed NCMP framework serves as a practical and scalable path toward enhancing the graph representational power of classical GNNs.

Brian Godwin Lim, Galvin Brice Lim, Renzo Roel Tan +2

Nara Institute of Science and Technology, Kyoto University, and Ateneo de Manila University · UNI-President Information Philippines Corporation · Nara Institute of Science and Technology and Ateneo de Manila University +2

Graph Neural Networks Graph Representation Learning GNN Expressivity Message Passing Neural Networks

Nov 14, 2025

GraphToxin: Reconstructing Full Unlearned Graphs from Graph Unlearning

Graph unlearning (GU) has emerged as a promising solution to comply with "the right to be forgotten" regulations by enabling the removal of sensitive information upon request. However, this solution is not foolproof. The involvement of multiple parties creates new attack surfaces, and residual traces of deleted data can persist within the unlearned graph neural networks (GNNs). These vulnerabilities can be exploited by attackers to recover the supposedly erased samples, undermining the intended functionality of GU. In this work, we propose GraphToxin, the first full graph reconstruction attack against GU. We show that GraphToxin can recover not only a deleted individual's information and personal links but also sensitive content of their neighbors, thereby posing substantially more detrimental threats than prior membership inference attacks (MIAs). Specifically, we introduce a novel curvature matching module to provide fine-grained guidance for full unlearned graph recovery. We further extend GraphToxin to multiple-node removal under both white-box and black-box settings, showcasing its practical feasibility and potential to cause considerable harm. We highlight the necessity of worst-case analysis and propose a systematic evaluation framework to assess attack performance under both random and worst-case node removal scenarios. Our extensive experiments demonstrate the effectiveness and flexibility of GraphToxin. Notably, current defense mechanisms are largely ineffective against this attack. Additionally, our findings reveal that existing GU verification standards based on MIAs can be misleading: they achieve membership-level protection, while the full unlearned graph remains recoverable through GraphToxin.

Ying Song, Balaji Palanisamy

University of Pittsburgh Pittsburgh, PA, USA

Graph Neural Networks Graph Unlearning Machine Unlearning

Oct 29, 2025

Robust GNN Watermarking via Implicit Perception of Topological Invariants

Graph Neural Networks (GNNs) represent valuable intellectual property, yet watermarks based on out-of-distribution triggers can weaken under pruning, fine-tuning, and distillation. We present InvGNN-WM, which links ownership verification to graph-invariant prediction. By supervising a shared GNN backbone to predict normalized algebraic connectivity on owner-private carrier graphs, InvGNN-WM enables calibrated multi-bit black-box verification through either an auxiliary scalar endpoint or a fixed owner-side decoder of ordinary task logits. We provide conditional guarantees for task-loss control, decision preservation, and key separation, and prove NP-completeness of the exact-removal decision problem for a restricted class of monotone separable decoders. Experiments on node- and graph-classification benchmarks demonstrate high watermark fidelity with small changes in task performance. The task-logit deployment achieves higher detection rates than PreGIP-adapted in matched comparisons and retains detection under the evaluated extraction and retraining budgets. Watermark-assisted distillation further enables owner-side recovery using private verification material.

Jipeng Li, Yanning Shen

Department of Electrical and Computer Engineering, University of California, Davis, Davis, CA 95616, USA · Department of Electrical Engineering and Computer Science, University of California, Irvine, Irvine, CA 92697, USA

GNN Watermarking Robust Watermarking Multi-Bit Watermarking Graph Neural Networks

Oct 22, 2025

PRGCN: A Graph Memory Network for Cross-Sequence Pattern Reuse in 3D Human Pose Estimation

Monocular 3D human pose estimation remains a fundamentally ill-posed inverse problem due to the inherent depth ambiguity in 2D-to-3D lifting. While contemporary video-based methods leverage temporal context to enhance spatial reasoning, they operate under a critical paradigm limitation: processing each sequence in isolation, thereby failing to exploit the strong structural regularities and repetitive motion patterns that pervade human movement across sequences. This work introduces the Pattern Reuse Graph Convolutional Network (PRGCN), a novel framework that formalizes pose estimation as a problem of pattern retrieval and adaptation. At its core, PRGCN features a graph memory bank that learns and stores a compact set of pose prototypes, encoded as relational graphs, which are dynamically retrieved via an attention mechanism to provide structured priors. These priors are adaptively fused with hard-coded anatomical constraints through a memory-driven graph convolution, ensuring geometrical plausibility. To underpin this retrieval process with robust spatiotemporal features, we design a dual-stream hybrid architecture that synergistically combines the linear-complexity, local temporal modeling of Mamba-based state-space models with the global relational capacity of self-attention. Extensive evaluations on Human3.6M and MPI-INF-3DHP benchmarks demonstrate that PRGCN establishes a new state-of-the-art, achieving an MPJPE of 37.1mm and 13.4mm, respectively, while exhibiting enhanced cross-domain generalization capability. Our work posits that the long-overlooked mechanism of cross-sequence pattern reuse is pivotal to advancing the field, shifting the paradigm from per-sequence optimization towards cumulative knowledge learning.

Zhuoyang Xie, Yibo Zhao, Hui Huang +2

College of Computer Science and Artificial Intelligence, Wenzhou University, Wenzhou, 325035, P.R China. · the Key Laboratory of Computer Vision and System, Ministry of Education, Tianjin University of Technology, Tianjin, 300384, China. · School of Data Science and Artificial Intelligence, Wenzhou University of Technology, Wenzhou, 325000, P.R China. +1

Memory-Augmented Neural Networks Graph Neural Networks 3D Human Pose Estimation

Oct 13, 2025

Variational Mixture of Graph Neural Experts for Alzheimer's Disease Recognition across Frequency Bands in EEG Brain Networks

Dementia disorders such as Alzheimer's disease (AD) and frontotemporal dementia (FTD) exhibit overlapping electrophysiological signatures in EEG that challenge accurate diagnosis. Existing EEG-based methods are limited by full-band frequency analysis, which hinders the precise differentiation of dementia subtypes and severity stages. To address this limitation, we propose a Variational Mixture of Graph Neural Experts (VMoGE) framework that integrates multi-band EEG analysis with variational graph neural networks and a mixture-of-experts architecture. Each expert specializes in a specific EEG frequency band and models brain connectivity using a Gaussian Markov random field prior, while a variational gating mechanism adaptively integrates the expert outputs. This design enables the model to learn frequency-specific brain network representations while modeling latent uncertainty through variational inference. Experimental results on two EEG dementia datasets show that VMoGE achieves strong performance, with an AUC of 0.89 for HC vs. AD classification in the main comparison and competitive results across dementia subtyping and CDR staging tasks. Clinically, VMoGE offers three key translational values: the expert gating weights correlate with MMSE scores and CDR severity; slow-wave

δ

- and

θ

-band contributions are associated with AD-related EEG slowing and disease progression; and spatially localized activation maps reveal posterior

θ

- and

α

-band alterations and region-specific

β

-band changes, providing neurophysiologically interpretable markers aligned with known AD neuropathology.

Jun-En Ding, Anna Zilverstand, Shihao Yang +2

Department of Industrial and Systems Engineering, Rutgers University, Piscataway, NJ, USA · Department of Psychiatry and Behavioral Sciences, University of Minnesota, Minneapolis, MN, USA · Institute of Brain Science, College of Medicine, National Yang-Ming Chiao Tung University, Taipei City, Taiwan

Alzheimer's Disease Electroencephalography Graph Neural Networks Frequency-Domain Feature Learning Alzheimer's Disease Classification Mixture-of-Experts Models

Oct 12, 2025

Structured Spectral Graph Representation Learning for Multi-label Abnormality Analysis from 3D CT Scans

With the growing volume of CT examinations, there is an increasing demand for automated tools such as organ segmentation, abnormality detection, and report generation to support radiologists in managing their clinical workload. Multi-label classification of 3D Chest CT scans remains a critical yet challenging problem due to the complex spatial relationships inherent in volumetric data and the wide variability of abnormalities. Existing methods based on 3D convolutional neural networks struggle to capture long-range dependencies, while Vision Transformers often require extensive pre-training on large-scale, domain-specific datasets to perform competitively. In this work, we propose a 2.5D alternative by introducing a new graph-based framework that represents 3D CT volumes as structured graphs, where axial slice triplets serve as nodes processed through spectral graph convolution, enabling the model to reason over inter-slice dependencies while maintaining complexity compatible with clinical deployment. Our method, trained and evaluated on 3 datasets from independent institutions, achieves strong cross-dataset generalization, and shows competitive performance compared to state-of-the-art visual encoders. We further conduct comprehensive ablation studies to evaluate the impact of various aggregation strategies, edge-weighting schemes, and graph connectivity patterns. Additionally, we demonstrate the broader applicability of our approach through transfer experiments on automated radiology report generation and abdominal CT data.

Theo Di Piazza, Carole Lazarus, Olivier Nempont +1

INSA Lyon, University of Lyon, CNRS, INSERM, CREATIS UMR 5220, U1294, Villeurbanne, France · Hospices Civil de Lyon, Lyon, France · Philips Clinical Informatics, Innovation Paris, France

Graph Neural Networks Graph Representation Learning Medical Image Classification Spectral Graph Convolution Computed Tomography

Oct 10, 2025

CRPS-LAM: Probabilistic Regional Weather Forecasting with Continuous Ranked Probability Score

Limited-Area Models (LAMs) enable weather forecasting over regional domains at higher resolutions than what is computationally feasible for global models. At such high resolutions, machine learning approaches for weather prediction increasingly rely on ensemble methods to produce probabilistic forecasts. However, existing machine learning LAMs are not scalable due to relying on computationally costly diffusion models or inefficient graph neural networks. We tackle this by introducing a new hybrid CNN/GNN architecture, tailored to the LAM weather forecasting problem. Using this architecture, we construct the DET-LAM deterministic model, producing LAM forecasts both more efficiently and accurately than its graph-based competitor. We then tackle the ensemble forecasting problem, by using this architecture as a backbone for the generative model CRPS-LAM. CRPS-LAM is trained using a Continuous Ranked Probability Score (CRPS) objective, enabling efficient training and sampling in a single forward pass. This yields a speedup of

\approx \times 39

compared to diffusion-based baselines. We evaluate our approach on regional domains in northern Europe, demonstrating that CRPS-LAM produces skillful and well-calibrated forecasts across a range of atmospheric variables.

Erik Larsson, Joel Oskarsson, Tomas Landelius +1

Linköping University · ETH AI Center · SMHI & Linköping University

Graph Neural Networks Ensemble Learning Probabilistic Forecasting Spatiotemporal Forecasting Weather Forecasting

Oct 6, 2025

Fractional Heat Kernel for Semi-Supervised Graph Learning with Small Training Sample Size

We develop a source-driven fractional heat-kernel framework for semi-super-vised graph learning that combines nonlocal propagation with sustained label information. A fixed nonzero label source compatible with the Laplacian null space prevents asymptotic collapse into that space, providing a mechanism for mitigating oversmoothing at long diffusion times. The fractional order controls the relative modal attenuation and the spectral weighting of the sustained response, while the diffusion time sets the propagation horizon. We characterize conservation laws and equilibria on normalized and disconnected graphs, develop a null-space deflation, and analyze the approximation of the propagators. On Two-Moon, fractional orders improve source-free propagation, while compatible source-driven diffusion exceeds

96\%

mean accuracy with one training label per class at orders

0.8

and

1

. On Cora and CiteSeer, the source-driven pipeline improves mean accuracy over GAT by

9.2

and

8.0

percentage points at one training label per class, with model selection on

500

labeled validation nodes and closely comparable classical and fractional pipeline configurations; it matches GAT on PubMed and trails it at ten and twenty labels per class on Cora. Within GraphHeat, validation-based exponent selection at a common diffusion time yields a paired gain of

1.45

percentage points at one label per class.

Farid Bozorgnia, Vyacheslav Kungurtsev, Shirali Kadyrov +1

Over-Smoothing in GNNs Graph-Based Semi-Supervised Learning Graph-Based Label Propagation Graph Diffusion Graph Neural Networks

Oct 5, 2025

Toward Uncertainty-Aware and Generalizable Neural Decoding for Quantum LDPC Codes

Quantum error correction (QEC) is essential for scalable quantum computing, yet decoding errors via conventional algorithms result in limited accuracy (i.e., suppression of logical errors) and high overheads, both of which can be alleviated by inference-based decoders. To date, such machine-learning (ML) decoders lack two key properties crucial for practical fault tolerance: reliable uncertainty quantification and robust generalization to previously unseen QEC codes. To address this gap, we propose a Quantum Bayesian graph Attention decoder (QuBA) that enables expressive error-pattern recognition alongside calibrated uncertainty estimates. Building on QuBA, we further develop a multi-phase training framework with enhanced cross-domain robustness enabling decoding beyond the training set called Sequential Aggregate Generalization under Uncertainty (SAGU). Experiments on bivariate bicycle (BB) codes and their coprime variants demonstrate that (i)QuBA consistently outperforms the classical baseline belief propagation (BP), achieving up to a two orders of magnitude reduction in logical error rate (LER) under confident-decision bounds on the coprime BB code

[[154,6,16]]

; (ii) SAGU achieves decoding performance comparable to or even outperforming QuBA's domain-specific training approach.

Xiangjun Mi, Frank Mueller

North Carolina State University, Raleigh, NC 27695, USA

Quantum LDPC Codes Quantum Error Correction Decoding OOD Generalization Uncertainty Quantification Graph Neural Networks

Sep 28, 2025

GraphIFE: Rethinking Graph Imbalance Node Classification via Invariant Learning

The class imbalance problem refers to the disproportionate distribution of samples across different classes within a dataset, where the minority classes are significantly underrepresented. This issue is also prevalent in graph-structured data. Most graph neural networks (GNNs) implicitly assume a balanced class distribution and therefore often fail to account for the challenges introduced by class imbalance, which can lead to biased learning and degraded performance on minority classes. We identify a quality inconsistency problem in synthesized nodes, which leads to suboptimal performance under graph imbalance conditions. To mitigate this issue, we propose GraphIFE (Graph Invariant Feature Extraction), a novel framework designed to mitigate quality inconsistency in synthesized nodes. Our approach incorporates two key concepts from graph invariant learning and introduces strategies to strengthen the embedding space representation, thereby enhancing the model's ability to identify invariant features. Extensive experiments demonstrate the framework's efficiency and robust generalization, as GraphIFE consistently outperforms various baselines across multiple datasets. The code is publicly available at https://github.com/flzeng1/GraphIFE.

Fanlong Zeng, Wensheng Gan, Kangjie Chen +1

School of Intelligent Systems Science and Engineering, Jinan University, Zhuhai 519070, China · School of Cybersecurity, Tianjin University, Tianjin 300354, China · University of Illinois Chicago, Chicago, USA

Class-Imbalanced Learning Graph Neural Networks Data Augmentation Invariant Representation Learning Node Classification Graph Data Augmentation

Sep 26, 2025

Self-Improving Neural Pruning: A Graph Neural Network Framework for Scalable Mixed Bundle Pricing

Mixed bundle pricing is a classic revenue management problem arising in industries such as e-commerce, tourism, and video games. It refers to designing product combinations (i.e., bundles) and determining their prices to maximize expected profit. Exact mixed-bundling formulations capture this structure but are computationally intractable because the number of possible bundles grows exponentially with the number of products. We propose a graph neural network (GNN)-guided pruning framework for scalable (non-)additive bundle pricing. Instead of learning on the exponential bundle-level formulation, we encode each instance as a compact customer-product graph and train an edge-output GNN to learn the product-assignment probabilities from optimal mixed-bundling solutions. The predicted probabilities are then converted into restricted candidate bundle families through fixed cutoff pruning and progressive cutoff pruning; the final prices and assignments are obtained by solving the mixed bundling formulation over the retained bundles. We further introduce a GNN-guided local search and an iterative self-improvement procedure for larger instances. The local search refines the retained bundle family by prioritizing high-confidence add/drop moves, while the iterative self-improvement procedure generates high-quality solutions on larger instances for retraining. Theoretically, we show that under mild distinguishability conditions the proposed edge-output GNN class is expressive enough to recover the optimal product-assignment mapping. Experiments show that the proposed policies recover over 98% of the optimal profit on small instances and outperform bundle-size pricing on larger instances with substantial runtime savings.

Liangyu Ding, Chenghan Wu, Guokai Li +1

School of Data Science, The Chinese University of Hong Kong, Shenzhen, Guangdong, China

Graph Neural Networks Combinatorial Optimization Neural Combinatorial Optimization

Sep 23, 2025

Tackling GNARLy Problems: Graph Neural Algorithmic Reasoning Reimagined through Reinforcement Learning

Neural algorithmic reasoning (NAR) is a paradigm that trains neural networks to execute classic algorithms by supervised learning. Despite its successes, important limitations remain: inability to construct valid solutions without post-processing and to reason about multiple correct ones, poor performance on combinatorial NP-hard problems, and inapplicability to problems for which strong algorithms are not yet known. To address these limitations, we reframe the problem of learning algorithm trajectories as a Markov decision process, which imposes structure on the solution construction procedure and unlocks the powerful tools of imitation and reinforcement learning (RL). We propose the GNARL framework, encompassing the methodology to translate problem formulations from NAR to RL and a learning architecture suitable for a wide range of graph-based problems. We achieve high rates of reaching correct states on several CLRS-30 problems and performance matching or exceeding much narrower NAR approaches for NP-hard problems. Remarkably, GNARL remains applicable when no expert algorithm is available, though reward-driven learning can exhibit greater variability than direct supervision.

Alex Schutz, Victor-Alexandru Darvariu, Efimia Panagiotaki +2

Oxford Robotics Institute, University of Oxford · Stateful Robotics

Graph Neural Networks Reinforcement Learning Neural Algorithmic Reasoning RL for Combinatorial Optimization Algorithmic Reasoning Neural Combinatorial Optimization