Evaluating Graph Neural Networks for Change-Criticality Classification in Maritime Navigation Charts

Graph neural networks (GNNs) are a class of neural networks suitable for learning on graph-structured data. Their application to spatial data is a natural extension, however its relatively unclear which message-passing operations, architectural configurations, and graph representation is best suited for classifying changes to objects in electronic navigational charts (ENCs)--geospatial vector datasets used for marine navigation. Maintaining these datasets is a challenge, and categorizing changes to objects in the ENC based on their significance to navigational safety is of particular importance. Here, we propose to represent these vector navigation datasets as a graph structure where the spatial objects serve as nodes and their spatial and semantic relationships form edges. We encode both the old ENC dataset and new ENC dataset into a pair of graphs and frame the task as a graph-pair classification problem. Building on this representation, we investigate the use of GNN architectures to classify whether the encoded graphs constitutes a critical or non-critical risk to navigational safety. We train and evaluate several GNN architectures and model configurations on ENC changes reviewed by maritime experts. Our results demonstrate that graph-based representations improve the classification of ENC updates, providing a scalable approach for automating or improving ENC maintenance workflows.

Task-Specific Prompt with Global Context for Multi-Task Graph Pre-Training

Graph prompt learning is an effective paradigm to adapt pre-trained graph models to downstream tasks in low-resource scenarios. However, existing multi-task graph pre-training frameworks generally use randomly initialized prompts, leading to poor alignment between the prompt space, pretext objectives and graph structural characteristics. This greatly weakens the task relevance, structural awareness and transferability of prompt representations. To address this challenge, we propose TPGC, a dual-prior prompt initialization solution that explicitly models the synergy between task prior and structural prior. Specifically, the Task-Prior Injection Module first conducts a short homologous multi-task pre-training on an auxiliary graph, enabling prompt initialization to inherit optimization preferences associated with multiple pretext tasks. Built on the task-aware representations, the Structure-Prior Injection Module further extracts transferable global structural context from the auxiliary graph, converting it into layer-wise prompt vectors by aggregating structurally informative node embeddings. Extensive experiments on 6 mainstream benchmarks covering node and graph classification show that TPGC achieves consistently better performance under few-shot settings than state-of-the-art baselines, with fewer downstream tunable parameters and lower runtime. The code is available at https://github.com/Virgilqiu/TPGC

Inductive Correlation Clustering with Graph Neural Networks

Correlation Clustering (CC) is a natural formulation of clustering in combinatorial optimization, which uses a graph representation of the input and does not require a pre-specified number of clusters. Given $n$ objects and a pairwise similarity function, the goal is to cluster the objects so that similar objects are put in the same cluster and dissimilar objects are put in different clusters. Despite its versatility, existing CC algorithms suffer from significant scalability issues and are inherently transductive: i.e., the algorithm must be executed from scratch for any new problem instance. In this work, we bridge this gap by leveraging Graph Neural Networks (GNNs) to solve Inductive Correlation Clustering, a novel generalization of the CC problem designed to handle unseen graph instances. By learning to exploit common structural patterns and node features during training, our framework generalizes to new graphs drawn from the same distribution with minimal computational overhead with respect to standard algorithms. We demonstrate the effectiveness and scalability of our approach through extensive experiments. Our framework not only excels in the inductive setting, e.g., lowering the inference time up to $5$ order of magnitude, while maintaining an approximation ratio within $~10\%$ of the best baseline solution, but also achieves competitive results on standard (transductive) CC benchmarks. Finally, we showcase a practical application of our framework as a learnable pooling mechanism for graph classification. Our results indicate that our method serves as an efficient pooling layer, enhancing the ability of GNNs to capture hierarchical structural information in networks.

Structured Learning on Mapper Representations

Modern machine learning (ML) methods are highly effective for prediction tasks, but many commonly used representations reduce complex data to fixed dimensional embeddings that may suppress multiscale structural organization. The Mapper algorithm from topological data analysis (TDA) provides a different perspective by decomposing data into overlapping local regions connected through a nerve construction, producing a structured representation that captures geometric organization, local statistical behavior, and relational connectivity simultaneously. In this work, we develop a framework for learning over Mapper induced structured representations. Rather than treating Mapper as a preprocessing step that produces a graph for downstream learning, we treat the full Mapper construction as part of the representation itself. We study mathematical properties of these representations, including invariance under relabeling, a distance functional on the space of Mapper representations, structural complexity of multiscale decompositions, and learning oriented stability under representation perturbations. Experiments on time series and graph classification datasets validate the proposed framework through controlled studies of representation ablation, Mapper parameter sensitivity, and the geometry of the induced representation space. Together, these results demonstrate how the proposed mathematical framework enables systematic comparison, interpretation, and analysis of Mapper representations, providing practical tools for studying representation geometry, structural complexity, and learning stability in learning tasks.

Predicting Resource Efficient Hamiltonian Decomposition for Continuous-Time Quantum Walk Simulations

Simulating a continuous-time quantum walk (CTQW) on a graph in the circuit model of quantum computing requires decomposing its Hamiltonian into terms that can be Trotterized into hardware-native gates. We consider two such decompositions: the standard Pauli decomposition and the recently introduced matching decomposition. Prior work suggests that the matching decomposition uses fewer CX gates on sparse graphs, while the Pauli decomposition uses fewer on denser graphs. Since CX gates dominate error and runtime on current hardware, we train machine learning models to predict, for a given graph, which of the two decompositions produces the smaller CX gate count. We train and evaluate on the complete population of all 11,117 connected eight-vertex graphs from Brendan McKay's database, so the class balance and overlap are measured directly rather than estimated. We use twelve features: ten topological properties of the graph and two that count the terms the Pauli and matching decompositions produce (n_Pauli and n_match), both computable without transpiling the simulation circuit. Standard topological properties alone provide little predictive power. Instead, the dominant signal comes from n_Pauli, a property of the Hamiltonian decomposition rather than an intrinsic property of the graph; degree variance is the only other feature that carries signal. Across a range of models the Matthews correlation coefficient (MCC) falls in a narrow band, from 0.569 untuned to 0.593 after tuning, so no single architecture stands out. We adopt a single-hidden-layer neural network at MCC 0.593. Applied frozen to a held-out, class-balanced test set of larger graphs (up to 256 vertices) from structured and Erdos-Renyi families, the model transfers, with MCC rising from 0.785 at N=8 to 1 at N>=64.

Differentiable Lifting for Topological Neural Networks

Topological neural networks (TNNs) enable leveraging high-order structures on graphs (e.g., cycles and cliques) to boost the expressive power of message-passing neural networks. In turn, however, these structures are typically identified a priori through an unsupervised graph lifting operation. Notwithstanding, this choice is crucial and may have a drastic impact on a TNN's performance on downstream tasks. To circumvent this issue, we propose $\partial$lift (DiffLift), a general framework for learning graph liftings to hypergraphs and cellular- and simplicial complexes in an end-to-end fashion. In particular, our approach leverages learned vertex-level latent representations to identify and parameterize distributions over candidate higher-order cells for inclusion. This results in a scalable model which can be readily integrated into any TNN. Our experiments show that $\partial$lift outperforms existing lifting methods on multiple benchmarks for graph and node classification across different TNN architectures. Notably, our approach leads to gains of up to 45% over static liftings, including both connectivity- and feature-based ones.

HP-JEPA: Hierarchical Partitioning for Multi-Resolution Graph Joint-Embedding Predictive Learning

Graph self-supervised learning aims to learn transferable representations from large-scale unlabeled graph data. Joint-embedding predictive architectures (JEPAs) avoid explicit negative-pair construction and raw-input reconstruction by predicting masked targets directly in latent space. However, existing graph JEPAs typically rely on a single predefined graph partition, biasing the learned representations toward one structural granularity and limiting their ability to capture complementary patterns at different graph scales. To address this limitation, we propose HP-JEPA, a hierarchical partitioning framework for multi-resolution graph joint-embedding prediction. HP-JEPA organizes each graph into an ordered bank of coarse-to-fine partition resolutions and performs context-target latent prediction separately at each resolution using an online encoder, an exponential-moving-average target encoder, and a latent predictor. The resulting resolution-specific graph representations are subsequently integrated through concatenation or task-specific resolution weighting, allowing downstream models to combine complementary local, regional, and global structural information. Experiments on seven graph classification benchmarks and one graph regression benchmark show that HP-JEPA outperforms the fixed-resolution Graph-JEPA baseline on 6 of 8 tasks, improving upon Graph-JEPA on most evaluated benchmarks. Size-stratified analyses further show that HP-JEPA achieves higher accuracy than Graph-JEPA in most evaluated graph-size quartiles on three representative datasets. These results highlight the effectiveness of hierarchical multi-resolution partitioning for transferable graph representation learning.

TopoFormer: Topology Meets Attention for Graph Learning

We introduce Topoformer, a lightweight and scalable framework for graph representation learning that encodes topological structure into attention-friendly sequences. At the core of our method is Topo-Scan, a novel module that decomposes a graph into a short, ordered sequence of topological tokens by slicing over node or edge filtrations. These sequences capture multi-scale structural patterns, from local motifs to global organization, and are processed by a Transformer to produce expressive graph-level embeddings. Unlike traditional persistent homology pipelines, Topo-Scan is parallelizable, avoids costly diagram computations, and integrates seamlessly with standard deep learning architectures. We provide theoretical guarantees on the stability of our topological encodings and demonstrate state-of-the-art performance across graph classification and molecular property prediction benchmarks. Our results show that Topoformer matches or exceeds strong GNN and topology-based baselines while offering predictable and efficient compute. This work opens a new path for parallelizable and unifying approaches to graph representation learning that integrate topological inductive biases into attention frameworks.

Surprisingly Simple and Effective Multi-Domain Graph Foundation Model through Graph-to-Table Alignment

Graph Foundation Models (GFMs) have emerged as a promising paradigm for learning transferable representations across diverse graph domains. Recent advancements in GFMs have been largely dominated by two paradigms: Graph Neural Network and Large Language Model (LLM) based methods. However, these methods often face a fundamental dilemma between training with limited data and a heavy reliance on textual attributes. Tabular foundation models (TFMs) offer a potential alternative, as node features and representations can be naturally organized in a tabular form. However, how to enable TFMs to effectively capture structural information of graphs remains largely unexplored. The key challenge is to learn a graph-to-table alignment mechanism that enables graph structural understanding for TFMs. To address this, we propose GTAlign, a surprisingly simple yet effective Graph-to-Table Alignment framework for text-free Graph Foundation Model. Specifically, we first pretrain a graph encoder that maps diverse graphs into a unified latent space to capture domain-agnostic graph representations. To further bridge the gap between graph topology and the tabular representation space, we propose community-guided continual pre-training, where pseudo-labels derived from graph community are used to construct few-shot prediction episodes. Lastly, we adapt the graph encoder for an unseen target domain and perform in-context inference. Extensive experiments on five benchmark datasets demonstrate that GTAlign significantly outperforms state-of-the-art baselines on both node and graph classification, offering a simple, effective, and text-free GFM model. Code will be released upon acceptance.

path_boost: A Python Package for Interpretable Graph-Level Prediction using Path-Based Gradient Boosting

We present path_boost, a Python package for interpretable supervised learning on graph-structured input data. The package implements PathBoost, a gradient boosting algorithm that automatically discovers predictive labeled paths within graphs during the learning process. Unlike graph neural networks, which are generally difficult to interpret, PathBoost produces an additive prediction model over path-based features that explicitly reveals which substructures drive predictions. To avoid an exhaustive enumeration of all possible paths, the algorithm iteratively selects and extends paths during learning based on their predictive power, using boosting to combine weak learners into a strong ensemble. The package supports both regression and binary classification. Key features include compatibility with scikit-learn workflows, support for custom base learners and selectors, automatic starting node selection, parallel training across anchor nodes, and built-in variable importance computation. We demonstrate PathBoost on molecular property prediction of transition metal compounds, where atoms serve as nodes and bonds as edges, and further benchmark PathBoost against an established graph neural network and a graph kernel method across six molecular datasets. The package is available on PyPI and GitHub under an open-source license.

Graph Classification via Network Usable Information: From Representation Evaluation to Structure Selection

We propose NetinfoGC, a framework for graph classification that extends the Network Usable Information (NUI) paradigm to graph-level learning. Unlike conventional graph neural network approaches that rely on end-to-end training of black-box embeddings, NetinfoGC constructs a family of permutation-invariant graph representations derived from propagation-based mechanisms and classical structural descriptors, including graph centrality measures. To evaluate representation quality, we introduce a training-free NUI estimation procedure based on clustering consistency with ground-truth labels, providing a proxy for task-relevant information without supervised learning. We further exploit the same representations using sparse-group LASSO regularization, enabling automatic selection of informative structural descriptors while suppressing redundant ones. Experiments on benchmark datasets show that classical centrality measures are highly competitive with learned propagation-based representations, and in several cases yield superior performance. Moreover, we observe a strong correlation between estimated NUI and downstream classification accuracy, validating NUI as an effective measure of representation utility. Overall, NetinfoGC provides a unified and interpretable framework for evaluating and exploiting graph representations without requiring end-to-end neural training.

Graph Neural Networks for the Graphical Bootstrap

We study a graph classification problem involving over 20 million graphs, arising from high-order perturbative computations of correlators in planar $\mathcal{N}=4$ super-Yang--Mills, a model closely related to the theory of the strong nuclear force. We benchmark graph neural networks, including graph transformers, achieving robust generalization to larger graphs with up to $99.996\%$ ROC AUC. Then, we analyze how the models can be used to gain a computational speedup compared to the traditional graphical bootstrap algorithm, through shrinking the redundant data by up to $85.5\%$ at the level of denominator graphs. Finally, we study the embeddings of the models to investigate their interpretability.

GLIP: Graph and LLM Joint Pretraining for Graph-Level Tasks

Graphs are widely used to model relational systems, with applications in domains such as social networks, finance, and biomedicine. Graph neural networks (GNNs) have become a mainstream approach for learning graph representations. With the rise of large language models (LLMs), recent studies have attempted to combine GNNs with LLMs. However, most existing works concentrate on node-level and edge-level tasks, while graph-level tasks, which require capturing more complex structural and feature information, remain relatively underexplored. Moreover, graph pretraining is a widely adopted strategy to alleviate the challenge of label scarcity. Most existing approaches are designed solely for GNNs such as GraphCL, leaving LLMs uninvolved in the process. To address these limitations, we propose GLIP, a Graph-LLM JoInt Pretraining framework for graph-level tasks. GLIP first performs graph augmentation to construct positive and negative pairs and introduces a multi-token selection strategy to identify patches informative in both structure and features. It further leverages a diffusion-based projector to enrich them with contextual information, enabling GLIP to capture signals from both global and local perspectives. Finally, GLIP employs a joint objective that integrates the LLM's semantic judgments with a contrastive alignment loss, ensuring consistent supervision at both the semantic and structural levels. After pretraining, GLIP is fine-tuned with limited labeled data for downstream tasks, and extensive experiments show that it outperforms state-of-the-art methods on graph-level classification and reasoning tasks. Our source code is publicly available at https://anonymous.4open.science/r/GLIP.

A General Framework for Learning Algebraic Properties from Cayley Graphs using Graph Neural Networks

In this work, we present a general Graph Neural Network (GNN) framework for learning algebraic properties of finite groups from their Cayley graph representations. The framework provides a unified computational pipeline consisting of a common graph construction procedure, feature representation, training methodology, and GNN architecture, with only the target labeling function varying across classification tasks. To demonstrate the generality of the proposed approach, we consider three representative algebraic properties: abelianity, nilpotency, and solvability. Experiments were conducted on a benchmark of 176 finite groups drawn from several classical families, with all groups included in each classification task. To address class imbalance, class-weighted cross-entropy loss was employed where appropriate during training. Furthermore, the family PSL(2,q) was reserved exclusively for testing, enabling evaluation of the framework's ability to generalize to previously unseen group families. The best-performing models achieved test balanced accuracies of 1.000, 0.856, and 0.875 for abelianity, nilpotency, and solvability, respectively. Although the same computational framework was employed across all tasks, different GNN architectures proved optimal for different algebraic properties, suggesting that the representational complexity required to learn a property depends on its underlying algebraic structure. These results demonstrate that GNNs can effectively learn multiple algebraic properties directly from Cayley graph representations while exhibiting strong generalization to unseen group families. More broadly, the proposed framework establishes a computational methodology for studying algebraic properties of finite groups using graph-based machine learning.

Learning Graphs through Continuous Information Entropy Fields

Graph theory is inherently descriptive, capturing what relationships exist but not why they arise, because it treats edges as primitive constructs. This paper proposes a new explanatory framework for graph learning, where relationships emerge from latent continuous information entropy fields, and a graph becomes a discrete instantiation of an underlying field. To formalize this field, we introduce the Field-informed Graph Network (FGN). It learns a scalar field from node features and leverages it to modulate message passing. The information-theoretic objective balances structural fidelity with field smoothness, forming a self-reinforcing loop. In this loop, the field modulates information diffusion through field-modulated weighting, and the updated node representations iteratively refine the field. As a result, FGN learns by simulating its own co-evolution. Extensive experiments on node classification and graph classification benchmarks demonstrate superior performance, robustness to perturbations, and structurally coherent field representations.

Controlled Dynamics Attractor Transformer

Transformer architectures have dramatically advanced representation learning and inference in deep models through self-attention mechanisms. In parallel,associative memory (AM) frameworks map representations onto energy landscapes, offering interpretable retrieval mechanisms. However, their continuous-time inference dynamics lack the biological plausibility of classical Continuous Attractor Neural Networks (CANNs). To bridge this gap, we propose Controlled Dynamics Attractor Transformer (CDAT), which couples a mixture von Mises-Fisher (Mo-vMF) attention energy with a Hopfield refinement energy, while augmenting energy descent with a CANN-inspired excitation-inhibition modulation. CDAT instantiates a topology-constrained dynamical system whose couplings encode relational structure among tokens, thereby linking attractor-style dynamics to modern energy-based attention. We further provide a constructive dissipation analysis to formally establish their controlled inference dynamics. Benefiting from these robust and structured dynamics, CDAT achieves state-of-the-art performance across multiple benchmarks in graph anomaly detection and graph classification.

$k$-Nearest Neighbors in Gromov--Wasserstein Space

The Gromov--Wasserstein (GW) distance provides a framework for comparing metric measure spaces, regardless of their underlying structure or geometry. For network-based data, it enables direct comparisons of graphs with different numbers of nodes, without requiring an embedding or other abstraction. Furthermore, through a variant of GW known as fused Gromov--Wasserstein (fGW), it is also possible to incorporate node features in addition to graph structure. In this work, we implement $k$-nearest neighbors ($k$-NN) classification using the GW and fGW distances. We prove the universal consistency of the GW-$k$-NN classifier on the space of equivalence classes of metric measure spaces with finite support and uniform probability measure. By viewing graphs as finitely supported metric measure spaces equipped with the pairwise distance metric and a uniform probability measure on the nodes, we obtain universal consistency of GW-$k$-NN for the space of graphs. Likewise for fGW-$k$-NN, we prove universal consistency on the space of weak isomorphism classes of structured objects consisting of metric measure spaces with finite support and uniform probability measure and feature maps into Euclidean space, thus establishing universal consistency on the space of node-attributed graphs. Our numerical experiments show that GW-$k$-NN and fGW-$k$-NN consistently perform well across multiple graph datasets, suggesting that metric classifiers such as $k$-NN work well in the GW framework.

A Closed-Form Persistence-Landmark Pipeline for Certified Point-Cloud and Graph Classification

We introduce PLACE (Persistence-Landmark Analytic Classification Engine), a closed-form pipeline for classifying point clouds and graphs through their persistent-homology signatures. Three quantitative guarantees -- a margin-based excess-risk rate, a closed-form descriptor-selection rule, and a per-prediction certificate -- are derived from training labels alone, with no learned weights or held-out calibration. The embedding sums Mitra-Virk single-point coordinate functions over a sparse landmark grid; closed-form weights maximize a structural distortion constant $λ(ν)$ (a Lipschitz lower bound on $\mathcal{D}_n$ under non-interference). (i) An $O(kR/(Δ\sqrt{m_{\min}}))$ margin bound, driven by class-mean separation $Δ$ and embedding radius $R$, matched by a sample-starved minimax lower bound. (ii) The Mahalanobis margin under Ledoit-Wolf-shrunk covariance is the strongest closed-form descriptor selector on a heterogeneous 64-descriptor chemical-graph pool (mean Spearman $ρ\approx +0.54$ across 10 benchmarks, positive on 9 of 10); the isotropic surrogate $Δ/\sqrt\ell$ admits a closed-form selection-consistency rate on homogeneous (14-15 descriptor) protein/social pools. (iii) A training-time-decided certificate with no per-prediction overhead, in non-asymptotic Pinelis and asymptotic Gaussian plug-in forms. Empirically, PLACE is the strongest diagram-based method on Orbit5k and matches the strongest topology-based baseline within statistical noise on MUTAG and COX2. The remaining gaps fall into two diagnosable regimes: descriptor blindness on NCI1/NCI109, and pool-coverage limits elsewhere. Both radii exceed the firing threshold $\hatΔ/2$ on every benchmark at our training-set sizes, dominated by the $\sqrt\ell$ scaling of the multivariate-norm bound; the per-prediction certificate is constructive but not yet operational at these sizes.