Knowledge graph embedding (KGE) demonstrates its effectiveness for predicting missing links in knowledge graphs (KGs) by projecting entities and relations into a low-dimensional vector space. It is crucial for KGE models to effectively capture inference patterns (patterns) inherent in KGs, such as symmetry/antisymmetry, inversion and composition. Although recent KGE models exhibit strong capabilities in modeling such diverse patterns, they suffer from inherent limitations stemming from pattern over-generalization, where embeddings learned from only a single pattern instance inevitably generalize that pattern to all related instances, i.e., generalize the pattern universally. To address this issue, we propose PogRE (Pattern Over-Generalization Robust Embedding), a simple but effective method that utilizes dense linear transformations and compound operations for relation representation. Our theoretical analysis demonstrates that a dense linear transformation allows a pattern to become progressively universal as more triples are observed in the pattern. Furthermore, after observing d+1 linearly independent entities (d+1 denotes the dimension of entity), the linear transformation guarantees universal generalization of the pattern across all related instances. Experimental results on three standard benchmark datasets show that PogRE outperforms existing state-of-the-art KGE models in link prediction. Moreover, our empirical results indicate that PogRE effectively addresses the negative impact of over-generalization.
Path representation learning (PRL) for road networks has received increasing research attention, due to various path-related applications. Existing works on PRL typically exploit the co-occurrence relationship among road segments and paths to learn a vector as the path representation, without exploring the varied traveler behaviors and the regional correlation on the path. In this work, we propose to learn distributional representations, which provide valuable information for use in path-related applications, by capturing the varied traveler behaviors as well as the various dependencies within regions of road segments. We propose a novel Transformer-based Multi-view Distributional Representation Learning (TraveL) framework to encode a path along with a travel starting time to a distributional representation, which can be used to decode possible samples of on-path traveler behavior. Moreover, by analyzing the regional correlation which reveals various road segment relationships, we propose a regional attention to encode these correlations in a path. Also, we explore the idea of Kolmogorov-Smirnov (K-S) test to compare the sampled traveler behavior against the collected ground truth to facilitate training. Experimental results show that the proposed TraveL model outperforms the state-of-the-art methods on both synthetic and real-world datasets, by 14.7% in Mean K-S distance for travel time distribution estimation, 16.7% in Mean Absolute Error (MAE) for path similarity prediction, and 3.97% in MAE for destination prediction.
Kernelized graph methods - spectral clustering, diffusion maps, and sparse kernel -regression graphs - that use Gaussian kernels depend on the choice of Gaussian bandwidth sigma, which governs the spectral character of the local kernel operator. When sigma is too small, the kernel overestimates local complexity and treats each sample as an independent direction; when sigma is too large, the kernel collapses multiple directions together, the condition number diverges, and all geometric discrimination is lost. We propose a choice of scale to make the spectral complexity of the kernel consistent with the intrinsic complexity of the underlying manifold. We propose a per-node bandwidth criterion that operationalizes this principle by jointly matching the kernel's effective rank to the local intrinsic dimension estimated via minimum spanning tree, anchoring the search in the manifold-consistent log-log scaling regime. We evaluate SSL embeddings from six encoders on CIFAR-100, showing that adaptive bandwidth consistently improves leave-one-out (LOO) classification and label propagation (LP) accuracy over fixed-bandwidth methods and competing adaptive methods.
Existing graph-clustering methods typically improve clustering performance by optimizing model parameters and node representations. Effective means of further improving the clustering results of an already trained and frozen model, however, remain limited. We study post-processing for frozen graph clustering. After checkpoint fixation, the procedure uses no labels and updates neither model parameters, node representations, nor the original graph structure. Instead, it exploits an attribute hypergraph to supplement higher-order relations that ordinary graphs cannot readily express, thereby refining existing cluster assignments. Because global hypergraph refinement can yield both performance gains and erroneous updates, we propose Selective Hypergraph Refinement (SHR). The method generates candidate residual directions from the hypergraph and evaluates their reliability using graph structure, node attributes, and matched-null evidence. It updates only nodes with sufficient support and otherwise retains their original assignments. Further analysis shows that whether a node changes cluster is jointly governed by its native assignment gap and the directional strength of the refinement. In a controlled common-suite evaluation, 13 of 15 backbone-dataset cells had a positive mean macro gain, one produced exact no-action, and one was negative. The cell-equal macro gain was 0.066 pp (95% bootstrap CI, [0.030, 0.107] pp), while only 0.209% of hard assignments changed on average. A broader 15-combination native-interface evaluation yielded a macro gain of 0.137 pp at a mean change ratio of 0.375%. These results indicate that frozen clustering outputs retain a limited but measurable refinement space after training. The effect is heterogeneous across backbone-dataset pairs, and broader coverage also increases exposure to negative transfer.
Ucchwas Talukder Utsha, Sakib Mostafa, James Zou +1cs.LG
Networks describe systems in biology and beyond, from protein interactions and social relationships to power grids and citation records. Reasoning about such systems requires understanding their structure: which elements are central, which connections bridge separate communities, and how it changes when elements are removed. Although large language models (LLMs) excel at natural language, they struggle with such questions when networks are given as edge lists, sentences or measurement tables, because their structural meaning must be inferred. Here we introduce BioGlyph, which compiles network topology into an interpretable and transferable language of structural roles. BioGlyph combines graph partitioning and structural measurements to identify roles such as hubs, community cores and cross-community connectors, and fixed rules to translate them into a universal vocabulary. The representation describes each element through its structural role, supporting evidence and semantic consequences, leaving both the network and the LLM unchanged. Across twenty networks spanning five domains, BioGlyph substantially improves open LLMs' ability to answer structural reasoning questions, outperforming edge-based, numerical and learned representations by up to 26 percentage points in system accuracy. Ablations show that the gain comes from explicitly encoding structural roles in semantically interpretable terms. The gain is more prominent in dense, community-structured networks and diminishes in sparse networks whose topology is more readily inferred from text. In a budding-yeast protein-interaction network, BioGlyph exposes biological organization: cross-community connectors are enriched for essential genes, whereas peripheral proteins are depleted. BioGlyph thus provides an interpretable representation for both language models and scientists to reason about network structure.
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.
Guillaume Méroué, Fabien Gandon, Pierre Monnincs.LG
Knowledge graphs have become an important source of structured knowledge for Web applications, including search, question answering, and recommender systems. In these applications, link prediction can serve either as a prediction task itself or as a means to enrich incomplete knowledge graphs for downstream tasks. Interestingly, different link prediction models, or even different training runs of the same model, can produce substantially different predictions for the same query. This suggests a variability in the capture of the underlying knowledge by models, thus raising a fundamental question: to what extent do different models capture complementary knowledge, and how much of this knowledge could be recovered by combining them? We propose to measure model complementarity through the performance of an oracle that, for each query, selects the best prediction among a considered set of models, hence providing an upper bound on the performance achievable through model combination. Across several architectures and benchmarks, we find a substantial gap between individual models and their oracle, revealing that different models capture complementary knowledge. Yet, this complementarity rapidly saturates as more models are added, leaving a persistent subset of queries unsolved even by a large number of models. These findings reveal both the potential of model complementarity and a fundamental limit to what current link prediction models can collectively recover; thereby highlighting the need for further research to build robust Web applications.
The conventional approach to machine learning, that is, collecting data, training models, and performing inference in a single location, faces fundamental limitations, including scalability and privacy, that restrict its applicability. To address these challenges, recent research has explored collaborative learning approaches, including federated learning and decentralized learning, where individual agents perform training and inference locally, with limited collaboration. Most collaborative learning research focuses on Euclidean data with regular, grid-like structure (e.g., images, text). However, these approaches fail to capture the relational patterns in many real-world applications, best represented by graphs. Learning on graphs relies on message-passing mechanisms to propagate information between connected nodes, making it conceptually well-suited for collaborative environments where agents must exchange information. Yet, the opportunities and challenges of learning on graph-structured data in collaborative settings remain largely underexplored. This survey provides a comprehensive investigation of collaborative learning from Euclidean to graph-structured data, aiming to consolidate this emerging field. We begin by reviewing its foundational principles for Euclidean data, organizing them along three core dimensions: learning effectiveness, efficiency, and privacy preservation. We then extend the discussion to graph-structured data, introducing a taxonomy of graph distribution scenarios, characterizing associated statistical heterogeneities, and developing standardized problem formulations and algorithmic frameworks. Finally, we systematically identify open challenges and promising research directions.
Md Abrar Jahin, Taufikur Rahman Fuad, Jay Pujara +1cs.LG cs.AI
Uncertain knowledge graphs (UKGs) extend knowledge graphs by assigning each triple a continuous confidence score. Since most possible triples lack observed confidences, recent methods rely on semi-supervised learning to generate pseudo-labels. These methods initialize entity embeddings without using the confidence-weighted graph, discarding its global community and hub structure. We introduce QUEST, which adds no trainable parameters to the standard confidence-distribution learning pipeline. First, QUEST initializes entity embeddings using the smallest non-trivial eigenvectors of the confidence-weighted graph Laplacian, incorporating community and hub structure before training. Second, QUEST applies an unbiased mini-batch Dirichlet energy regularizer to enforce early-stage structural consistency. On two UKG datasets, QUEST improves confidence prediction and link prediction on six of eight metric-dataset pairs over prior methods and matches the previous best on the remaining two, while removing the instability spike observed on dense graphs. These results indicate that spectral structural priors combined with a graph Dirichlet energy regularizer improve accuracy, training stability, and checkpoint reliability in UKG completion.
Taufikur Rahman Fuad, Md Abrar Jahin, Amir Hussaincs.LG cs.AI
Zero-shot graph anomaly detection seeks to deploy a detector trained on source graphs to unseen, unlabeled targets, yet domain shift can make source-derived notions of normality unreliable. We introduce RINSE (Robust Iterative Normality Self-Estimation), a gradient-free target-time framework that keeps the source-trained detector fixed while sequentially estimating target normality, representation calibration, and evidence reliability from the target graph. Its core idea is to identify a reliable subset of low-residual target nodes, use them to construct a trimmed target-aware normality model, and combine complementary anomaly evidence through reliability-gated rank fusion and encoder ensembling. Across eight unseen target graphs, RINSE achieves the highest average AUPRC among the evaluated methods under two separate preprocessing protocols, while block ablations and sensitivity analyses support the combined design. These results support robust target-time estimation as a practical approach to generalist graph anomaly detection without target labels, gradients, or per-target tuning.
Learning graph structures from data is a fundamental problem that spans a wide range of signal processing and machine learning tasks. While significant effort has been made to tackle the problem, existing research has largely evolved along two parallel directions. The first seeks to infer the topology of an individual graph from observations supported on it, whereas the second seeks to learn a generative distribution from observed graph instances, enabling the sampling of new graphs. This review presents a unified framework that connects these formulations by viewing them as inverse problems of a common generation process for graph data. We review the major methodologies within this framework, highlight their relationships, strengths, and limitations, and identify opportunities for integrating ideas across paradigms. By bridging graph topology learning and graph generation, this review provides a broader cross-disciplinary perspective on the field and outlines promising directions for future research.
Inductive knowledge graph completion (IKGC) aims to predict missing links involving entities unseen during training, requiring models to learn transferable relational and structural patterns. Existing subgraph- and path-based approaches often encode relational paths independently of their surrounding query subgraphs, although the predictive relevance of a path may vary across structural contexts. We propose PEARL, a Path-Entity Aligned Relational Learning framework that models paths as context-conditioned reasoning signals. PEARL constructs a query-specific contextual subgraph from the union of the query entities' neighborhoods and uses a large language model (LLM)-guided retriever to distill semantically relevant paths. It then builds a bipartite interaction graph over paths, contextual entities, and a global subgraph representation, allowing path embeddings to adapt to local and global structural evidence. To suppress noise introduced by the enlarged context, PEARL employs a dual-view contrastive objective that promotes representation consistency under stochastic contextual perturbations. Experiments on WN18RR, FB15k-237, and NELL-995 show that PEARL obtains the best average Hits@10 among the compared IKGC methods on all three benchmarks. Ablation studies, efficiency analyses, and case studies further validate the contributions of contextual subgraph modeling, semantic path retrieval, path-entity interaction, and contrastive regularization.
Philipp Schlinge, Jean-Luc Schnipper, Martin Atzmuellercs.SI cs.LG stat.ML
Dynamic networks are being applied in many domains, from social media to logistics systems, each with their own set of special characteristics. A model employed on this type of data must capture the duality between temporal/structural and feature-based information. Yet state-of-the-art deep learning models often struggle to learn especially short-term behavioral interaction signals, such as sender intensity or interaction inertia, directly from raw event streams. To address this gap, we propose a statistical feature augmentation method that explicitly encodes behavioral interaction statistics into the input feature space. We evaluate our proposed method on an anomaly detection task across three real-world datasets (Reddit, Wikipedia, MOOC) and seven models spanning both continuous-time and discrete-time architectures. As a baseline, we apply the same models trained on the original embeddings. Our results show, that augmentation consistently improves detection performance. Beyond performance, the enriched input enables fine-grained post-hoc analysis of behavioral importance, since each statistic occupies a dedicated input dimension. In particular, this work showcases a promising approach for merging classical network analysis with deep learning.
Hugo Schnoering, Roman Bresson, Michalis Vazirgianniscs.LG
Bitcoin's pseudonymous nature makes it challenging to analyze user-level activity, since a single user may control multiple identifiers (addresses). Existing heuristic-based methods attempt to identify addresses belonging to the same user, but they often produce flat cluster assignments with limited modularity and are prone to errors such as merging different users together. In this work, we propose a method for refining heuristic-obtained clusters by grounding our clustering on contrastive embeddings yielded by graph neural networks. Our contributions are threefold: (i) we release a publicly available dataset of Bitcoin transaction graphs containing a substantial number of clusters; (ii) we propose a methodology for learning address embeddings consistent with heuristics, and back it up with theoretical guiding intuitions; (iii) through hierarchical clustering, we enable a finer analysis of heuristic clusters and provide a quantitative criterion for flagging suspicious merges.
Graph neural networks (GNN) based on message passing are provably no more powerful than the one-dimensional Weisfeiler--Leman colour-refinement test (1-WL): two graphs it cannot tell apart receive identical representations, however deep or wide the network. A common remedy augments node or edge features with precomputed structural descriptors, most often counts of a fixed small subgraph such as triangles or longer cycles, but such counts require committing in advance to the size of the substructure counted, a choice usually made blind to the data. We study a descriptor that avoids this choice. The edge-girth of an edge is the length of a shortest cycle through it, and its multiplicity is the number of such shortest cycles; together they form a per-edge invariant that reports cycles of arbitrary length, computable exactly by a single breadth-first search per edge. Injected into a gated message-passing architecture, EGAGNN, it reaches a test MAE a factor three below the closest gated comparator on the ZINC-12k regression benchmark at 104k parameters; against bounded cycle-counting descriptors under the same architecture, it matches only a dictionary counting cycles up to length eight, using twice as many channels, while a dictionary capped at length four performs no better than no structural information at all. On graph discrimination we prove a matching limitation: on graphs where every edge sees the same number of shortest cycles of the same length, the descriptor becomes constant and any model built on it collapses back to the 1-WL bound. This holds without exception across all 400 pairs of the BREC benchmark: not one of the 90 such pairs is distinguished.
Oleksii Kolesnichenko, Jakub Peleška, Gustav Šírcs.PL cs.DB cs.LG
Relational Deep Learning (RDL) has become a powerful paradigm for learning from multi-tabular data. However, manually defining RDL prediction tasks is a laborious process that frequently results in data leakage. To address this issue, we introduce Relational Task Generation Language (RTGL) - an open-source declarative language that streamlines RDL task formulation by abstracting away low-level SQL details. We showcase RTGL by reconstructing existing RDL benchmark tasks and uncovering their inconsistencies stemming from manually crafted SQL definitions of RDL prediction targets, thereby underscoring the value of a dedicated declarative language. In addition, we demonstrate the practical utility of RTGL by designing various new tasks with diverse forms and target types. Our experiments confirm the robustness and usability of RTGL, as well as its seamless integration with the existing RDL frameworks, making it widely accessible to the community.
Traditional network models from network science, such as the Erdos-Renyi and configuration models, generate random networks that reproduce few selected topological properties observed in real-world networks. Deep graph generative models emerge as a data-driven approach, leveraging deep neural network architectures to learn complex structural distributions directly from real-world networks to generate more realistic synthetic networks. Because real social contact networks cannot be shared due to privacy risks, synthetic networks serve as an alternative for developing and evaluating epidemic mitigation strategies. In this work, we evaluate deep graph generative models as well as the configuration from a network science perspective by assessing both the topological similarity between generated and real-world networks and their utility in identifying effective node immunization strategies to sup- press epidemic/misinformation spreading. It is found that two deep graph generative models produce synthetic networks that closely resemble the structural properties of real-world networks, enabling them to identify effective immunization strategies.
Large language models extracting knowledge graphs from text capture only explicitly stated facts, often leaving semantically related entities disconnected across documents. We present an additive, engine-neutral second pass that discovers these latent ties without altering extracted facts. Each document is chunked and embedded once; top-k nearest- neighbor queries across existing chunks yield candidate node pairs via entity membership maps. Candidate pairs are scored using Shepard inverse-distance weighting with a rescaled chord distance metric, avoiding the threshold-collapsing flaw of affine cosine scoring behind a k-NN gate. Un-gated per-pair accumulators form a commutative monoid, ensuring the pipeline is strictly order-independent and scales incrementally without recomputing prior documents. Implemented across FalkorDB, Kinetica, ArangoDB, and Neo4j, our method shows that 768- and 240-dimensional embeddings retain 92% and 72% edge fidelity against a 3072-D baseline while achieving a 25x faster top-k formulation.
Ontology alignment (OA) has evolved through several methodological paradigms, ranging from lexical and structural aligners to knowledge graph embedding (KGE) models and, more recently, Large Language Model (LLM)-based approaches. Although modern OA frameworks provide unified ecosystems for deploying these heterogeneous aligners, mechanisms for systematically reconciling their complementary and sometimes conflicting predictions remain relatively underexplored. We present OntoAligner-Ensemble, a modular and aligner-agnostic framework that combines candidate correspondences through a configurable two-stage process comprising voting-based fusion strategies followed by post-fusion selection policies. The framework supports any aligner implemented within OntoAligner that produces candidate correspondences, enabling diverse alignment paradigms to be integrated through a unified decision process. To demonstrate its effectiveness, we instantiate the framework using representative lightweight string-aligner, KGE-based, and Retrieval-Augmented Generation aligners powered by both open-weight and API-based LLMs. We evaluate individual aligners and ensemble configurations across eight benchmark tasks from five OAEI tracks spanning biomedical to beyond-equivalence. The results show that ensemble fusion consistently improves the balance between precision and recall and frequently outperforms standalone aligners across diverse domains. Furthermore, our analysis reveals that ensemble composition directly affects the precision-recall trade-off: heterogeneous cross-paradigm ensembles generally improve precision, whereas homogeneous LLM ensembles more often achieve higher overall F1-scores. These findings demonstrate that systematic ensemble learning offers a robust and reproducible strategy for OA while providing practical guidance for selecting ensemble compositions under different alignment scenarios.
Rotational symmetry is one of the most important structural principles in machine learning on 3D data. In applications ranging from physics and materials science to 3D computer vision, predictions should not depend on an arbitrary choice of coordinate frame. Rotational equivariance captures this requirement mathematically by enforcing that a rotation of the input induces a corresponding transformation of the model output. This tutorial provides a comprehensive introduction to rotational equivariance, starting from the physical and geometric intuition behind coordinate independence and building up the necessary machinery from geometric deep learning, group theory, and representation theory. We introduce message passing on Euclidean graphs, group actions and representations, spherical harmonics, Wigner matrices, tensor products, and Clebsch-Gordan decomposition, and explain how these ingredients give rise to modern equivariant architectures. We then survey the principal strategies for incorporating rotational equivariance in deep learning, including group convolutions, internal tensorial representations, and canonicalization-based methods, and discuss their practical strengths and limitations. The tutorial aims to lower the barrier to the subject by connecting the underlying mathematics to practical model design, by unifying ideas that are often expressed in different formal languages, and by helping practitioners choose among competing approaches through a clear discussion of their trade-offs.
Yasmin Tousinejad, Vera Koponenmath.CO cs.AI math.PR
Let $r\geq3$ be fixed, and let $\mathbf{G}_n$ be the set of all simple graphs with vertex set $[n]=\{1,\ldots,n\}$. We consider an exponential random graph model which gives higher probability to $G \in \mathbf{G}_n$ than to $H \in \mathbf{G}_n$ if $G$ has fewer $r$-cliques than $H$. But all graphs in $\mathbf{G}_n$ have positive probability. The degree to which graphs with fewer $r$-cliques are given higher probability is determined by a positive weight $w$. We prove that, asymptotically almost surely as $n \to \infty$, a random graph from $\mathbf{G}_n$ has a vertex partition into $r-1$ parts of roughly equal size, the density of edges between the parts is close to $1/2$, and for every $\varepsilon > 0$ the density of edges within any part is less than $\varepsilon$. The asymptotic structural properties are independent of the weight $w$ as long as it is positive. We also extend the result to the context of several clique sizes, each one with its own weight.
Embedding methods have become popular due to their scalability on link prediction and/or triple classification tasks on Knowledge Graphs (KGs). Embedding models are trained relying on both positive and negative samples of triples. However, since KGs generally contain only positive assertions, negative samples are artificially generated through negative sampling strategies, ranging from simple random corruption to more sophisticated approaches that exploit structural, semantic, or embedding information. The design and implementation of advanced negative samplers remains challenging, as most popular Knowledge Graph Embedding (KGE) libraries provide support only for basic strategies and lack a unified framework for developing more advanced and customized solutions. To address this gap, we introduce PyKEEN-NSX, an extension of PyKEEN, the popular KGE framework, that provides a modular engineered abstraction for negative sampling. The proposed architecture separates the generation of candidate negative pools, conditioned on an explicit context, from the selection strategy, enabling the development and integration of static, schema-aware and dynamic approaches within a consistent framework. Based on this abstraction, we implement six negative samplers, while remaining fully compatible with existing PyKEEN workflows and pipelines. As a proof of concept, we study negative availability across four datasets, showing that constrained pools frequently fall below the requested number of negatives, so that the encoded criterion is to a large extent replaced by the random fallback that supplements them.
Dain Kwon, Kanghyun Choi, Hyeyoon Lee +4cs.LG cs.AI
Existing GNN quantization methods suffer from considerable quantization overhead, which severely limits their practical usage in real-world scenarios. To this end, we present TopGQ, an accurate post-training GNN quantization framework, alleviating redundant quantization overhead. We propose dual-axis scale absorption, which enables activation quantization along both the outer and inner dimensions by merging one into the adjacency matrix. On top of that, we introduce TopPIN, a proxy for nodes' local structure, and use it to group nodes with similar topology during quantization. Experimental results show that TopGQ reduces quantization time by an order of magnitude while preserving accuracy.
Knowledge graph completion requires models to use both textual descriptions and relational structure. Existing LLM-based methods either encode KG structure as discrete tokens or refine a restricted set of candidate entities, and these two directions have largely been studied separately. We propose CoSC for LLM-based KGC, which combines discrete structural coding with similar entity information. Specifically, an LLM generates an initial candidate entity ranking from discrete structural codes, after which information from entities with structures similar to that of the query entity refines the ranking. Experiments on FB15k-237 show that CoSC outperforms existing baselines on MRR and Hits@10 while remaining competitive on Hits@1.
Graph positional encodings are widely used in graph neural networks and graph Transformers, yet it remains unclear when the code itself can identify nodes. We study a hybrid distance-spectral encoding that combines anchor-distance profiles with quantized low-frequency Laplacian-energy coordinates. Treating the encoding as an observation map yields a simplex-refined converse, an exact collision factorization \(κ_H=κ_Dκ_{S|D}\), and the collision information \(I_H=-\logκ_D-\logκ_{S|D}\). On random regular graphs, the criterion is made explicit through a bounded-correlation Gaussian-wave surrogate; for actual Laplacian-energy coordinates, we give the distance-conditioned spectral collision condition sufficient for conditional actual-coordinate achievability. Experiments show that \(I_H/\log n\) calibrates localization success, and PE-only structural task probes on Universal Dependencies trees show that hybrid encodings better recover syntactic-tree geometry than distance-only or spectral-only baselines.
Formal Concept Analysis (FCA) is an approach for conceptual classification building and rule discovery from a binary table describing a set of objects by a set of attributes. Extensions have been proposed to deal with non-binary and more complex data, such as Relational Concept Analysis (RCA) for multi-relational data. RCA aims to highlight groups of objects characterized by their relationships with other groups of objects. The richer and more complex nature of the underlying data allows RCA to produce richer results than FCA, at the expense of higher computational and interpretive complexity. The most commonly used conceptual classification structure in FCA is the concept lattice. However, in many applications, concept lattice substructures, such as AOC-posets, are preferred over the full lattice, either to mitigate combinatorial blow-up or to focus on the most informative parts of the structure. Indeed, in an AOC-poset, only concepts introducing an object or an attribute are represented, which makes AOC-posets smaller and easier to compute and use than concept lattices. Although RCA was originally defined on concept lattices, it can also be instantiated on AOC-posets. RCA is iterative and its convergence is guaranteed in the lattice-based setting, but this guarantee is lost when using AOC-posets. In this paper, we investigate this loss of convergence in detail. We show why convergence is no longer guaranteed in the general case, identify conditions under which it can still be ensured, and discuss how a dataset can be transformed to recover convergence. We also propose a convergent variant of the process, which preserves the AOC-poset structure: relational attributes, once created, are never removed, which guarantees convergence at the price of attributes that may refer to concepts absent from the final structures.
We study unsupervised hypergraph alignment, where the goal is to infer node correspondences between two hypergraphs using only structural information, without node features, labels, seed matches, or side information. Direct higher-order formulations can represent hyperedge interactions faithfully, but they can be computationally demanding and cumbersome for non-uniform hypergraphs. Graph-reduction approaches introduce a different challenge: clique expansions keep the alignment problem on the original node set but collapse all hyperedge evidence into one pairwise graph, whereas bipartite expansions preserve incidence structure but enlarge the problem from nodes to nodes plus hyperedges. We introduce FALCON (Filtration-based hypergrAph aLignment via Cross-scale Optimal traNsport), an unsupervised optimal-transport framework for hypergraph alignment. Instead of representing each hypergraph by a single collapsed clique graph, FALCON constructs a filtration-induced sequence of clique-based co-occurrence dissimilarity matrices and jointly aligns all levels through one shared multi-scale Gromov--Wasserstein (GW) objective. The shared transport plan enforces a globally consistent node correspondence across filtration levels while avoiding the auxiliary hyperedge nodes introduced by bipartite expansion. Experiments on perturbation benchmarks derived from real-world hypergraphs show that FALCON is robust to structural noise and in almost all cases outperforms strong graph- and hypergraph-alignment baselines.
Reasoning over text-attributed graphs (TAGs) requires large language models (LLMs) to combine a node's text with evidence distributed across its neighbourhood. Existing methods fix the set of accessible neighbours before generation, forcing reasoning to operate over a static context and preventing the model from acquiring missing evidence during inference. We argue that neighbour selection should itself be part of the reasoning process. To this end, we propose Call Neighbours Yourself (CNY), a framework that enables LLMs to proactively explore graph neighbourhoods through topology-constrained graph-walk actions. Instead of reasoning over a pre-selected neighbour set, CNY exposes lightweight neighbour previews and learns when to expand candidate neighbours for additional evidence. To address the delayed-credit challenge of neighbour exploration, we introduce destination-conditioned on-policy self-distillation, which retrospectively evaluates a selected neighbour after its content is revealed and converts the resulting change in action preference into an action-level training signal. Experiments on standard TAG reasoning benchmarks under a unified raw-text setting show that CNY consistently outperforms fixed-context post-training baselines. Furthermore, the learned exploration policy transfers to unseen graphs and to a graph-level task not encountered during training. Code is available at https://github.com/superallen13/CNY.
Zhiyang Qiu, Yangtao Wang, Xiaocui Li +3cs.LG cs.AI
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
Spatio-temporal graphs are widely used in modeling complex dynamic processes such as temporal forecasting, molecular dynamics, and healthcare monitoring. Recently, stringent privacy regulations such as GDPR and CCPA have introduced significant new challenges for existing spatio-temporal graph models, requiring complete unlearning of unauthorized data. Since each node in a spatio-temporal graph diffuses information globally across both spatial and temporal dimensions, existing unlearning methods primarily designed for static graphs and localized data removal cannot efficiently erase a single node without incurring costs nearly equivalent to full model retraining. To address this, we propose CallosumNet, a spatio-temporal graph unlearning framework biologically inspired by the corpus callosum structure. CallosumNet makes two key technical contributions: (1) it reconstructs subgraphs using biologically-inspired virtual edges; and (2) it restores interlinked spatio-temporal dependencies among subgraphs via a lightweight meta-graph integration layer. Empirical results on four diverse real-world datasets show that CallosumNet achieves complete unlearning while maintaining accuracy very close to the gold model. The code is publicly available at https://github.com/wenlu-lab/STGraphUnlearning.