Graph Embedding

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3 papers in the last four weeks, down 40% on the four weeks before. 0.0% of all new papers.

Jul 13Week of Sep 28

Latest papers 34

Oct 5, 2026cs.LG

Hyperbolic Graph Representation Learning: Embed in One Metric, Optimize with Another

Hierarchical graphs embed in hyperbolic space with lower distortion than in Euclidean space owing to its negative curvature. However, their gradient-based learning is hampered at large radii, where the Poincaré ball and the Lorentz hyperboloid models fail numerically. Polar coordinates avoid this problem, but the hyperbolic metric scales the angular step by the hyperbolic sine of the radius, freezing angular motion. We observe that this factor is a choice, silently fixed by existing implementations: the Euclidean tangent parametrization, for instance, uses the radius itself. We show that other choices are not only possible but preferable. They are endpoints of a one-parameter family of optimization preconditioners with curvatures from

-1

to

0

, while the embedding remains at curvature

-1

. We show that since the Euclidean preconditioner rearranges a layout but refines it poorly, while an intermediate one refines far better once a layout is in place, combining them in two stages reduces the loss on real-world trees by 46-74% over the best single curvature.

Federico Larroca, Paola Bermolen, Marcelo Fiori +1

Facultad de Ingenier´ıa Universidad de la Rep´ublica Uruguay

Riemannian Optimization Hierarchical Representation Learning Graph Embedding Hyperbolic Representation Learning

Oct 1, 2026cs.LG

Learning Commute-Time-Preserving World Models for Planning

World models allow agents to plan in latent space by choosing a sequence of actions that most reduces the distance to a given goal state. Thus, planning can benefit from latent representations whose distances mirror commute-times in the environment. The spectral embedding space of the graph Laplacian provides such a representation, if it obeys a specific eigenvalue-dependent scaling. Unfortunately, instantiating the graph Laplacian is intractable in large, continuous environments. Self-supervised learning offers a natural route to such commute-time-preserving embeddings at scale. However, here we show that existing methods, which commonly encourage isotropic representations to prevent representational collapse, tend to degrade the "correct" eigenvalue-dependent scaling, leading to an inaccurate representation of commute times. To address this problem, we introduce Commute-Time-Preserving World Models (CTWMs), combining a latent displacement predictor and a log-determinant regularizer that prevents collapse, which provably recover the correctly scaled Laplacian representation under reversible deterministic dynamics and at the predictor's fixed point. In numerical simulations, CTWM matches or outperforms LeWM, a task-agnostic baseline, on several complex, continuous goal-reaching benchmarks, while using half the parameters.

Michael Hauri, Peter Buttaroni, Fabian A. Mikulasch +1

Friedrich Miescher Institute for Biomedical Research, Basel, Switzerland · Faculty of Science, University of Basel, Switzerland

Representation Learning World Model Learning Latent Dynamics Modeling World Model-Based Planning Model-Based Planning Graph Embedding

Sep 28, 2026cs.LG

GeoGAE: Scalable Graph-Level Autoencoding via Hyperball Cloud Representations

Embedding structured objects into Euclidean spaces has enabled a wide range of successful machine learning applications. Such objects include words, documents, image patches, time series, and graph nodes. In contrast, embedding entire graphs remains a challenging problem. Existing methods either sustain the original order of the graph nodes or match the output nodes to the input ones, both of which create scalability issues. In this work, we propose a graph representation as a cloud of hyperballs, which allows us to define a specific, typically unique, node ordering. Based on this representation, we propose GeoGAE, an autoencoder, in which the Transformer encoder translates a hyperball cloud into a graph-level embedding, and the Transformer decoder translates the graph-level embedding back into the graph. This formulation enables the model to capture both the global graph structure and local relational patterns. We evaluate our method on multiple graph datasets, spanning various domains. The results demonstrate effectiveness of our method in encoding and reconstructing graphs from their embeddings.

Radosław Nowak, Anna Bielawska, Bogusz Stefańczyk +2

Institute of Theoretical and Applied Informatics Polish Academy of Sciences · IDEAS Research Institute · Faculty of Mathematics, Informatics and Mechanics Warsaw University of Technology

Graph Neural Networks Graph Representation Learning Graph Embedding

Sep 8, 2026cs.LG

Topology-induced Operators Reveal Complementary Graph Representations without Training

Graph representation learning has largely focused on designing increasingly sophisticated models to transform graph topology into vector representations, or embeddings. However, the extent to which embedding quality depends on model learning, rather than on the underlying topological transformations, remains unclear. Here, we show that informative embeddings can be derived without complicated model design and gradient-based training. Propagating random features through implicit hierarchical structures induced by random walks and anonymous walks yields embeddings that capture node proximity and structural role, respectively. These two training-free embeddings preserve complementary aspects of graph organization and perform competitively with classic and recent methods across various node-, edge-, and graph-level tasks. They often require substantially less computation, resulting in a favorable quality-efficiency trade-off. Combining the two types of embeddings further improves inference quality of some tasks compared with using either embedding type alone. Our results suggest that informative graph embeddings can arise from carefully chosen topological transformations before any learning operation is applied.

Meng Qin, Jinqiang Cui, Hongwei Zheng +2

Department of Strategic & Advanced Interdisciplinary Research, Pengcheng Laboratory (PCL), Shenzhen, Guangdong, China. · Beijing Academy of Blockchain and Edge Computing, Beijing, China. · LMIB, NLSDE, and School of Artificial Intelligence, Beihang University, Beijing, China. +1

Graph Representation Learning Graph Embedding Topological Representation Learning

Sep 2, 2026cs.CR

Population-Calibrated Graph Screening at 835-Million-Address Scale, with Label-Free Transfer to New Chains

Compliance screening of blockchain addresses is, in practice, a lookup against sanctions registries plus clustering heuristics; it fails on unlabelled addresses and on chains with no label coverage at all. We describe a deployed system that scores an address by its position in a multi-chain transaction graph rather than by its presence in a list. The substrate is a single graph of 835,330,427 addresses and 15,826,261,934 edges across five EVM chains; a shared inductive encoder with per-chain normalisation feeds two scoring heads. Decision thresholds are exact quantiles of the score distribution over the full population, scanned per chain segment, so the alert volume is known in advance. We report: label-free transfer: heads trained on two chains recall 0.8598 / 0.8182 / 0.9967 of held-out positives on Base, Arbitrum and Gnosis at a

10^{-3}

population alert rate, with no target-chain labels in head training; a static lead-time replay over 68 external registry events: 40 of 68 (58.8%) flagged at the 0.1% budget,

\times

152 over an event-level random-flagging baseline, with first on-chain appearance a median of 528.8 days (Ethereum) / 647.8 days (Tron) before public designation; a serving path whose score is bit-identical to the offline artefact at end-to-end p50 151 ms, gated by a 2,882-address drift panel; and an adversarial harness of eight recurrent reinforcement-learned archetypes that passes an 8-criterion degeneracy audit and, on a detector-independent snapshot, exposes a measured blind spot of the deployed heads against synthesised behaviour.

Yury Korolev

AIDECISIONS, London

Financial Fraud Detection Graph Embedding

Sep 2, 2026cs.LG

Spectral Initialization and Scheduled Graph Smoothness for Uncertain Knowledge Graph Completion

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.

Md Abrar Jahin, Taufikur Rahman Fuad, Jay Pujara +1

University of Southern California · Islamic University of Technology

KG Completion Link Prediction Graph Embedding Spectral Regularization

Aug 29, 2026cs.LG

Effective Graph and Rank-based Contextual Embeddings for Textual and Multimedia Data

In a data-driven world, efficiently organizing and mapping relationships between objects is crucial. Graphs are powerful tools for modeling these connections, being widely used in social networks, telecommunications, and biology. However, graph-based methods often face high computational costs, particularly in memory and space usage. To address this, graph embedding techniques, also referred to as Network Representation Learning, encode graph information into lower-dimensional representations while preserving structural aspects. Traditional methods, however, lack interpretable dimensions. RaDE (Rank Diffusion Embedding) introduces a new approach using rank-based information, with a key step being the selection of a representative subset of nodes to provide interpretability for its dimensions and improve retrieval tasks. Despite its potential, RaDE's original proposal did not fully explore the effectiveness of representative subset selection across different classes or evaluate embeddings in tasks like classification and clustering. Inspired by RaDE, this work introduces GRaCE (Graph and Rank-based Contextual Embeddings), a fully unsupervised framework that generates interpretable embeddings by leveraging robust rank-based measures for representative subset selection and node embedding. GRaCE surpasses RaDE and Original Features across diverse datasets, including textual and image collections, excelling in retrieval, classification, and clustering tasks, considering state-of-the-art Transformer models as feature descriptors and Graph Convolutional Networks models in classification tasks.

Thiago César Castilho Almeida, Gustavo Rosseto Letício, Lucas Pascotti Valem +2

Department of Statistics, Applied Math. and Computing, State University of S˜ao Paulo (UNESP), Rio Claro, Brazil · Institute of Mathematical Sciences and Computing, University of S˜ao Paulo (USP), S˜ao Carlos, Brazil · Department of Computer Science, University of Manchester, Manchester, United Kingdom +1

Graph Representation Learning Unsupervised Representation Learning Graph Embedding

Aug 19, 2026cs.LG

Enhancing Distance-Based Graph Autoencoders with Structural Penalties for Dynamic Graph Embedding

Graph autoencoders (GAEs) are widely used for learning representations of dynamic graphs. However, their optimisation objectives typically do not take structural heterogeneity across nodes into account. We propose three distance-based GAE variants that incorporate structural penalties into the reconstruction loss. All variants share a two-layer Graph Convolutional Network encoder and a Euclidean-distance decoder trained with distance-based reconstruction objectives. We extend sparsity-corrected loss with two node-level regularization terms: (i) a hub penalty based on degree centrality, and (ii) a penalty based on Natural Community Local Intrinsic Dimensionality (NC-LID). The paper is motivated by prior evidence linking high NC-LID to reduced embedding quality. The proposed methods are designed to emphasize reconstruction errors for structurally ambiguous nodes. Experiments on multiple dynamic graph data sets show that incorporating NC-LID-based regularization consistently improves reconstruction performance over the baseline without structural regularization and the method using hub-aware regularization. These findings highlight NC-LID as a useful structural signal for enhancing distance-based graph autoencoders in dynamic settings.

Aleksandar Tomčić, Miloš Savić, Miloš Radovanović

Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Serbia Trg Dositeja Obradovi´ca 4, 21000 Novi Sad, Serbia

Graph Neural Networks Dynamic Graph Learning Graph Embedding

Aug 11, 2026stat.ML

Spectral Embeddings of Degree- $α$ Laplacians in Random Dot Product Graphs

Spectral clustering methods for network data are commonly based on a few matrix representations, such as the adjacency matrix and the symmetric Laplacian. We study a continuum of degree-normalized spectral embeddings that includes these commonly used choices as special cases. Under a random dot product graph model, we establish a row-wise central limit theorem for this family of embeddings. The result provides an explicit description of how degree normalization affects both population geometry and the local uncertainty of embedded nodes. We use the limiting distributions to compare different normalizations in two-community stochastic block models through a projected-Gaussian Bayes-error diagnostic. These comparisons show that no single normalization is uniformly preferred. Instead, the favored normalization depends on network density, community imbalance, and block-probability structure. Typically, stronger normalization is favored in lower-density or more imbalanced settings. These results provide a unified distributional understanding of when and why alternative normalizations may improve spectral clustering.

John Park, Ning Hao

University of Hong Kong · University of Arizona

Clustering Spectral Clustering Graph Embedding

Aug 3, 2026cs.SE

Pretraining on Call Graphs: When Binary Analysis Tasks Profit From Context

Binary function embedding models are trained to encode the semantics of binary code in such a way that they can be generalized to a variety of reverse engineering tasks, such as binary code search, vulnerability detection, or malware classification. While many models only take the function in question as contextual input, there have been successful attempts to improve function embeddings by leveraging information from the call graph. In this study, we dissect the implications of these embedding refinements. We conduct experiments using a range of graph-based models on the embeddings generated by two state-of-the-art binary function embedding models. Integrating inter-procedural context, we show that improvements on binary code similarity detection (BCSD) will not necessarily generalize to downstream tasks, neither of semantic nor of syntactic nature. More generally, we find that optimizing for semantic similarity tasks correlates with worse performance on syntactic tasks. By conducting an explanatory analysis on the dataset, we find that the call graph-based enhancements significantly enhance the robustness of embeddings, particularly in scenarios where the initial models struggle. Furthermore, we observe that the added context is more beneficial for namespace-related functions than for those focused on individual logic, confirming that the call graph can be leveraged most effectively in context-dependent scenarios.

Samuel Valenzuela, Johannes Kinder

Ludwig-Maximilians-Universität München · Munich Center for Machine Learning · Center for Digital Technology and Management +1

Representation Learning Graph Representation Learning Graph Embedding

Jul 31, 2026cs.SI

Multi-Granularity Position Embedding of Graphs via Granular-Ball for Link Prediction

Link prediction aims to identify potential or future connections within a given graph structure. Position information is essential for link prediction, as it distinguishes homogeneous nodes through their relative relationships, facilitating the accurate capture of structural patterns and implicit connections. Previous studies derive node positional information as distances to single-granularity landmarks, defined as the centers of homophilic regions, while neglecting the multi-granularity nature of homophilic structures and their hierarchical interrelations. We propose the Multi-Granularity Position Embedding of Graphs via Granular-Ball for Link Prediction (MGLP) method to obtain multi-granularity position embedding of graphs. Specifically, MGLP introduces an Adaptive Granular-Ball Graph Refinement mechanism to adaptively refine the graph into homophilic subdomains with optimal levels of granularity. The central nodes within subdomains are treated as landmarks, which form a Hierarchical Central Graph. Moreover, a novel Multi-granularity Hierarchical Distance encoding mechanism is proposed to capture both the homophilic structures within a graph and their hierarchical correlations, improving the discriminative power of nodes. Experimental results demonstrate that the multi-granularity position embedding generated by our method exhibits excellent performance and strong competitiveness compared to baseline algorithms for link prediction. Our codes are available in https://anonymous.4open.science/r/MGLP-D3C5/.

Sen Zhao, Cheng Liu, Shuyin Xia +4

Chongqing Key Laboratory of Computational Intelligence, Key Laboratory of Big Data Intelligent Computing, Key Laboratory of Cyberspace Big Data Intelligent Security, Ministry of Education, School of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China · Chongqing Key Laboratory of Computational Intelligence, Key Laboratory of Big Data Intelligent Computing, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China · Chongqing Ant ConsumerFinance Co,. Ltd, Ant Group, Chongqing, 400065, China

Graph Representation Learning Link Prediction Hierarchical Representation Learning Graph Embedding

Jul 30, 2026cs.LG

Kohn-Sham Spectral Embedding on Sparse Graphs at the Nishimori Temperature for Image Classification

We propose Kohn-Sham Spectral Embedding (KSSE), an energy-based model replacing the top-layer classifier of convolutional networks with a sparse-graph spectral embedding at the Nishimori temperature of an associated Random-Bond Ising Model the spectral detectability threshold where class structure becomes marginally distinguishable from disorder. Mapping pre-trained features onto quasi-cyclic low-density parity-check graphs, we construct a regularized Laplacian (Bethe-Hessian) as an effective Kohn-Sham Hamiltonian, yielding D independent spectral problems-one per feature channel-solvable in

O(N log N + k_{mode}^{2} N)

time by FFT on circulant blocks (Pontryagin self-duality), with low-mode Rayleigh-Ritz refinement (

k_{mode}=5

). Physically, this is a k.p effective-mass reduction on a one-dimensional ring crystal: the circulant support is the perfect crystal, the data weights a slowly varying impurity potential, and the Nishimori crossing a Fermi level at the band edge. Star-domain surgery optimizes the graph: instead of eliminating all frustrated cycles impossible without destroying the codewords-edge shifts create certified convexity around codewords with bounded residual frustration, with multi-scale fractal certification (basins

D_{2}<1

vs rough landscapes

D_{2}>3

). The theory includes a generalized Ihara-Bass identity with a sharp spectral threshold, a non-backtracking growth trichotomy with frustration as a gauge-invariant

Z_{2}

flux, a trapping-set spectral test, exact channel separability with a cup-product obstruction, plus loop-series, convexity, surgery, and quasi-stationarity bounds. On ImageNet-1000 with frozen EfficientNet-B4 features (D=1792) under a transductive protocol, KSSE achieves 88.93% Top-1 accuracy with ~21.24M parameters-beating Swin-L (197M, 86.4-87.3%) and matching the lower end of ViT-H/14 (632M, 88.0-89.5%) with 10x and 30x fewer parameters.

V. S. Usatyuk, D. A. Sapozhnikov, S. I. Egorov

Department of Computer Engineering, South-West State University (SWSU), Kursk, 305040 Russia · T8 LLC, R&D Department, Information Theory Group, Moscow, 107076 Russia

Graph Representation Learning Energy-Based Models Graph Embedding Image Classification

Jul 11, 2026cs.LG

Distance-Preserving Embeddings in Inhomogeneous Random Graphs

Graph machine learning provides powerful tools for understanding complex networks and learning meaningful node representations. A central challenge, however, is designing embeddings with minimal distortion of both local and global functionals, such as shortest path lengths. Prior distortion guarantees for distance-preserving embeddings are worst-case in nature, producing overly pessimistic bounds that fail to capture the structure of typical large-scale networks. To address this, we analyze shortest-path approximation via landmark-based embeddings on inhomogeneous random graphs, a general model with type-dependent edge probabilities. By retaining shortest paths to a small set of reference nodes called landmarks, landmark-based methods effectively function as virtual graph spanners, where structural heterogeneity and controlled neighborhood expansion modeled via multi-type branching processes enable significantly tighter dimension-distortion trade-offs than classical worst-case bounds. We extend these guarantees to global, component-wide averages and unify the analysis across finite-type and continuous latent spaces through a novel metric sandwiching framework, establishing universal distortion bounds for general

L^2

kernel models, including heavy-tailed and power-law networks. Finally, we introduce a GNN-augmented variant that replaces rigid, computationally expensive exact shortest-path queries with flexible, structure-aware neural surrogates. By leveraging the inherent alignment between graph neural message-passing and the dynamic programming principles of shortest-path algorithms, our approach demonstrates that models trained on small-scale random graphs learn to extract universal distance-preserving features, achieving robust generalization to large-scale, real-world networks that match or exceed the fidelity of classical, exact landmark-based embeddings.

My Le, Luana Ruiz, Souvik Dhara

Department of Applied Mathematics & Statistics Johns Hopkins University Baltimore, MD 21218, USA · School of Industrial and Systems Engineering Georgia Institute of Technology Atlanta, GA 30332, USA

Graph Neural Networks Graph Embedding

Jul 7, 2026cs.LG

EntroPath: Maximum Entropy Path Ensemble Embedding for Manifold Learning

We introduce EntroPath, a manifold learning method that recovers geodesic geometry from data graphs through ensembles of diffusion paths. Many existing graph-based embeddings rely either on locally normalised random walks or on shortest-path distances. The former can concentrate diffusion in densely sampled regions, while the latter are sensitive to spurious shortcut edges in the graph. EntroPath instead builds its dissimilarities from the maximum entropy random walk (MERW), which aggregates the full ensemble of k-step paths between points rather than relying on any single trajectory. We show that the resulting free-energy dissimilarity converges to squared geodesic distance in the short-time limit, via Varadhan's heat-kernel formula. The diffusion depth k interpolates smoothly between local neighbourhood structure and global manifold geometry, and the symmetrised kernel admits an exact Gram factorisation connecting EntroPath to kernel methods. We further provide scalable extensions via landmark projection and diffusion-potential pseudotime. Across synthetic manifolds and single-cell benchmarks, EntroPath consistently matches or outperforms diffusion- and shortest-path-based methods, while remaining competitive with neighbourhood-preserving embeddings (UMAP, t-SNE) on local-structure metrics. Its gains are most pronounced on manifolds with non-uniform sampling density and well-separated branching trajectories, where path-ensemble diffusion more faithfully preserves the underlying geodesic geometry.

Przemysław Rola

Department of Mathematics, Krakow University of Economics

Manifold Learning Graph Embedding

Jul 3, 2026cs.CR

Enhanced Feature Extraction for IoT Network Intrusion Detection Using GNNs and KAN

Recent advancements in the Internet of Things (IoT) emphasize the urgent need for advanced network security, as IoT networks feature dynamic topologies, imbalanced traffic, and complex attack patterns. Unlike general IT networks, IoT environments exhibit extreme heterogeneity and sparse topologies. Traditional GNN-based intrusion detection methods often struggle to efficiently model node and edge features or capture fine-grained anomalies in such settings. To address this, we propose SKGFusionKAN, a novel IoT-tailored approach enhancing GraphSAGE with a multi-scale selective kernel attention mechanism. This enables adaptive extraction of node and edge features under diverse traffic conditions. Specifically, our edge-oriented message passing strengthens information propagation, while selective kernel attention adaptively weights edge-derived information from different scales to handle heterogeneity. We also introduce a gated fusion process to dynamically integrate multi-scale features, improving robustness against evolving attacks. Finally, we leverage Kolmogorov-Arnold Networks (KAN) for classification, offering superior nonlinear modeling capabilities essential for detecting intricate, low-frequency attacks. To our knowledge, this work presents a comprehensive integration of GNNs and KAN with dedicated architectural innovations for IoT intrusion detection. Extensive experiments on four NIDS benchmarks show that SKGFusionKAN consistently outperforms state-of-the-art approaches in binary and multiclass tasks, demonstrating its potential for IoT security.

Long Zhao, Shixun Ji, Bin Cheng +1

Department of Control Science & Engineering, Tongji University, Shanghai 201804, China · National Key Laboratory of Autonomous Intelligent Unmanned Systems, Shanghai 201203, China

Graph Neural Networks IoT Intrusion Detection Network Intrusion Detection Multi-Scale Feature Fusion Graph Embedding

Jun 30, 2026cs.LG

Visualizing High-Dimensional Graph Embeddings via Informed Multi-View Projections

Graphs are commonly visualized in 2D, where humans readily interpret spatial relationships, yet such layouts often distort higher-dimensional structure. We propose to embed graphs in high-dimensional space and search for informative 2D viewpoints that optimize aesthetic and readability metrics (e.g., edge crossings and angular resolution), enabled by a novel differentiable surrogate for edge crossings. Numerical experiments show that these viewpoints consistently outperform standard 2D layouts, and can even surpass methods explicitly designed to optimize these metrics. We further introduce DataFly, an interactive system for exploring multiple candidate viewpoints through seamless navigation. A usability study demonstrates that our approach reveals structural patterns that remain hidden in conventional 2D visualizations.

Ya Ji, Xuefeng Li, Timo Brand +4

Khoury College of Computer Sciences, Northeastern University, Seattle · School of Computation, Information and Technology, Technical University of Munich, Heilbronn, Germany

Scientific Visualization Data Visualization Visual Analytics Graph Embedding

Jun 30, 2026cs.IR

AGE: Adaptive-masking for Graph Embedding in Graph Retrieval-Augmented Generation

GraphRAG is an extension of retrieval-augmented generation (RAG) that supports large language models (LLMs) by referring to graph-structured data as external knowledge. While this technique ideally captures intricate relationships, it often struggles with graph representations for LLMs, particularly for frozen LLMs, due to the misalignment between graph-based and text-based latent features. We tackle this issue by introducing the {\it Adaptive-masking for Graph Embedding (AGE)}. AGE employs a Transformer in a mask-based self-supervised learning (SSL) approach. We designed the architecture similar to text embedding encoders, addressing the latent feature misalignment. In contrast to natural language texts, graphs are concise representations, and there exist {\it key nodes} that hold dominant contextual information, which are challenging to predict from their surroundings. Masking such key nodes leads to inefficiency in the SSL process. Therefore, AGE focuses on predicting nodes apart from key nodes, utilizing a learnable node sampler. Our experimental results indicate that AGE significantly improves approaches using non-parametric search component in GraphQA tasks, achieving superior accuracy across four benchmark datasets with distinct characteristics.

Bao Long Nguyen Huu, Atsushi Hashimoto

OMRON Corporation · OMRON SINIC X Corporation

Graph Representation Learning Graph SSL Graph Retrieval-Augmented Generation Knowledge Graph Question Answering Graph Embedding

Jun 20, 2026cs.DC

FeLoG: Scalable and Efficient Distributed Graph Embedding with Feedback Loop Mechanism

Graph embedding maps graph nodes into low-dimensional vectors to support applications such as recommendation, fraud detection, and graph-based retrieval-augmented generation (GraphRAG). As graphs scale to billions of edges, scalable and efficient graph embedding has become increasingly important. Existing frameworks commonly adopt a sampling-training paradigm, in which mini-batches are constructed by sampling nodes and their neighbors. However, sampling is typically decoupled from evolving embedding quality, causing redundant exploration of well-trained regions while under-sampling undertrained nodes. At the system level, such decoupling further leads to excessive communication, serialized execution, and low resource utilization in distributed environments. We present FeLoG, a feedback loop-driven system for scalable distributed graph embedding. (1) FeLoG introduces feedback-coupled sampling and training, dynamically prioritizing undertrained nodes according to real-time embedding-quality feedback, thereby reducing redundant computation and accelerating convergence. (2) It employs activity-aware communication that compresses frequently occurring node sequences to reduce intra-machine PCIe traffic and selectively synchronizes frequently updated embeddings to reduce inter-machine communication. (3) It adopts a round-interleaved pipeline that overlaps next-round sampling with current-round training to improve CPU-GPU utilization. Experiments against six state-of-the-art baselines on large-scale graphs show that FeLoG achieves an average speedup of 27.9x, reduces communication cost by more than 53.1%, and sustains over 80% CPU-GPU utilization.

Peng Fang, Arijit Khan, Ziqiang Wu +4

Huazhong University of Science and Technology · Bowling Green State University

Communication-Efficient Distributed Training Graph Embedding

Jun 16, 2026stat.ML

Compact Geometric Representations of Hierarchies

Computing geometric representations of data is a cornerstone of modern machine learning, typically achieved by training dual encoders which map queries and documents into a shared embedding space. Recent work of You et al. [NeurIPS '25] has extended this approach to hierarchical retrieval, where relevance is determined by the ancestor-descendant relationships in a Directed Acyclic Graph (DAG). While previous work has shown that valid embeddings exist when the number of descendants is small, these bounds degrade significantly for deep hierarchies, requiring dimensions as large as the total number of nodes. In this paper, we investigate compact reachability embeddings for more general graph classes and provide theoretical guarantees for representing hierarchies using embeddings whose dimension depends on structural graph parameters. We prove that for any directed tree, there exists a reachability embedding in constant dimension 3, independent of the tree's size or depth. We generalize this result to graphs characterized by treewidth

t

, constructing embeddings of dimension

O(t \log n)

, where

n

is the number of nodes. Complementing these upper bounds, we provide matching or near-matching lower bounds, showing that dimension

Ω(n)

is necessary for general DAGs and

Ω(t/\log(n/t))

is required for graphs of treewidth

t

. We also obtain upper and lower bounds parameterized by the number of cross-edges in the DAG. We additionally show that our embeddings can be constructed on real world datasets, and that they give much smaller dimensions in high recall regimes compared to prior embeddings with theoretical guarantees.

Prashant Gokhale, Piotr Indyk, Yuhao Liu +3

UW-Madison · MIT

Hierarchical Representation Learning Geometric Representation Learning Graph-Based Retrieval Graph Embedding

Jun 6, 2026cs.LG

On solving symmetric multi-type orthogonal non-negative matrix tri-factorization problem

We study the symmetric multi-type orthogonal non-negative matrix tri-factorization problem, where several symmetric non-negative matrices are simultaneously approximated by factors of the form

GS_{i}G^{\top}

, with a shared non-negative and orthogonal factor

G

. This model is motivated by clustering and network analysis, where non-negativity improves interpretability and orthogonality gives a natural assignment-type structure to the latent factor. Since the resulting optimization problem is highly non-convex, we develop two heuristic algorithms for computing high-quality local solutions. The first one is a fixed point method derived from the Karush-Kuhn-Tucker conditions after adding a penalty term for the orthogonality constraint. The second one is a three-stage ADAM-based method that combines non-negativity-preserving optimization, orthogonalization, and restricted ADAM refinement on the feasible set. We evaluate both methods on synthetic data, including noisy instances, and on citation network benchmarks. The synthetic experiments show that both algorithms recover factorizations close to the optimum and remain stable under noise. On real networks, the learned embeddings are competitive with or better than standard baselines such as SVD, node2vec, and classical link prediction heuristics in link prediction, node clustering, and node classification tasks.

Rok Hribar, Gregor Papa, Janez Povh +1

Computer Systems Department, Jožef Stefan Institute, Jamova cesta 39, Ljubljana, 1000, Slovenia. · Laboratory for Engineering Design, Faculty of Mechanical Engineering, University of Ljubljana, Aškerčeva cesta 6, Ljubljana, 1000, Slovenia. · Rudolfovo – Science and Technology Centre Novo mesto, Podbreznik 15, Novo mesto, 8000, Slovenia. +1

Non-Negative Matrix Factorization Graph Clustering Matrix Optimization Graph Embedding

Jun 5, 2026cs.CL

Geometry of Semantic Space: Comparative Study of Discrete and Continuous Models

This work examines the semantic geometry underlying NLP models. We compare supervised vector embeddings, such as CamemBERT, with lexical co-occurrence graphs that encode semantic relations more directly. While transformer-based embeddings achieve strong performance, their induced geometries often display unsatisfactory distributions. In contrast, graph-based models reveal a clearer and more human-readable organization of meaning. We have implemented a methodology that allows us to perform a comparative analysis either based on the structure of the graphs or based on the topology of the embeddings induced by these two approaches. The results of the comparison -- applied to the French "Great National Debate" corpus a collection of citizen contributions to the public debate -- show a similar local topology but a very different overall structure and topology. Theses findings suggest complementary perspectives between deep supervised models and graph-based models, considering a new pathway to guide neural architectures toward more stable and interpretable convergence with graphs structures.

Gabriel Bounias, Sabine Ploux

ISC-PIF (Institut des Systemes Complexes de Paris IdF), CNRS, France · CAMS (Centre d’analyse et de mathématique sociales), CNRS & EHESS, Paris, France

Neural Representation Geometry Graph Embedding Text Embedding Models

May 21, 2026cs.AI

Epicure: Navigating the Emergent Geometry of Food Ingredient Embeddings

We present Epicure, a family of three sibling skip-gram ingredient embeddings retrained from scratch on a multilingual recipe corpus. We aggregate 4.14M recipes from 11 sources spanning seven languages, English, Chinese, Russian, Vietnamese, Spanish, Turkish, Indonesian, German, and Indian-English, and normalise the raw ingredient strings to 1,790 canonical entries via an LLM-augmented pipeline. A 203,508-edge ingredient-ingredient NPMI graph and an 80,019-edge typed FlavorDB ingredient-compound graph, 2,247 typed compound nodes across 15 categories, seed three Metapath2Vec variants that share architecture and hyperparameters and differ only in the random-walk schema: Cooc walks the co-occurrence graph only, Chem walks the typed compound metapaths only, and Core blends both via injected ingredient-ingredient walks at controlled mixing, placing each model at a distinct point on the chemistry-vs-recipe-context spectrum.

Jakub Radzikowski, Josef Chen

Graph Embedding

May 21, 2026stat.ML

The ASE-LSE Disagreement Landscape: An End-to-End Characterisation of Extremes and Structural Drivers

Two of the most widely used methods for analysing graph data, Adjacency Spectral Embedding and Laplacian Spectral Embedding, often produce different results when applied to the same graph. Yet the structural reasons behind this disagreement remain incompletely understood. This paper provides an end-to-end account of ASE-LSE latent subspace disagreement. We first prove that the two methods produce identical latent subspaces for every embedding dimension whenever the Laplacian is a scalar multiple of the adjacency matrix, and show that this scalar relationship holds if and only if the graph is either regular or bipartite biregular. This anchor result identifies a sufficient condition for perfect agreement that pins down the floor of the disagreement spectrum and supplies the baseline for the perturbation analysis. We then prove that no maximal-disagreement graph or family of graphs exists: the disagreement is always strictly below its theoretical ceiling, and we exhibit a witness family demonstrating that no finite maximum is attainable, so the disagreement landscape has no maximiser. With both endpoints established, we derive a Regularity Departure Bound whose two terms isolate degree heterogeneity and eigengap as the primary structural factors influencing disagreement in the middle regime. Empirical validation across thousands of simulated graphs confirms the mechanisms predicted by the bound: heterogeneity pushes disagreement up, eigengap suppresses it, and their joint ratio emerges as a unified predictor of ASE-LSE disagreement, suggesting when the two embeddings can be treated as interchangeable and when they cannot.

Minh Triet Pham, Ian Gallagher

School of Mathematics and Statistics The University of Melbourne, Australia

Graph Embedding Spectral Methods

May 19, 2026cs.LG

Euclidean Embedding of Data Using Local Distances

We study the problem of recovering a globally consistent Euclidean embedding of data, given only a local distance graph and propose a method that optimally represents these distances. The method operates solely on a neighborhood graph weighted by pairwise distances, without requiring any prior vector representation of the data. The embedding is obtained by solving a variational problem that matches local, on-graph distances to the Euclidean metric, induced by the differentials of the embedding functions. The resulting Euler-Lagrange equations are derived in a coordinate-free form, enabling direct evaluation of all operators from the distance graph alone. Though non-linear and missing an explicit expression for their non-linearity, these equations are shown to be resolved as an iteratively updated sparse linear problem. The main contributions of the proposed approach are (a) the derivation of the functional equations governing the optimal Euclidean embedding in the continuum, (b) a representation-free formulation that requires only a neighborhood distance graph and no feature vectors and (c) an estimation procedure based exclusively on local graph operations. We experimentally evaluate the resulting non-parametric algorithm on synthetic manifolds and real datasets, demonstrating consistent preservation of local metric structure and neighboring relations, while approximating the global isometric embedding.

Dimitris Arabadjis

Department of Statistics and Actuarial-Financial Mathematics University of the Aegean Karlovassi, Samos, PA 83200

Manifold Learning Dimensionality Reduction Graph Embedding

May 11, 2026cs.LG

CORE: Cyclic Orthotope Relation Embedding for Knowledge Graph Completion

Knowledge graph completion (KGC) aims to automatically infer missing facts in multi-relational data by mapping entities and relations into continuous representation spaces. Recent region-based embedding models have shown great promise in capturing complex logical patterns by representing relations as geometric regions. However, these models inevitably suffer from absolute boundary constraints during optimization. Conversely, without such constraints, relation regions expand indefinitely. To address the limitation, we propose \textbf{CORE} (Cyclic Orthotope Relation Embedding), a novel KGC model that embeds entities and relations onto a boundary-less torus manifold.CORE represents relations as cyclic orthotopes on the torus manifold, allowing regions to seamlessly wrap around spatial boundaries to ensure smooth gradient conduction. Furthermore, an adaptive width regularization is introduced to prevent unconditional region expansion. Theoretical analysis proves that CORE can capture various complex relation patterns such as subsumption and intersection. Extensive experiments on four benchmark datasets demonstrate that CORE achieves highly competitive performance, significantly improving link prediction accuracy in dense semantic environments.

Yingqi Zeng, Luying Wang, Huiling Zhu

Graph Representation Learning KG Embedding Graph Embedding KG Completion

May 10, 2026cs.LG

GravityGraphSAGE: Link Prediction in Directed Attributed Graphs

Link prediction (inferring missing or future connections between nodes in a graph) is a fundamental problem in network science with widespread applications in, e.g., biological systems, recommender systems, finance and cybersecurity. The ability to accurately predict links has significant real-world applications, such as detecting fraudulent financial transactions or identifying drug-target interactions in biomedicine. Despite a rich literature, link prediction is still challenging, especially for graphs enriched with information on edges (direction) and nodes (attributes). In fact, research on link prediction, especially the one based on Graph Deep Learning (GDL), has mostly focused on undirected graphs, without fully leveraging node attributes. Here, we fill this gap by proposing Gravity-GraphSAGE (GG-SAGE), a modified version of GraphSAGE, a GDL model for node embeddings, composed of a gravity-inspired decoder. This implementation is the first example in the literature of a GraphSAGE backbone adopted for directed link prediction. Using the benchmark datasets Cora, Citeseer, PubMed and 16 real-world graphs from the online Netzschleuder repository, we show that our proposed model outperforms state-of-the-art GDL link prediction techniques. Using further experimental evidence, we relate the quality of the output of our model with various characteristics of the graph, suggesting that our framework scales well when applied to data of increasing complexity.

Riccardo Porcedda, Francesca Chiaromonte, Fabrizio Lillo +1

Department of Excellence L’EMbeDS, Sant’Anna School of Advanced Studies, Pisa, Italy · Department of Statistics and Huck Institutes of the Life Sciences, The Pennsylvania State University, USA · Class of Science, Scuola Normale Superiore, Pisa, Italy +1

Graph Neural Networks Graph Representation Learning Link Prediction Graph Embedding

May 6, 2026stat.ML

Multiscale Euclidean Network Trajectories: Second-Moment Geometry, Attribution, and Change Points

A central challenge in dynamic network analysis is to represent temporal evolution in a way that is both geometrically meaningful and statistically identifiable. One approach embeds a sequence of network snapshots as trajectories in a Euclidean space and relates these trajectories to node embeddings. In multilayer and unfolded spectral constructions, however, node embeddings and their underlying latent positions are identifiable only up to general linear transformations. Although this ambiguity preserves edge probabilities, it can distort geometry and invalidate distance based temporal comparisons at both the trajectory and node-levels. We develop Multiscale Euclidean Network Trajectories (MENT), a framework for multiscale temporal trajectories based on second-moment geometry. By imposing an isotropic normalization on the anchor latent positions, we reduce the relevant ambiguity to orthogonal transformations and prevent distortion of the second-moment geometry. In this canonical representation, we define a trace variation distance and mode-wise variation distances along orthogonal directions, and use multidimensional scaling to obtain low-dimensional trajectories of time points at both global and mode-wise levels. The resulting trajectories support interpretation and inference. They admit mode-wise decompositions, support attribution of global and mode-wise temporal changes to nodes, and enable change point detection through 1D trajectories. We prove consistency of the proposed unfolded spectral embedding and of the induced temporal trajectories. Experiments on two synthetic and two real dynamic networks illustrate stable and interpretable recovery of temporal structure and show strong performance against existing change point detection baselines.

Haruka Ezoe, Ryohei Hisano

Graduate School of Information Science and Technology The University of Tokyo · The Canon Institute for Global Studies

Dynamic Graph Learning Change-Point Detection Graph Embedding

Apr 30, 2026cs.LG

A Unified Framework of Hyperbolic Graph Representation Learning Methods

Hyperbolic geometry has emerged as an effective latent space for representing complex networks, owing to its ability to capture hierarchical organization and heterogeneous connectivity patterns using low-dimensional embeddings. As a result, numerous hyperbolic graph representation learning methods have been proposed in recent years. However, their practical adoption and systematic comparison remain challenging, as implementations are fragmented and shared tools for reproducible and fair evaluation are lacking. In this work, we introduce a unified open-source framework for hyperbolic graph representation learning that integrates several widely used embedding methods under a common optimization interface. The novel framework enables consistent training, visualization, and evaluation of hyperbolic embeddings, and interfaces seamlessly with standard network analysis tools. Leveraging this unified setup, we conduct an experimental study of hyperbolic embedding methods on real-world networks, focusing on two canonical downstream tasks: link prediction and node classification. Beyond predictive accuracy, the study offers practical insights into the strengths and limitations of existing approaches, thereby facilitating informed method selection and fostering reproducible research in hyperbolic graph representation learning.

Sofía Pérez Casulo, Marcelo Fiori, Bernardo Marenco +1

Facultad de Ingenier´ıa, Universidad de la Rep´ublica, Uruguay · Centro Interdisciplinario en Ciencia de Datos y Aprendizaje Autom´atico (CICADA), Universidad de la Rep´ublica, Uruguay

Graph Representation Learning Graph Embedding Hyperbolic Representation Learning

Apr 21, 2026cs.LG

Revisiting Catastrophic Forgetting in Continual Knowledge Graph Embedding

Knowledge Graph Embeddings (KGEs) support a wide range of downstream tasks over Knowledge Graphs (KGs). In practice, KGs evolve as new entities and facts are added, motivating Continual Knowledge Graph Embedding (CKGE) methods that update embeddings over time. Current CKGE approaches address catastrophic forgetting (i.e., the performance degradation on previously learned tasks) primarily by limiting changes to existing embeddings. However, we show that this view is incomplete. When new entities are introduced, their embeddings can interfere with previously learned ones, causing the model to predict them in place of previously correct answers. This phenomenon, which we call entity interference, has been largely overlooked and is not accounted for in current CKGE evaluation protocols. As a result, the assessment of catastrophic forgetting becomes misleading, and CKGE methods performance is systematically overestimated. To address this issue, we introduce a corrected CKGE evaluation protocol that accounts for entity interference. Through experiments on multiple benchmarks, we show that ignoring this effect can lead to performance overestimation of up to 25%, particularly in scenarios with significant entity growth. We further analyze how different CKGE methods and KGE models are affected by the different sources of forgetting, and introduce a catastrophic forgetting metric tailored to CKGE.

Gerard Pons, Carlos Escolano, Besim Bilalli +1

Data-intensive Technologies and Knowledge Systems (DTAK), Department of Service and Information System Engineering, Universitat Politècnica de Catalunya, Barcelona, 08034, Catalonia, Spain · Intelligent Data Science and Artificial Intelligence Research Center (IDEAI), Department of Computer Science, Universitat Politècnica de Catalunya, Barcelona, 08034, Catalonia, Spain

Graph Representation Learning KG Embedding Graph Embedding KG Completion Catastrophic Forgetting

Apr 16, 2026cs.LG

How Embeddings Shape Graph Neural Networks: Classical vs Quantum-Oriented Node Representations

Node embeddings act as the information interface for graph neural networks, yet their empirical impact is often reported under mismatched backbones, splits, and training budgets. This paper provides a controlled benchmark of embedding choices for graph classification, comparing classical baselines with quantum-oriented node representations under a unified pipeline. We evaluate two classical baselines alongside quantum-oriented alternatives, including a circuit-defined variational embedding and quantum-inspired embeddings computed via graph operators and linear-algebraic constructions. All variants are trained and tested with the same backbone, stratified splits, identical optimization and early stopping, and consistent metrics. Experiments on five different TU datasets and on QM9 converted to classification via target binning show clear dataset dependence: quantum-oriented embeddings yield the most consistent gains on structure-driven benchmarks, while social graphs with limited node attributes remain well served by classical baselines. The study highlights practical trade-offs between inductive bias, trainability, and stability under a fixed training budget, and offers a reproducible reference point for selecting quantum-oriented embeddings in graph learning.

Nouhaila Innan, Antonello Rosato, Alberto Marchisio +1

eBRAIN Lab, Division of Engineering, New York University Abu Dhabi (NYUAD), Abu Dhabi, UAE · Department of Information Engineering, Electronics and Telecommunications, Sapienza University of Rome, Rome, Italy · Center for Quantum and Topological Systems (CQTS), NYUAD Research Institute, NYUAD, Abu Dhabi, UAE

Quantum Machine Learning Quantum-Inspired ML Graph Classification Graph Embedding