Magnus H. Strømme, Alex G. C. de Sá, David B. Aschercs.LG
Molecular toxicity prediction is increasingly used to prioritise compounds before experimental testing, but conventional benchmark performance can overstate practical utility when structurally related molecules occur across training and test folds. We introduce ToxLens, a reproducible multi-task graph-learning framework for 11 toxicity endpoints spanning Ames mutagenicity, acute oral toxicity, hERG inhibition, and Tox21 nuclear-receptor and stress-response assays. The workflow combines conservative chemical curation, sphere-exclusion filtering, a leakage-aware UMAP-HDBSCAN split, parallel graph and global-feature encoders joined by late concatenation, temperature-scaled Monte Carlo dropout with conformal-style prediction sets, applicability-domain analysis, and SHAP-guided toxicophore discovery with occlusion controls. On the leakage-controlled test fold, a five-seed soft-voting ensemble achieved a Matthews correlation coefficient score of 0.44, an area under the receiver operating characteristic curve score of 0.83, and an area under the precision-recall curve score of 0.58. It exceeded four ECFP4-based shallow baselines on all 11 endpoints under the same split and validation-based threshold-selection protocol. Controlled ablations showed that the global pathway was important, whereas late concatenation outperformed the tested gated and feature-wise linear modulation fusion variants. Conformal-style prediction sets revealed substantial endpoint-specific variation in set efficiency, and discrimination and calibration improved with similarity to the training domain. Retraining on fixed published Tox21 Challenge and TDA folds produced competitive, but not uniformly state-of-the-art, performance. SHAP-guided occlusion and consensus subgraph mining yielded model-derived structural hypotheses, 44 of which contained at least one occurrence that passed the predefined counterfactual criteria.
Directed graph learning naturally leads to trainable nonsymmetric propagation operators with distinct right and left spectral structures. Building on the two-sided cone Rayleigh framework for generalized pencils \[ B_θ-λG, \] we develop a learning-oriented methodology for spectral certification, sensitivity analysis, and control without requiring symmetry, nonnegativity, or cone preservation. In the positive-orthant setting, computable lower and upper cone bounds provide an a posteriori enclosure of a distinguished cone level, while smooth soft-min/max surrogates preserve rigorous one-sided bounds with explicit approximation errors and remain differentiable with respect to the trainable parameters. For a simple interior level, the right and left modes satisfy \[ Dλ_C(B)[H]=v_C^T H u_C, \] yielding first-order optimal graph-supported interventions under prescribed perturbation budgets and motivating adaptive spectral control. Numerical experiments demonstrate the applicability of the approach beyond cone-preserving operators and in directed learning settings. Signed nonsymmetric perturbations reveal a transition from interior eigenpairs to boundary complementary quasi-pairs, including non-spectral cone levels, while controlled experiments show that symmetrization can remove predictive information carried solely by edge direction. On the directed Cora citation network, adaptive recomputation of the right--left sensitivity reduces the distinguished spectral level by approximately $21.5\%$ under a cumulative edge-weight reduction budget of $0.5\%$, with no observed change in test accuracy for the trained model and data split considered.
Finger vein verification is a promising biometric modality for secure authentication because vascular patterns are internal, difficult to observe externally, and relatively resistant to presentation attacks. However, reliable verification remains challenging in open-set settings, where test identities are unseen during training and non-enrolled probes must be rejected at inference. This paper presents OpenVeinNet, a finger vein verification framework designed for cross-dataset and open-set evaluation. The proposed model combines Dynamic Snake Convolution with graph-based feature modelling. Dynamic Snake Convolution extracts local curvilinear and tubular vein structures using adaptive sampling, while the graph convolutional backbone models long-range topological relationships between vein regions. To improve the discriminative quality of the embedding space, we introduce a Centroid Angular Hybrid Loss, which jointly encourages intra-class compactness and inter-class angular separation for cosinesimilaritybased verification. Experiments are conducted on five public finger vein datasets: FV-300, MMCBNU, FV-USM, PolyU, and VERA. The method is evaluated using leaveonedatasetout training under both enrolmentbased unknownrejection and fullsubject verification protocols, and is compared with handcrafted and recent deep learning-based baselines. The results show that OpenVeinNet achieves strong cross-dataset generalisation, consistently low equal error rates, and competitive true accept rates at fixed false accept rate operating points. Ablation studies further confirm the individual and combined contributions of adaptive tubular feature extraction, graph-based relational modelling, and the proposed loss function. These findings indicate that explicitly modelling local vein geometry, global vascular relationships, and angularly compact embeddings is effective for openset finger vein verification.
While large language models (LLMs) possess vast zero-shot procedural knowledge, their tendency to produce homogenized logic often obscures the unique, idiosyncratic execution processes of individual human creators. In this paper, we investigate the computational discovery of procedural personas from unstructured data. To achieve this, we introduce ViralRecipesTrans, a new dataset of procedurally aligned execution flow graphs extracted from popular culinary video transcripts and explicitly mapped to specific creators. We formulate procedural stylometry as a graph learning and process discovery task, revealing a fundamental duality: while traditional lexical classifiers overfit via semantic leakage, discrete topological metrics successfully capture the rigid physical constraints of a creator's workflow. Building upon this characterization, we extend our framework into a novel generative task--predicting a creator's exact structural execution graph for unseen dishes. We expose a fundamental dichotomy in style generation between global macro-planning and local structural execution. Our results demonstrate that few-shot LLMs dominate semantic assignment but suffer from persistent macro-planning deficits, whereas our structured two-stage model achieves superior topological control via rigid Markovian priors. Together, an ensemble approach to procedural generation combines the strengths from both sides, dynamically synthesizing global semantic reasoning with localized topological footprints to automate the discovery and generation of personalized workflows.
Network topology inference from graph signals is central to graph signal processing with applications in neuroscience, sensor, and social networks. In practice, target-domain samples are scarce while heterogeneous source-domain data are abundant. Fusing these sources is challenging: Euclidean averaging works for homogeneous sources but degrades sharply as inter-source divergence grows, collapsing distinct geometries into an inflated, biased consensus. We exploit the Wasserstein metric's distribution-preserving properties to counter heterogeneity while preserving each source's intrinsic geometry. We propose MS-WDRO, a multi-source Wasserstein distributionally robust graph learning framework that fuses heterogeneous sources via their weighted Wasserstein barycenter, a geometrically principled nominal distribution, then builds an ambiguity ball around it to hedge residual uncertainty. Minimizing worst-case risk yields a tractable regularized Laplacian estimator solved efficiently via a provably convergent ADMM scheme. We establish non-asymptotic guarantees: a finite-sample concentration bound for the empirical barycenter, a pooling bias lower bound proving naive aggregation is suboptimal, and an out-of-sample excess risk bound decaying at a parametric rate with only logarithmic dependence on source count. To calibrate hyperparameters governing robustness, sparsity, and source fusion, we unroll the solver into a differentiable architecture trained end-to-end, achieving data-adaptive calibration beyond cross-validation while retaining interpretability. Experiments on synthetic benchmarks and the multi-site ABIDE~I neuroimaging dataset show MS-WDRO consistently outperforms seven baselines in graph recovery, sample efficiency, and downstream diagnostic utility, with the largest gains in the sample-scarce regime.
Dalia Chakrabarty, Kangrui Wang, Chuqiao Zhang +1stat.ML cs.LG stat.AP
We present a new data-driven learning of a Random Geometric Graph (RGG) of a multivariate dataset, where the graph is drawn in a probabilistic metric space. This graph learning works for generic datasets, irrespective of the type of the observables; their probability distributions; or size of the data. We identify a metric of the space that the graph is drawn in, as a probability distribution of a random variable that we introduce, namely, a variable that represents the disparity between the connectedness of two vertices of the graph, and the correlation between the two random variables that are attached to the respective vertex. It is the closed-form {\it{cdf}} of this disparity variable that we advance as the distance function of the host space of the learnt RGG, such that the edge exists between any two nodes, if this inter-nodal distance falls short of a chosen cutoff probability. Drawing the RGG in this probabilistic space leads to the graph being an Soft RGG, such that any edge - if it exists - exists with an identified probability. We forward a simple Rejection Sampling-based technique for learning the probability of any edge. The expected degree distribution of a vertex of this RGG is identified as local, and dependent on the inter-observable correlation matrix. If said correlation matrix is not known, it can be learnt given the data, using its closed-form posterior probability density function, that we forward. We illustrate our graph learning method by learning multiple RGGs of highly multivariate real datasets.
Estimating interpretable conditional-dependence structures from multimodal visual-linguistic features remains largely unexplored. We propose CM-GLasso (Cross-Modal Graphical Lasso), a framework that bridges vision-language representation learning and sparse Gaussian Graphical Models. CM-GLasso introduces three key components: (i) a text visualization strategy that renders class-attribute descriptions as images and processes them through the same SigLIP-2 vision encoder as natural images, yielding prototype-indexed patch-level attention footprints in a shared feature coordinate system; (ii) a cross-attention distillation mechanism that condenses high-dimensional patches into a small set of semantic graph nodes, whose attention-footprint similarities yield cross-modal structural priors for non-uniform L1 penalization; (iii) a joint ADMM formulation that estimates shared and class-specific precision components within a single convex objective, avoiding the need to first estimate and then decompose separate class-wise graphs. The learned sparse graph topologies directly support a parameter-free, precision-based classification rule and a lightweight topology-aware segmentation head. Extensive experiments on eight benchmarks demonstrate that CM-GLasso achieves competitive or superior performance compared with strong feature-based and task-specific baselines. Under the matched controlled protocol, it attains the highest average classification accuracy (91.97%) and the highest segmentation mIoU among the controlled baselines on VOC (74.75%) and ADE20K (64.01%), while also yielding explicit sparse conditional-dependence graphs with common-specific decomposition.
The problem of networked information aggregation, studied in Kearns et al. (2026), involves a group of learners situated on the vertices of a directed acyclic graph $G$, each learning a linear predictor $\widehat Y$ for a fixed random variable $Y$ given access to a local feature, as well as the predictors learnt by its parents. Learning proceeds iteratively, with learners ordered according to a topological sort of $G$. The main quantity of interest is the error incurred by the current learner, constrained to this flow of information, with respect to the best linear predictor using all the features seen so far. When the studied error is the MSE, i.e., $\mathbb{E} (\widehat Y - Y)^2$, Kearns et al. (2026) show that the error is at most $O(1/\sqrt{D})$ along a path of length $D$. They also obtain a hard instance where the MSE is lower bounded by $Ω(1/D)$, leaving the correct order open. In this work, we resolve this central open problem, and obtain a family of worst case problem instances with a MSE lower bound of $Ω(1/\sqrt{D})$. By exploiting invariances in the structure of the learnt predictors, our analysis generalizes to all convex loss functions $\ell(\widehat Y, Y)$ satisfying regularity conditions which include strong convexity in a ball around the origin, and that the ideal predictor minimizing the population loss is positively correlated with the label. We show that networked information aggregation on a gaussian instance in our worst case family incurs an $\ell$-error lower bounded by $Ω(1/\sqrt{D})$ with respect to this ideal predictor. We demonstrate that a variety of common losses satisfy these regularity conditions. In particular, the logistic loss satisfies them, and hence our analysis also closes the gap between the upper and lower bounds in Bateni et al. (2026).
Electroencephalogram (EEG) is a non-invasive and relatively low-cost procedure that measures brain electricity for the detection of cognitive diseases. EEG-based classification of dementia-related conditions, including Alzheimer's disease (AD), mild cognitive impairment (MCI), and frontotemporal dementia (FTD), remains challenging because EEG signals are noisy, non-stationary, and vary across subjects. Segment-based learning provides a practical way to model long EEG recordings by converting them into fixed-length inputs. For each segment, discriminative information may be explored by using signals within each channel (i.e. electrode), as well as interactions between EEG channels. In this paper, we propose M-LINKX, a multi-view graph learning framework for EEG-based dementia classification. For each segment, we extract channel-level node features and construct multiple functional-connectivity (FC) graph views, where each view is defined by a specific combination of connectivity metric, frequency band, and topology filter, respectively. Instead of relying on message passing over the constructed graphs, M-LINKX follows a simple design in modeling node features and adjacency-based connectivity representations. The graph-view representations are fused using global trainable view weights, and subject-level prediction is obtained by averaging segment-level probabilities. Experiments on two three-class EEG datasets with different diagnostic groups, CAUEEG (HC/MCI/Dementia) and AHEAP (HC/AD/FTD), show that M-LINKX achieves the best subject-level performance under the main experimental settings. Our study suggests that multi-view functional connectivity can improve EEG-based dementia classification when integrated with an appropriate graph-learning architecture. Code and data are available at https://github.com/anphantt/MLINKX.
Laplacian-regularized minimization is fundamental in signal processing and machine learning, but is limited by the dense and ill-conditioned nature of the graph Laplacian pseudoinverse. While the Laplacian itself is sparse, its pseudoinverse is dense and often ill-conditioned, rendering direct computation impractical at scale. Moreover, pseudoinverse learning is more challenging than Laplacian learning. To address this challenge, this paper considers the setting where the graph Laplacian is given and proposes a Difference-of-Convex Regularizer (DCR) graph learning framework that approximates the spectral action of the Laplacian pseudoinverse without direct inversion via regularized Maximum Likelihood Estimation (MLE). By reformulating Laplacian-Regularized Nonnegative Least Squares (LR-NNLS) through a dual representation, DCR decouples pseudoinverse learning from instance-specific inference and enables efficient primal solution reconstruction via a differentiable dual-guided learning scheme. We establish theoretical guarantees on stability and the existence of a unique fixed point for DCR algorithm. Numerical experiments demonstrate improved performance over convex solvers and graph filtering baselines and robust performance across diverse graph topologies.
We study exact Kullback--Leibler (KL) projection for low-rank factorizations whose two nonnegative factors have prescribed row marginals and a shared, learned column marginal. For arbitrary positive row marginals of equal total mass, the joint KL projection reduces exactly to a strictly convex gauge-fixed dual with only $r-1$ effective variables; its Hessian is a sum of categorical covariance terms and admits $O((n+m)r)$ matrix-free Hessian--vector products. The projection theorem is objective-independent. We then specialize this geometry to doubly stochastic (DS) graph learning through $W=U\operatorname{Diag}(g)^{-1}V^\top$, where row-simplex factors with a common column mass induce an exactly DS graph without materializing an $n\times n$ optimization variable. Combined with observed-edge sparse fitting, a stochastic anchor-reduced manifold regularizer, and Bregman backtracking, the resulting mirror-descent method preserves exact feasibility at every accepted step. Under a nonvanishing latent-mass condition, it satisfies sufficient decrease and an $O(1/N)$ mirror-stationarity bound, while strictly positive accumulation points are KKT stationary. Matched clustering experiments show competitive accuracy, feasibility residuals near numerical precision, and favorable anytime behavior without a dense learned graph.
Temporal graph learning has become essential for analyzing real-world systems whose interactions continuously evolve over time, including financial transaction networks, communication systems, and online social platforms. However, learning from large-scale temporal graphs remains computationally challenging when networks are dense and rapidly changing. To address this limitation, we propose a network-curvature-inspired edge sparsification framework for dynamic graph learning. Our proposed method, TRicci, extends classical Forman-Ricci curvature to directed weighted temporal graphs by capturing structural support, temporal recency, and local interaction competition. Experiments on 9 transaction networks and 3 temporal graph benchmark datasets demonstrate that the proposed framework preserves predictive performance across multiple graph-level prediction tasks. The results show that TRicci sparsifies temporal graphs by approximately 80% while reducing end-to-end downstream training and inference time by an average of 55.94%, without substantial degradation in predictive performance. Our findings suggest that temporal curvature can serve as a principled basis for scalable temporal graph learning by preserving predictive temporal-structural information under substantial sparsification.
Sara Chehab, Giorgos Iacovides, Parisa Yazdanparast +1q-fin.PM cs.LG q-fin.ST
Current portfolio construction methods are either agnostic to the effects of idiosyncratic shocks (standard factor models) or to the latent data structure driving systematic returns (recent graph-based approaches). This presents an opportunity to combine the complementary market aspects captured by the factor and graph domains, allowing asset allocations to operate directly on the underlying market structure, rather than on its observed co-movement or its finite-sample artefacts. In this work, we introduce the Mutually-INformed Graph-Locality and Exposures framework (MINGLE), which mutually regularises the factor and graph domains by redefining graph locality through systematic factor exposure profiles, rather than via observed co-movements. This is formalised through a unified Alternating Direction Method of Multipliers (ADMM) framework that jointly learns a latent factor representation and its induced graph topology directly from market returns. The resulting exposure-similarity graph aligns more closely with established economic sectors than conventional correlation-based graphs. Portfolios constructed from this representation are shown to consistently outperform their correlation-based counterparts across a range of volatility regimes and transaction cost levels. For rigour, paired statistical testing confirms that these gains stem from the reconciliation of the graph and factor domains.
Compound flooding in managed coastal systems is influenced by hydrological conditions and water-management activity observed across multiple monitoring stations. Current forecasting models can capture temporal dependencies with low average errors, but global error metrics may conceal poor reproduction of prolonged high-water plateaus that are relevant to flood early warning. Because hydrometeorological and operational signals are distributed across heterogeneous gages, single-site records do not fully represent high-water dynamics. Nevertheless, unconstrained fusion of cross-site signals can degrade the stability of local temporal forecasts. This work proposes an anchored forecasting framework that incorporates cross-site information through state- and lead-dependent bounded residual corrections. A multi-source regime representation constructed from hydrometeorological and operational observations adaptively calibrates inter-site relationships and correction scales, enabling targeted cross-site adjustment while preserving the local temporal forecast as a stable anchor. Beyond conventional global error statistics, we evaluate event-scale high-water characteristics through the temporal alignment of forecasted and observed high-water processes. Experiments demonstrate that selectively integrating multi-station dynamic conditions improves the prediction reliability of sustained high-water plateaus while maintaining high accuracy during routine hydrological conditions, supporting flood early warning and water-management decision support.
Federated graph learning enables collaborative training over decentralized graph data without sharing raw graph information. As such risks evolve, clients must learn emerging classes from private multimodal graph streams, retain historical categories, and reject samples outside the known class space. In this setting, clients must learn emerging classes from private multimodal graph streams while preserving historical categories and rejecting samples outside the current known class space. The core challenge is catastrophic forgetting, which in federated multimodal graphs is not merely a classifier-level failure: old knowledge can be erased through modality-semantic overwriting, topology-induced structural erosion, and federated memory fragmentation. To address this challenge, we propose \textbf{FedOGL}, a semantic-structural memory preservation framework. On the client side, FedOGL preserves historical decision behavior through replay and task-start distillation, while protecting graph-propagation memory via projection onto a globally shared structure basis. On the server side, FedOGL maintains and transfers compact category prototypes to facilitate cross-client knowledge sharing without exposing raw graph data. Extensive experiments demonstrate that, compared with the best-performing baselines, FedOGL reduces performance degradation caused by catastrophic forgetting by \textbf{42.67\%}, while maintaining or improving performance on downstream tasks.
Zhendong Wang, Jintong Wang, Chen Liu +3cs.CV cs.GR
Digital sewing patterns typically consist of disjoint 2D panels without explicit stitch annotations, making downstream 3D modeling reliant on labor-intensive expert specification. In this paper, we present a graph-based learning framework that reconstructs two-level stitching information, coarse panel connectivity and fine-grained seam correspondence, from 2D panel geometry alone. At the coarse level, panel connectivity is inferred by predicting panel semantics associated with anatomical body regions, enforcing consistency with body structure and garment design conventions. Based on the reconstructed panel graph, fine-grained seam correspondences between panel pairs are inferred by learning latent edge representations that jointly encode local seam geometry and global garment context through graph message passing. The resulting edge embeddings are subsequently decoded into detailed seam correspondences. Our method supports complex sewing-pattern topologies, including many-to-one correspondences, intra-panel seams, and curved seams. Experiments demonstrate high stitching accuracy and strong generalization across garment styles.
Vision-language models (VLMs) provide a unified representation space for textual and visual information, yet their potential as general-purpose backbones for graph-structured data remains largely unexplored. In practice, attributed graphs exhibit substantial modality heterogeneity: some graphs contain only textual node attributes, others only visual attributes, while still others provide both. Existing graph learning approaches are typically designed for fixed modality schemas, requiring separate models for different settings and limiting scalability and cross-graph generalization. To bridge this gap, we present OMG-VLM (One Model, Many Graphs with Vision-Language Models), a unified framework for learning over attributed graphs across heterogeneous modality schemas. OMG-VLM leverages a pretrained VLM as a shared backbone and introduces structure-aware graph adapters that integrate neighborhood information while remaining compatible with the VLM's native embedding space. This design enables effective learning over text-attributed, image-attributed, and multi-attributed graphs within a single model. Extensive experiments across diverse domains show that OMG-VLM consistently outperforms state-of-the-art GNN- and LLM-based baselines on attributed graph learning tasks such as node classification and link prediction, while exhibiting strong generalization to unseen graphs and varying modality schemas. The source code is available at https://github.com/Jo-eyang/OMG-VLM.
Afonso S. Bandeira, Amit Singer, Thomas Strohmercs.LG cs.AI cs.IT math.PR
This book is about the mathematical foundations of data science. 1. Introduction 2. Curses, Blessings, and Surprises in High Dimensions 3. Singular Value Decomposition and Principal Component Analysis 4. Linear Regression and Regularization 5. Graphs, Networks, and Clustering 6. Nonlinear Dimension Reduction and Diffusion Maps 7. Linear Dimension Reduction via Random Projections 8. Optimization for Data Science 9. Classification 10. A Mathematical Introduction to Deep Learning 11. Large Sample Limit of Graph Laplacians 12. Community 13. Concentration of Measure and Gaussian Analysis 14. Matrix Concentration Inequalities 15. Compressive Sensing and Sparsity 16. Low-Rank Matrix Recovery
Intelligent industrial maintenance critically relies on reliable fault diagnosis of rotating machinery. However, it faces formidable challenges from unknown fault types and domain shifts induced by varying operating conditions, which is formally formulated as the open-set domain generalization (OSDG) problem. Existing methods are mainly data-driven, thereby overlooking the cascaded propagation of uncertainty across feature extraction, topological learning, and decision-making stages.To tackle this challenge, we propose PGU-OD, a novel Physics-Informed Graph Learning framework with Uncertainty Awareness for Open-set Domain generalization. First, it designs a physics-informed spectral attention module to extract condition-robust fault features, thereby suppressing perceptual uncertainty caused by frequency shifts. Further, it constructs an uncertainty aware adaptive graph learning mechanism to dynamically adjust the edge weights of the sample graph guided by class-scale Gaussian distribution parameters, which mitigates the structural propagation of uncertainty. Finally, a Gaussian-distribution-based adaptive boundary loss function and a dual-criteria open-set inference strategy are developed to optimize decision boundaries and reliably reject unknown faults. Extensive experimental evaluations on two public and widely used rotating machinery fault datasets demonstrate that the proposed PGU-OD outperforms state-of-the-art baselines in both known fault classification and unknown fault rejection under domain shifts.
Transformers have become general-purpose architectures, but their all-to-all self-attention is poorly matched to graph data, whose interactions are sparse, structured and multi-scale. Existing Graph Transformers address this mismatch through structural encodings, hybrid message-passing modules or learned attention constraints, often introducing additional complexity and limited interpretability. Here we introduce X-LogSMask, an explainable multi-head logarithmic structural mask that injects symmetrically normalized graph topology directly into attention logits. The logarithmic transform converts structural connectivity into a topology-aware gating signal, suppressing unsupported node interactions while preserving feature-dependent attention. By assigning different powers of the normalized adjacency matrix to different attention heads, X-LogSMask gives each head a defined structural radius and supports multi-hop information propagation within a single layer. We further show that a standard Transformer encoder can be interpreted as one-step message passing on a complete graph, motivating X-LogSMask as a topology-constrained alternative to unrestricted self-attention. Across 20 node-, edge- and graph-level benchmarks, Transformers equipped with X-LogSMask achieve state-of-the-art performance on 13 datasets and remain competitive in a lightweight one-layer configuration. These results show that simple, interpretable structural masks can make self-attention an effective graph-learning operator without changing the Transformer architecture. The code is available at https://github.com/LiLeyan-0120/X-LogSMask.
MultiModal Federated Graph Learning (MM-FGL) offers a natural collaborative training paradigm, but its practical deployment is challenged by two granularities of modality imbalance. Client-level imbalance occurs when certain clients lack entire modalities, while node-level imbalance occurs when individual nodes exhibit missing visual or textual attributes. While several relevant studies exist, our investigation reveals that they predominantly target graph-agnostic or centralized scenarios, rendering them difficult to adapt directly. To address these challenges, we formalize modality-imbalanced MM-FGL as an implicit graph-aware latent semantic representation synthesis problem. This paradigm recovers missing modal semantics directly within the representation space, thereby maximizing alignment with the original data's semantic distribution and mitigating the high variance induced by missing modalities. To this end, we propose FedMGS (Federated Modality-aware Graph Synthesis), which integrates three core components. The availability-aware graph encoder prevents missing modalities from contaminating local structural propagation. The prototype-guided latent semantic synthesizer establishes cross-client semantic anchors for unavailable modalities. The reliability-calibrated semantic fusion mechanism regulates the impact of recovered latent representations prior to predictive readout. Extensive experiments on four tasks show that FedMGS consistently outperforms competitive baselines with gains up to 17.41% with best efficiency-performance tradeoff.
Precise rover localization is a prerequisite for autonomous lunar exploration, yet the absence of Global Navigation Satellite System (GNSS) signals and the cumulative drift of local localization methods severely constrain long-range missions. Cross-view localization provides a promising drift-free global solution by matching rover-view and satellite-view imagery. However, the lunar environment poses unique challenges for correspondence alignment, including inter-entity entanglement, inter-viewpoint divergence, and simulation-to-real domain shift. To address these challenges, we propose Warped Alignment of Reprojected Graphs (WARG), a framework that leverages unified graph learning and reprojected graph matching for robust cross-view alignment. Pretrained on the synthetic LuSNAR dataset, WARG achieves an average test error of 0.32 m and demonstrates robust zero-shot generalization to the synthetic lunar south pole region with an error of 3.63 m. More importantly, when validated on real-world data from the YuTu-2 rover, WARG achieves a localization error of 1.68 m within a 100 m x 100 m search area, corresponding to nearly one-pixel precision in low-resolution satellite imagery with a spatial resolution of 1.40 m/pixel. Beyond accuracy, WARG is computationally efficient, containing only 1.56M parameters, corresponding to 16.12% of previous lightweight models, and operating at 5.49 Hz on an NVIDIA RTX A6000 GPU, approaching GNSS-level update frequency. Finally, we observe that WARG naturally develops low-level spatial awareness, including semantic segmentation and structural reasoning, through cross-view localization learning, highlighting its potential as a promising paradigm for spatial intelligence with minimal annotation cost. The source code is available at https://github.com/maochen-casia/warg.
Multimodal federated graph learning (MM-FGL) aims to collaboratively learn from decentralized graphs with text and images. However, real-world clients may not share a common modality basis: a visual-search client may contain image--interaction graphs but no seller descriptions, while a catalog client may provide text but no product images. We refer to this practical setting as client-level modality deficiency. Unlike random instance-wise missingness, a deficient client lacks the local semantic basis needed to reconstruct the absent modality. More importantly, in graph learning, incomplete representations initialize message passing, so imputation errors can be filtered, mixed, and amplified by the receiving topology. To address this gap, we propose \textbf{PRISM} (\textbf{P}roactive \textbf{R}etrieval and \textbf{I}mputation via \textbf{S}tructural \textbf{M}eta-prompting), a topology-aware federated cross-modal imputation framework. Rather than reconstructing the missing modality solely from local observations, PRISM recovers missing-modality semantics from the federation and introduces them into local graph propagation under topology-aware control. Experiments on six multimodal graph datasets across graph-centric and modality-centric tasks show that PRISM consistently improves modality-deficient clients, outperforming state-of-the-art baselines by \textbf{4.48}\% on average.
We study exact community recovery in the two-community stochastic block model on $n$ vertices under limited and noisy access to network data. The learner may query a noisy neighborhood oracle that reveals each true neighbor of a queried vertex independently with fixed probability and never returns non-neighbors, subject to a finite query budget. We consider both oracle-only access and a combined model where the learner also observes a single subsampled copy of the underlying graph. For oracle-only access, balanced uniform querying gives a sharp non-adaptive benchmark: when each vertex is queried the same integer number of times, the observations reduce to an SBM with attenuated edge probabilities and the Abbe-Bandeira-Hall exact-recovery threshold applies. We show that this benchmark is not adaptively optimal: a two-stage adaptive strategy succeeds with $n+o(n)$ queries in a regime where balanced uniform querying requires $m n$ queries for some $m>1$. With an additional subsampled graph, we prove a sublinear-query adaptivity gap: balanced data-independent uniform querying with a sublinear budget does not improve over the subsampled graph alone, whereas adaptive querying can target a small set of uncertain vertices and achieve exact recovery. Thus adaptive data acquisition can strictly improve the information-theoretic limits of exact recovery.
Electroencephalogram (EEG) signals are vital for automated seizure detection, but their inherent noise makes robust representation learning challenging. Existing graph construction methods, whether correlation-based or learning-based, often generate redundant or irrelevant edges due to the noisy nature of EEG data. This significantly impairs the quality of graph representation and limits downstream task performance. Motivated by the remarkable reasoning and contextual understanding capabilities of large language models (LLMs), we explore the idea of using LLMs as graph edge refiners. Specifically, we propose a two-stage framework: we first verify that LLM-based edge refinement can effectively identify and remove redundant connections, leading to significant improvements in seizure detection accuracy and more meaningful graph structures. Building on this insight, we further develop a robust solution where the initial graph is constructed using a Transformer-based edge predictor and multilayer perceptron, assigning probability scores to potential edges and applying a threshold to determine their existence. The LLM then acts as an edge set refiner, making informed decisions based on both textual and statistical features of node pairs to validate the remaining connections. Extensive experiments on TUSZ dataset demonstrate that our LLM-refined graph learning framework not only enhances task performance but also yields cleaner and more interpretable graph representations.
Branislav Kveton, Michal Valko, Matthai Phillipose +1cs.LG
This paper proposes an algorithm for real-time learning without explicit feedback. The algorithm combines the ideas of semi-supervised learning on graphs and online learning. In particular, it iteratively builds a graphical representation of its world and updates it with observed examples. Labeled examples constitute the initial bias of the algorithm and are provided offline, and a stream of unlabeled examples is collected online to update this bias. We motivate the algorithm, discuss how to implement it efficiently, prove a regret bound on the quality of its solutions, and apply it to the problem of real-time face recognition. Our recognizer runs in real time, and achieves superior precision and recall on 3 challenging video datasets.
Boyang Fan, Hengchuang Yin, Siyu Yi +5cs.LG q-bio.GN q-bio.MN
Motivation: Multi-omics integration can improve cancer subtyping, but modality informativeness and noise vary across cancer types and patients. Existing graph-based methods optimize modality weights jointly with the classification objective and therefore lack independent reliability estimates, so low-quality omics distort patient similarity graphs and amplify noise through message passing. Results: We propose CMGL, a two-stage framework that estimates per-sample modality reliability through evidential deep learning and uses the frozen confidence scores to guide cross-omics fusion and graph construction. On four MLOmics cancer-subtype tasks and the 32-class pan-cancer task, CMGL consistently improves over the strongest baseline, surpassing it by 4.03% in average accuracy on the four single-cancer tasks. Its representations recover the PAM50 intrinsic subtypes of breast invasive carcinoma (BRCA), and the BRCA-trained model transfers without fine-tuning to kidney renal clear cell carcinoma (KIRC), stratifying patients into prognostically distinct groups.