Graph Neural Networks

Fair machine learning seeks to identify and mitigate biases in predictions against unfavorable populations characterized by demographic attributes, such as race and gender. Recent research has extended fairness to graph data, such as social networks, but many studies neglect the causal relationships among data instances. This paper addresses a prevalent challenge in many fair machine learning research, which typically assumes independent and identically distributed (IID) data, from the causal perspective. Specifically, this work targets the circumstance where nodes with different neighborhood structures follow different causal mechanisms, violating the invariance assumptions required for classical structural causal models and do-calculus. We base our research on the Network Structural Causal Model (NSCM) framework and develop a Message Passing Variational Autoencoder for Causal Inference (MPVA) to compute interventional distributions for causally fair node classification. We establish theoretical soundness under two conditions: Decomposability and Graph Independence. These conditions formalize when causal mechanism heterogeneity can be overcome by constructing a structural representation that restores invariance and facilitates the computation of interventional distributions using do-calculus in non-IID settings. Empirical evaluations on semi-synthetic and real-world datasets demonstrate that MPVA outperforms conventional methods by effectively approximating interventional distributions and mitigating bias. Our findings demonstrate the potential of causality-based fairness in complex ML applications and motivate future work on relaxing the classic assumptions in algorithmic fairness.

This work presents a comprehensive evaluation of neural network graph compilers across heterogeneous hardware platforms, addressing the critical gap between theoretical optimization techniques and practical deployment scenarios. We demonstrate how vendor-specific optimizations can invalidate relative performance comparisons between architectural archetypes, with performance advantages sometimes completely reversing after compilation. Our systematic analysis reveals that graph compilers exhibit performance patterns highly dependent on both neural architecture and batch sizes. Through fine-grained block-level experimentation, we establish that vendor-specific compilers can leverage repeated patterns in simple architectures, yielding disproportionate throughput gains as model depth increases. We introduce novel metrics to quantify a compiler's ability to mitigate performance friction as batch size increases. Our methodology bridges the gap between academic research and practical deployment by incorporating compiler effects throughout the research process, providing actionable insights for practitioners navigating complex optimization landscapes across heterogeneous hardware environments.

Traffic prediction is difficult due to the complex interplay of temporal evolution, spatial interactions, and delayed spatio-temporal propagation over road networks. Existing methods either model spatial and temporal dependencies separately or employ unified spatio-temporal structures, but they often insufficiently characterize how neighboring sensors at historical timestamps influence a target node, while complex joint models may incur high computation. This paper proposes STEI-PCN, an efficient pure convolutional network based on spatio-temporal encoding and relation inference. It first builds a local causal joint spatio-temporal graph to restrict candidate interactions, then uses absolute position and relative distance encodings to infer dynamic edge weights. A single-layer graph convolution with a position-aware gated activation unit captures local joint dependencies, and temporal dilated causal convolutions complement long-range temporal patterns. A multi-view prediction module fuses raw, local propagation, and long-range temporal representations for direct multi-step forecasting. Experiments on PeMS03, PeMS04, PeMS07, PeMS08, and PeMS-Bay under multiple horizons show that STEI-PCN achieves competitive accuracy with moderate parameters and low training and inference costs. Ablation and fluctuation analyses further verify the contributions of the main components and empirically analyze the effects of the training-stage constraints under sharp speed changes. Our code is available at a GitHub link https://github.com/Jessez2/STEI-PCN.

Traffic Engineering (TE) in large-scale networks like cloud Wide Area Networks (WANs) and Low Earth Orbit (LEO) satellite constellations is a critical challenge. Although learning-based approaches have been proposed to address the scalability of traditional TE algorithms, their practical application is often hindered by a lack of generalization, high training overhead, and a failure to respect link capacities. This paper proposes TELGEN, a novel TE algorithm that learns to solve TE problems efficiently in large-scale network scenarios, while achieving superior generalizability across diverse network conditions. TELGEN is based on the novel idea of transforming the problem of "predicting the optimal TE solution" into "predicting the optimal TE algorithm", which enables TELGEN to learn and efficiently approximate the end-to-end solving process of classical optimal TE algorithms. The learned algorithm is agnostic to the exact underlying network topology or traffic patterns, and is able to very efficiently solve TE problems given arbitrary inputs and generalize well to unseen topologies and demands. We train and evaluate TELGEN with random and real-world topologies, with networks of up to 5000 nodes and 3.6x10^6 links in testing. TELGEN shows less than 3% optimality gap while ensuring feasibility in all testing scenarios, even when the test network has 2-20x more nodes than the largest training network. It also saves up to 84% TE solving time than traditional interior-point method, and reduces up to 79.6% training time per epoch than the state-of-the-art learning-based algorithm.

Dementia affects over 55 million people worldwide, projected to reach 139 million by 2050, with Alzheimer's disease (AD) accounting for 60-70% of cases. AD is associated with disruptions in metabolic brain connectivity. Detecting these disruptions early is crucial for AD management. FDG-PET is a useful tool for identifying such impairments. However, most studies rely on group-level analyses or thresholding, potentially masking individual differences and overlooking weaker yet biologically critical brain connections. Moreover, AD prediction largely focuses on univariate rather than multivariate outcomes. To address this, we introduce explainable graph-theoretical machine learning (XGML), a framework for constructing individual metabolic brain graphs and identifying subgraphs most predictive of multivariate disease-related outcomes. Using Alzheimer's Disease Neuroimaging Initiative (ADNI) FDG-PET data, we compared six graph representations against three non-graph baselines, each with six machine learning models using repeated stratified 3-fold cross-validation (10 repeats). The best configuration combined kernel density estimation with Hellinger distance and random forest. Across eight cognitive scores, it reached an overall Fisher-z-averaged Pearson correlation of r=0.595, with strongest performance for ADAS13 (r=0.67), ADAS11 (r=0.65), and ADASQ4 (r=0.62). We identified key edges that were jointly but differentially predictive across outcomes, suggesting their potential as network biomarkers of cognitive decline. Preliminary external feasibility validation on an OASIS3 cohort yielded weak predictive performance for CDRSB (r=0.26) and MMSE (r=0.18), likely reflecting cohort, protocol, and diagnostic differences. Overall, our results suggest the promise of graph-theoretical machine learning for biomarker discovery, disease prediction, and understanding the neural mechanisms underlying AD.

Proteins move and deform to ensure their biological functions. Despite significant progress in protein structure prediction, approximating conformational ensembles at physiological conditions remains a fundamental open problem. This paper presents a novel perspective on the problem by directly targeting continuous compact representations of protein motions inferred from sparse experimental observations. We develop a task-specific loss function enforcing data symmetries, including scaling and permutation operations. Our method PETIMOT (Protein sEquence and sTructure-based Inference of MOTions) leverages transfer learning from pre-trained protein language models through an SE(3)-equivariant graph neural network. When trained and evaluated on the Protein Data Bank, PETIMOT shows superior performance in time and accuracy, capturing protein dynamics, particularly large/slow conformational changes, compared to state-of-the-art diffusion and flow-matching approaches, as well as traditional physics-based models. Our code and protocols are available at https://github.com/PhyloSofS-Team/PETIMOT.

Rational design of lipid nanoparticles (LNPs) for tissue-specific delivery critically depends on predicting the composition of the protein corona that forms on the lipid surface after intravenous administration. However, conventional characterization of the protein corona relies on costly and time-consuming mass spectrometry experiments, which require physically prepared liposome samples and therefore cannot serve as a pre-synthesis screening strategy for large candidate lipid spaces. The adsorption of plasma proteins onto liposomal surfaces is shaped by lipid chemical structures, protein properties and the biological environment, making this process difficult to simulate directly. In this work, we propose that scoring lipid-plasma protein pairs and ranking the resulting scores can provide a practical signal for revealing the relative composition of the liposomal surface protein corona.Here we introduce GenShin, a geometry-enhanced pose-free graph neural network designed to score lipid-plasma protein pairs. GenShin is pretrained on compound-protein affinity data to initialize a generalizable scoring function and is then fine-tuned on a rank fine-tuning dataset constructed from liposomal protein-corona abundance measurements to adapt the model to lipid-plasma protein pair scoring. Before fine-tuning, GenShin achieves competitive pose-free affinity prediction on the PDBbind v2016 benchmark compared with representative pose-dependent models. CASF-2016 perturbation experiments using the pretrained GenShin model further show that pose-dependent inference substantially degrades when intermolecular poses are unreliable, whereas GenShin remains stable without requiring such poses. This supports the practical advantage of GenShin for large-scale lipid-protein scoring.

Text-Attributed Graphs (TAGs), where each node is associated with text descriptions, are ubiquitous in real-world scenarios. They typically exhibit distinctive structure and domain-specific knowledge, motivating the development of a Graph Foundation Model (GFM) that generalizes across diverse graphs and tasks. Despite large efforts to integrate Large Language Models (LLMs) and Graph Neural Networks (GNNs) for TAGs, existing approaches suffer from decoupled architectures with two-stage alignment, limiting their synergistic potential. Even worse, existing methods assign out-of-vocabulary (OOV) tokens to graph nodes, leading to graph-specific semantics, token explosion, and incompatibility with task-oriented prompt templates, which hinders cross-graph and cross-task transferability. To address these challenges, we propose PromptGFM, a versatile GFM for TAGs grounded in graph vocabulary learning. PromptGFM comprises two key components: (1) Graph Understanding Module, which explicitly prompts LLMs to replicate the finest GNN workflow within the text space, facilitating seamless GNN-LLM integration and elegant graph-text alignment; (2) Graph Inference Module, which establishes a language-based graph vocabulary ensuring expressiveness, transferability, and scalability, enabling readable instructions for LLM fine-tuning. Extensive experiments demonstrate our superiority and transferability across diverse graphs and tasks. The code is available at this: https://github.com/agiresearch/PromptGFM.

Graph neural networks (GNNs) have demonstrated success in modeling relational data primarily under the assumption of homophily. However, many real-world graphs exhibit heterophily, where linked nodes belong to different categories or possess diverse attributes, such as webpages, Wikipedia articles, social networks, and e-commerce platforms. Additionally, nodes in many domains are associated with textual descriptions, forming heterophilic text-attributed graphs (TAGs). Despite their significance, heterophilic TAGs remain underexplored due to the lack of dedicated benchmarks that jointly capture heterophilic structures and rich textual attributes. To address this gap, we introduce the \textbf{He}terophilic \textbf{T}ext-attributed \textbf{G}raph \textbf{B}enchmark (HeTGB), a novel benchmark comprising five real-world heterophilic graph datasets from diverse domains, with nodes enriched by extensive textual descriptions. HeTGB enables systematic evaluation of GNNs, pre-trained language models (PLMs) and co-training methods on the node classification task. Through extensive benchmarking experiments, we showcase the utility of text attributes in heterophilic graphs, analyze the challenges posed by heterophilic TAGs and the limitations of existing models, and provide insights into the interplay between graph structures and textual attributes.

After the achievement of solving two-player zero-sum games, more AI researchers focus on solving multiplayer games. Urban Network Security Games (\textbf{UNSGs}) represent a class of such games, modeling real-world scenarios where law enforcement must strategically allocate limited resources to intercept criminals escaping within urban networks, and have gained considerable research attention. However, progress in this field has been limited by the absence of a standardized experimental platform and realistic benchmarks with heterogeneous travel costs. To address this limitation, we introduce \textbf{GraphChase}, an open-source platform designed to support the development and evaluation of algorithms for UNSGs. GraphChase offers a unified environment for modeling diverse UNSG variants on unweighted and weighted road networks across urban topologies. It also incorporates learning-based algorithms as baseline references for researchers. Furthermore, our experiments with GraphChase reveal that existing approaches to UNSGs still face challenges in terms of robustness and scalability, and suffer performance degradation when deployed under weighted edge costs, highlighting a sim-to-real generalization gap. GraphChase thus provides a realistic testbed for developing and validating UNSGs solvers under realistic travel-time heterogeneity.

Edge-attributed multigraphs, in which multiple edges with distinct attributes connect the same pair of nodes, arise naturally in many real-world systems. In these graphs, effective learning requires preserving information from repeated interactions while distinguishing contributions from different neighbors. Existing neural network solutions for edge-attributed multigraphs remain limited: some lose information from repeated interactions, while others break permutation equivariance. To address this, we introduce \emph{neighbor-aware aggregation}, an operator that first combines multi-edge features for each neighbor and then aggregates across neighbors. This operator captures per-neighbor statistics that standard single-stage aggregation cannot represent. Building on this operator, we present MEGA-GNN, a model-agnostic message-passing framework for edge-attributed multigraphs. We show that MEGA-GNN is permutation equivariant and has the same asymptotic complexity as standard GNNs with edge updates. We evaluate our approach on datasets from social networks and financial transaction networks. Neighbor-aware aggregation consistently improves GNN performance and matches or surpasses state-of-the-art methods.

Over the past decade, Graph Neural Networks (GNNs) have achieved great success on machine learning tasks with relational data. However, recent studies have found that heterophily can cause significant performance degradation of GNNs, especially on node-level tasks. Numerous heterophilic benchmark datasets have been put forward to validate the efficacy of heterophily-specific GNNs, and various homophily metrics have been designed to help recognize these challenging datasets. Nevertheless, there still exist multiple pitfalls that severely hinder the proper evaluation of new models and metrics: 1) lack of hyperparameter tuning; 2) insufficient evaluation on the truly challenging heterophilic datasets; 3) missing quantitative evaluation for homophily metrics on synthetic graphs. To overcome these challenges, we first train and fine-tune baseline models on $27$ most widely used benchmark datasets, and categorize them into three distinct groups: malignant, benign and ambiguous heterophilic datasets. We identify malignant and ambiguous heterophily as the truly challenging subsets of tasks, and to our best knowledge, we are the first to propose such taxonomy. Then, we re-evaluate $11$ state-of-the-arts (SOTA) GNNs, covering six popular methods, with fine-tuned hyperparameters on different groups of heterophilic datasets. Based on the model performance, we comprehensively reassess the effectiveness of different methods on heterophily. At last, we evaluate $11$ popular homophily metrics on synthetic graphs with three different graph generation approaches. To overcome the unreliability of observation-based comparison and evaluation, we conduct the first quantitative evaluation and provide detailed analysis.

We study the problem of restricting a Markov equivalence class of maximal ancestral graphs (MAGs) to only those MAGs that contain certain edge marks, which we refer to as expert or orientation knowledge. Such a restriction of the Markov equivalence class can be uniquely represented by a restricted essential ancestral graph. Our contributions are several-fold. First, we prove certain properties for the entire Markov equivalence class including a conjecture from Ali et al. (2009). Second, we present several new sound graphical orientation rules for adding orientation knowledge to an essential ancestral graph. We also show that some orientation rules of Zhang (2008b) are not needed for restricting the Markov equivalence class with orientation knowledge. Third, we provide an algorithm for including this orientation knowledge and show that in certain settings the output of our algorithm is a restricted essential ancestral graph. Finally, outside of the specified settings, we provide an algorithm for checking whether a graph is a restricted essential graph and discuss its runtime. This work can be seen as a generalization of Meek (1995) to settings which allow for latent confounding.

The rapid adoption, usefulness, and resource-intensive training of Graph Neural Network (GNN) models have made them an invaluable intellectual property in graph-based machine learning. However, their wide-spread adoption also makes them susceptible to stealing, necessitating robust Ownership Demonstration (OD) techniques. Watermarking is a promising OD framework for deep neural networks, but existing methods fail to generalize to GNNs due to the non-Euclidean nature of graph data. Existing works on GNN watermarking primarily focus on node and graph classification, overlooking Link Prediction (LP). In this paper, we propose GENIE (watermarking Graph nEural Networks for lInk prEdiction), the first scheme to watermark GNNs for LP. GENIE creates a novel backdoor for both node-representation and subgraph-based LP methods, utilizing a unique trigger set and a secret watermark vector. Our OD scheme is equipped with Dynamic Watermark Thresholding (DWT), ensuring high verification probability while addressing practical issues in existing OD schemes. We extensively evaluate GENIE across 4 diverse model architectures (i.e., SEAL, GCN, GraphSAGE and NeoGNN), 7 real-world datasets and 21 watermark removal techniques and demonstrate its robustness to watermark removal and ownership piracy attacks. Finally, we discuss adaptive attacks against GENIE and a defense strategy to counter it. The codebase and related artifacts are publicly available at our Project Page.

Continuous-Time Dynamic Graphs (CTDGs) enable fine-grained modeling of evolving relational systems. However, most existing CTDG representation learning methods are tailored to in-distribution settings and exhibit limited robustness under out-of-distribution (OOD) shifts. Although recent causal approaches learn invariant representations via interventions, they are primarily designed for static or discrete-time graphs and become computationally prohibitive for CTDGs due to the combinatorial explosion of structural and temporal variations. To address these challenges, we propose CIR, a framework grounded in a novel structural causal model termed the ICCM. To avoid exhaustive interventions, we leverage the Normalized Weighted Geometric Mean (NWGM) to efficiently approximate interventional predictions. We further instantiate ICCM within a practical deep learning architecture that jointly captures invariant structural and temporal patterns through dedicated subgraph extractors, and maintains an environment memory bank to model distributional shifts across evolving contexts. Extensive experiments demonstrate that CIR consistently outperforms existing methods under diverse OOD scenarios.

Unitarity is a useful principle for stabilizing deep neural networks, but in graph neural networks (GNNs) instability is induced not only by learnable parameters but also by the graph propagation operator. Motivated by this distinction, we propose Graph Unitary Message Passing (GUMP), a message-passing framework that uses a unitary propagation operator on a transformed graph to avoid graph-induced exponential decay under repeated propagation. GUMP combines (i) a graph transformation that maps an input graph to an Eulerian line-graph construction admitting unitary adjacency matrices, and (ii) a practical unitary projection procedure based on Newton-Schulz iteration. Theoretical analysis clarifies that, under standard analysis assumptions, unitary propagation keeps the graph-propagation term depth-stable, while vanilla normalized propagation exhibits exponential decay in its non-trivial spectral components. Across synthetic long-range tasks, TUDataset benchmarks, and LRGB datasets, GUMP improves over vanilla message passing and achieves competitive or superior performance against strong baselines. Code is available at https://github.com/ucker/gump_code.

This manuscript provides a comprehensive review of the Maximum Clique Problem, a computational problem that involves finding subsets of vertices in a graph that are all pairwise adjacent to each other. As such, this review is a continuation of the series of previous reviews from 1994, 1999 and 2014. The manuscript covers in a simple way classical algorithms and includes a review of recent developments in graph neural networks and quantum algorithms.

Graph clustering, an important unsupervised problem, has been shown to be more resistant to advances in Graph Neural Networks (GNNs). In addition, almost all clustering methods focus on homophilic graphs and ignore heterophily. This significantly limits their applicability in practice, since real-world graphs exhibit a structural disparity and cannot simply be classified as homophily and heterophily. Thus, a principled way to handle practical graphs is urgently needed. To fill this gap, we provide a novel solution with theoretical support. Interestingly, we find that most homophilic and heterophilic edges can be correctly identified on the basis of neighbor information. Motivated by this finding, we construct two graphs that are highly homophilic and heterophilic, respectively. They are used to build low-pass and high-pass filters to capture holistic information. Important features are further enhanced by the squeeze-and-excitation block. We validate our approach through extensive experiments on both homophilic and heterophilic graphs. Empirical results demonstrate the superiority of our method compared to state-of-the-art clustering methods.

In this paper, we consider the problem of partitioning a small data sample of size $n$ drawn from a mixture of $2$ sub-gaussian distributions in $\mathbb{R}^p$. We consider semidefinite programming relaxations of an integer quadratic program that is formulated essentially as finding the maximum cut on a graph, where edge weights in the cut represent dissimilarity scores between two nodes based on their $p$ features. We define the signal-to-noise ratio (SNR) as $s^2 := \min\{n p γ^2, Δ^2\}$, where $Δ^2 := p γ$ denotes the $\ell_2^2$ distance between the two cluster centers. Our contributions are twofold. First, we provide a unified framework for analyzing three computationally efficient algorithms: SDP1, BalancedSDP, and Spectral clustering, yielding universal polynomial-rate misclassification guarantees for all three algorithms. Moreover, our theory allows for partial recovery (success rate $< 100\%$) as long as $s^2$ is lower bounded by a constant. Second, we prove that the misclassification errors for SDP1 and BalancedSDP decay exponentially with respect to the SNR $s^2$ and the BalancedSDP requires no explicit debiasing when the two clusters have equal sizes. To our knowledge, this is the first time such results are obtained for semidefinite relaxations of MAX CUT in population clustering. We provide simulation evidence illuminating the theoretical predictions.

Because most scientific literature data are unlabeled, semantic representation learning based on unsupervised graphs has become crucial. To enrich scientific-literature features, this paper proposes a semantic representation learning method based on adaptive features and graph neural networks. By introducing adaptive feature processing, scientific-literature features are considered globally and locally. The graph attention mechanism weights and aggregates features of scientific documents connected by citation relations, so that correlations among different documents can be expressed more effectively. In addition, an unsupervised graph neural network semantic representation learning method is proposed. By comparing the mutual information between positive and negative local semantic representations of scientific literature and the global graph semantic representation in the latent space, the graph neural network captures local and global information and improves semantic representation learning. Experimental results show that the proposed method is competitive for scientific literature classification.

The storage, management, and application of massive spatio-temporal data are widely used in practical scenarios, including public safety. However, due to the unique spatio-temporal distribution characteristics of real-world data, existing methods still face limitations in preserving spatio-temporal proximity and achieving load balancing in distributed storage. This paper proposes an efficient partitioning method for large-scale public safety spatio-temporal data based on information loss constraints, named IFL-LSTP. The model combines a spatio-temporal partitioning module (STPM) and a graph partitioning module (GPM). STPM reduces the scale of data under a predefined information-loss threshold, while GPM uses graph representation learning to obtain balanced graph partitions. Experiments on multiple real-world datasets show that IFL-LSTP can reduce data scale, shorten graph model training time, preserve spatio-temporal proximity, and improve load-balancing effectiveness.

Sampled point and voxel methods are usually employed to downsample the dense events into sparse ones. After that, one popular way is to leverage a graph model which treats the sparse points/voxels as nodes and adopts graph neural networks (GNNs) to learn the representation of event data. Although good performance can be obtained, however, their results are still limited mainly due to two issues. (1) Existing event GNNs generally adopt the additional max (or mean) pooling layer to summarize all node embeddings into a single graph-level representation for the whole event data representation. However, this approach fails to capture the importance of graph nodes and also fails to be fully aware of the node representations. (2) Existing methods generally employ either a sparse point or voxel graph representation model which thus lacks consideration of the complementary between these two types of representation models. To address these issues, we propose a novel dual point-voxel absorbing graph representation learning for event stream data representation. To be specific, given the input event stream, we first transform it into the sparse event cloud and voxel grids and build dual absorbing graph models for them respectively. Then, we design a novel absorbing graph convolutional network (AGCN) for our dual absorbing graph representation and learning. The key aspect of the proposed AGCN is its ability to effectively capture the importance of nodes and thus be fully aware of node representations in summarizing all node representations through the introduced absorbing nodes. Extensive experiments on multiple event-based classification benchmark datasets fully validated the effectiveness of our framework.

For deep learning problems on graph-structured data, pooling layers are important for down sampling, reducing computational cost, and to minimize overfitting. We define a pooling layer, nervePool, for data structured as simplicial complexes, which are generalizations of graphs that include higher-dimensional simplices beyond vertices and edges; this structure allows for greater flexibility in modeling higher-order relationships. The proposed simplicial coarsening scheme is built upon partitions of vertices, which allow us to generate hierarchical representations of simplicial complexes, collapsing information in a learned fashion. NervePool builds on the learned vertex cluster assignments and extends to coarsening of higher dimensional simplices in a deterministic fashion. While in practice the pooling operations are computed via a series of matrix operations, the topological motivation is a set-theoretic construction based on unions of stars of simplices and the nerve complex.

Deep neural networks (DNNs) are highly vulnerable to adversarial attacks. Ideally, a robust model should perform well on both perturbed training data and unseen perturbed test data. While DNNs can fit perturbed training data, generalizing to perturbed test data remains a significant challenge. This motivates the study of generalization guarantees from a learning theory perspective. This paper focuses on adversarial Rademacher complexity (ARC), first introduced by Khim and Loh (2018) and Yin et al. (2019). Their work primarily addressed linear functions and highlighted the open question of how to bound ARC for neural networks. Since then, several attempts have been made, with the latest results applying ARC only to two-layer neural networks. The main challenge arises from the dynamic nature and unknown closed-form solution of adversarial examples. In this paper, we resolve this issue and provide the first bound on ARC for deep neural networks. Our bound is qualitatively comparable to Rademacher complexity bounds in similar settings. The key ingredient is a new concept we introduce, termed intermediate adversarial examples, along with a framework for calculating the covering number that is compatible with them. Finally, we present experiments to analyze poor robust generalization, demonstrating that the weight norm is a crucial factor influencing the robust generalization gap.

Vertex-level clustering for directed graphs (digraphs) remains challenging as edge directionality breaks the key assumptions underlying popular spectral methods, which also incur the overhead of eigen-decomposition. This paper proposes Parametrized Power-Iteration Clustering (ParPIC), a random-walk-based clustering method for weakly connected digraphs. This builds over the Power-Iteration Clustering paradigm, which uses the rows of the iterated diffusion operator as a data embedding. ParPIC has three important features: the use of parametrized reversible random walk operators, the automatic tuning of the diffusion time, and the efficient truncation of the final embedding, which produces low-dimensional data representations and reduces complexity. Empirical results on synthetic and real-world graphs demonstrate that ParPIC achieves competitive clustering accuracy with improved scalability relative to spectral and teleportation-based methods.

Structured data is widely used in domains such as healthcare, finance, and scientific data management. Recent studies on structured data foundation models (SFMs) aim to support data analysis and mining tasks over such data, but still face scalability and generalization challenges when applied to real-world enterprise databases. First, many SFMs rely on full self-attention, which introduces an O(N^2) computational bottleneck and limits the number of tuples that can be processed jointly. Second, directly replacing attention with linear-complexity sequence models may conflict with the permutation-invariant nature of structured data, introducing artificial order bias and degrading representation quality. Moreover, models trained only on synthetic data may struggle to generalize to the heavy-tailed and heterogeneous distributions commonly found in real-world databases. To address these challenges, we propose FEAT, a linear-complexity foundation model for extremely large structured data. FEAT replaces quadratic attention with a multi-layer dual-axis encoding architecture. It integrates an adaptive-fusion bidirectional state-space model (AFBM) with convolutional gated linear attention (Conv-GLA), enabling cross-tuple contextualization in O(N) time while supporting permutation-invariant representation learning. To improve robustness under real-world data skewness, FEAT further adopts a hybrid structural causal pre-training pipeline with a robust reconstruction objective. Experiments on 12 real-world database benchmarks show that FEAT consistently outperforms representative SFMs on zero-shot tasks and scales linearly with structured-data sample length, achieving up to 50x faster inference latency.

Mean-field characterizations of first-order iterative algorithms -- including Approximate Message Passing (AMP), stochastic and proximal gradient descent, and Langevin diffusions -- have enabled a precise understanding of learning dynamics in many statistical applications. For algorithms whose non-linearities have a coordinate-separable form, it is known that such characterizations enjoy a degree of universality with respect to the underlying data distribution. However, mean-field characterizations of non-separable algorithm dynamics have largely remained restricted to i.i.d. Gaussian or rotationally-invariant data. In this work, we initiate a study of universality for non-separable AMP algorithms. We identify a general condition for AMP with polynomial non-linearities, in terms of a Bounded Composition Property (BCP) for their representing tensors, to admit a state evolution that holds universally for matrices with non-Gaussian entries. We then formalize a condition of BCP-approximability for Lipschitz AMP algorithms to enjoy a similar universal guarantee. We demonstrate that many common classes of non-separable non-linearities are BCP-approximable, including local denoisers, spectral denoisers for generic signals, and compositions of separable functions with generic linear maps, implying the universality of state evolution for AMP algorithms employing these non-linearities.

Geospatial foundation models (GFMs) have been proposed as generalizable backbones for disaster response, land-cover mapping, food-security monitoring, and other high-stakes Earth-observation tasks. Yet the published work about these models does not give reviewers or users enough information to tell which model fits a given task. We argue that nobody knows what the current state of the art is in geospatial foundation models. The methods may be useful, but the GFM literature does not standardize evaluations, training and testing protocols, released weights, or pretraining controls well enough for anyone to compare or rank them. In a 152-paper audit, we find 46 cross-paper disagreements of at least 10 points for the same model, benchmark, and protocol; 94/126 papers with extractable pretraining data use a configuration no other paper uses; and 39% of GFM papers release no model weights. This lack of community standards can be solved. We propose six concrete expectations: named-license weight release, shared core evaluations, copied-versus-rerun baseline annotations, variance reporting, one shared evaluation harness, and data-vs-architecture-vs-algorithm controls. These gaps are a coordination failure, not a fault of any individual lab; the authors of this paper, like many others in the GFM community, have contributed to them. Rather than just critiquing the community, we aim to provide concrete steps toward a shared understanding of how to innovate GFMs.

Reconstructing complex network topologies from data is a fundamental challenge in cybernetics and 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.