Graph Neural Networks

Mechanistic understanding and rational design of complex chemical systems depend on fast and accurate predictions of electronic structures beyond individual building blocks. However, if the system exceeds hundreds of atoms, first-principles quantum mechanical (QM) modeling becomes impractical. In this study, we developed FB-GNN-MBE by integrating a fragment-based graph neural network (FB-GNN) into the many-body expansion (MBE) theory and demonstrated its capacity to reproduce first-principles potential energy surfaces (PES) for hierarchically structured systems with manageable accuracy, complexity, and interpretability. Specifically, we divided the entire system into basic building blocks (fragments), evaluated their one-fragment energies using a QM model, and addressed many-fragment interactions using the structure-property relationships trained by FB-GNNs. Our investigation shows that FB-GNN-MBE achieves chemical accuracy in predicting two-body (2B) and three-body (3B) energies across water, phenol, and mixture benchmarks, as well as the one-dimensional dissociation curves of water and phenol dimers. To transfer the success of FB-GNN-MBE across various systems with minimal computational costs and data demands, we developed and validated a teacher-student learning protocol. A heavy-weight FB-GNN trained on a mixed-density water cluster ensemble (teacher) distills its learned knowledge and passes it to a light-weight GNN (student), which is later fine-tuned on a uniform-density (H2O)21 cluster ensemble. This transfer learning strategy resulted in efficient and accurate prediction of 2B and 3B energies for variously sized water clusters without retraining. Our transferable FB-GNN-MBE framework outperformed conventional non-FB-GNN-based models and provided a scalable and accurate route toward interaction energies of large molecular assemblies.

Software supply chain security compromises often stem from cascaded interactions of vulnerabilities, for example, between multiple vulnerable components. Yet, Software Bill of Materials (SBOM)-based pipelines for security analysis typically treat scanner findings as independent per-CVE (Common Vulnerabilities and Exposures) records. We propose a new research direction based on learning multi-vulnerability attack chains through a novel SBOM-driven graph-learning approach. This treats SBOM structure and scanner outputs as a dependency-constrained evidence graph rather than a flat list of vulnerabilities. We represent vulnerability-enriched CycloneDX SBOMs as heterogeneous graphs whose nodes capture software components and known vulnerabilities (i.e, CVEs), connected by typed relations, such as dependency and vulnerability links. We train a Heterogeneous Graph Attention Network (HGAT) to predict whether a component is associated with at least one known vulnerability as a feasibility check for learning over this structure. Additionally, we frame the discovery of cascading vulnerabilities as CVE-pair link prediction using a lightweight Multi-Layer Perceptron (MLP) neural network trained on documented multi-vulnerability chains. Validated on 200 real-world SBOMs from the Wild SBOMs public dataset, the HGAT component classifier achieves 91.03% Accuracy and 74.02% F1-score, while the cascade predictor model (MLP) achieves a Receiver Operating Characteristic - Area Under Curve (ROC-AUC) of 0.93 on a seed set of 35 documented attack chains.

Generative models for crystalline materials often rely on equivariant graph neural networks, which capture geometric structure well but are costly to train and slow to sample. We present Crystalite, a lightweight diffusion Transformer for crystal modeling built around two simple inductive biases. The first is Subatomic Tokenization, a compact chemically structured atom representation that replaces high-dimensional one-hot encodings and is better suited to continuous diffusion. The second is the Geometry Enhancement Module (GEM), which injects periodic minimum-image pair geometry directly into attention through additive geometric biases. Together, these components preserve the simplicity and efficiency of a standard Transformer while making it better matched to the structure of crystalline materials. Crystalite achieves state-of-the-art results on crystal structure prediction benchmarks, and de novo generation performance, attaining the best S.U.N. discovery score among the evaluated baselines while sampling substantially faster than geometry-heavy alternatives.

Longitudinal neuroimaging is essential for modeling disease progression in Alzheimer's disease (AD), yet irregular sampling and missing visits pose substantial challenges for learning reliable temporal representations. To address this challenge, we propose SDE-HGNN, a stochastic differential equation (SDE)-driven spatio-temporal hypergraph neural network for irregular longitudinal fMRI connectome modeling. The framework first employs an SDE-based reconstruction module to recover continuous latent trajectories from irregular observations. Based on these reconstructed representations, dynamic hypergraphs are constructed to capture higher-order interactions among brain regions over time. To further model temporal evolution, hypergraph convolution parameters evolve through SDE-controlled recurrent dynamics conditioned on inter-visit intervals, enabling disease-stage-adaptive connectivity modeling. We also incorporate a sparsity-based importance learning mechanism to identify salient brain regions and discriminative connectivity patterns. Extensive experiments on the OASIS-3 and ADNI cohorts demonstrate consistent improvements over state-of-the-art graph and hypergraph baselines in AD progression prediction. The source code is available at https://anonymous.4open.science/r/SDE-HGNN-017F.

Understanding the internal mechanisms of transformer-based large language models (LLMs) is crucial for their reliable deployment and effective operation. While recent efforts have yielded a plethora of attribution methods attempting to balance faithfulness and computational efficiency, dense component attribution remains prohibitively expensive. In this work, we introduce Dual Path Attribution (DPA), a novel framework that faithfully traces information flow on the frozen transformer in one forward and one backward pass without requiring counterfactual examples. DPA analytically decomposes and linearizes the computational structure of the SwiGLU Transformers into distinct pathways along which it propagates a targeted unembedding vector to receive the effective representation at each residual position. This target-centric propagation achieves O(1) time complexity with respect to the number of model components, scaling to long input sequences and dense component attribution. Extensive experiments on standard interpretability benchmarks demonstrate that DPA achieves state-of-the-art faithfulness and unprecedented efficiency compared to existing baselines.

Spatial graphs provide a lightweight and elegant representation of curvilinear anatomical structures such as blood vessels, lung airways, and neuronal networks. Accurately modeling these graphs is crucial in clinical and (bio-)medical research. However, the high spatial resolution of large networks drastically increases their complexity, resulting in significant computational challenges. In this work, we aim to tackle these challenges by proposing VesselTok, a framework that approaches spatially dense graphs from a parametric shape perspective to learn latent representations (tokens). VesselTok leverages centerline points with a pseudo radius to effectively encode tubular geometry. Specifically, we learn a novel latent representation conditioned on centerline points to encode neural implicit representations of vessel-like, tubular structures. We demonstrate VesselTok's performance across diverse anatomies, including lung airways, lung vessels, and brain vessels, highlighting its ability to robustly encode complex topologies. To prove the effectiveness of VesselTok's learnt latent representations, we show that they (i) generalize to unseen anatomies, (ii) support generative modeling of plausible anatomical graphs, and (iii) transfer effectively to downstream inverse problems, such as link prediction.

With the advent of system-in-package (SiP) chiplet-based design and heterogeneous 2.5D/3D integration, thermal-induced warpage has become a critical reliability concern. While conventional numerical approaches can deliver highly accurate results, they often incur prohibitively high computational costs, limiting their scalability for complex chiplet-package systems. In this paper, we present WarPGNN, an efficient and accurate parametric thermal warpage analysis framework powered by Graph Neural Networks (GNNs). By operating directly on graphs constructed from the floorplans, WarPGNN enables fast warpage-aware floorplan exploration and exhibits strong transferability across diverse package configurations. Our method first encodes multi-die floorplans into reduced Transitive Closure Graphs (rTCGs), then a Graph Convolution Network (GCN)-based encoder extracts hierarchical structural features, followed by a U-Net inspired decoder that reconstructs warpage maps from graph feature embeddings. Furthermore, to address the long-tailed pattern of warpage data distribution, we developed a physics-informed loss and revised a message-passing encoder based on Graph Isomorphic Network (GIN) that further enhance learning performance for extreme cases and expressiveness of graph embeddings. Numerical results show that WarPGNN achieves more than 205.91x speedup compared with the 2-D efficient FEM-based method and over 119766.64x acceleration with 3-D FEM method COMSOL, respectively, while maintaining comparable accuracy at only 1.26% full-scale normalized RMSE and 2.21% warpage value error. Compared with recent DeepONet-based model, our method achieved comparable prediction accuracy and inference speedup with 3.4x lower training time. In addition, WarPGNN demonstrates remarkable transferability on unseen datasets with up to 3.69% normalized RMSE and similar runtime.

We define an information-complexity property for aggregation functions, capturing a vast range of practical aggregations, and prove that any Message-Passing Graph Neural Network (MP-GNN) model with such aggregations induces only a polynomial number of equivalence classes on all graphs - while the number of non-isomorphic graphs is super-exponential (in number of vertices). Adding a familiar perspective, we observe that merely 2 iterations of Color Refinement (CR) induce at least an exponential number of equivalence classes, making the aforementioned MP-GNNs relatively infinitely weaker. Previous studies state that sum-aggregation MP-GNNs match full CR however they consider a weak, 'non-uniform', notion of distinguishing-power where each graph size may require a different MP-GNN to distinguish graphs up to that size. Our results concern both distinguishing between non-equivariant vertices and distinguishing between non-isomorphic graphs.

Motion planning through narrow passages remains a core challenge: sampling-based planners rarely place samples inside these narrow but critical regions, and even when samples land inside a passage, the straight-line connections between them run close to obstacle boundaries and are frequently rejected by collision checking. Decomposition-based planners resolve both issues by partitioning free space into convex cells -- every passage is captured exactly as a cell boundary, and any path within a cell is collision-free by construction. However, the number of candidate corridors through the cell graph grows combinatorially with environment complexity, creating a bottleneck in corridor selection. We present GNN-DIP, a framework that addresses this by integrating a Graph Neural Network (GNN) with a two-phase Decomposition-Informed Planner (DIP). The GNN predicts portal scores on the cell adjacency graph to bias corridor search toward near-optimal regions while preserving completeness. In 2D, Constrained Delaunay Triangulation (CDT) with the Funnel algorithm yields exact shortest paths within corridors; in 3D, Slab convex decomposition with portal-face sampling provides near-optimal path evaluation. Benchmarks on 2D narrow-passage scenarios, 3D bottleneck environments with up to 246 obstacles, and dynamic 2D settings show that GNN-DIP achieves 99--100% success rates with 2--280 times speedup over sampling-based baselines.

In this paper, we propose a fast method for estimating the condition number of sparse matrices using graph neural networks (GNNs). For efficient deployment of GNNs, we introduce a graph feature construction with $\mathrm{O}(\mathrm{nnz} + n)$ complexity, where $\mathrm{nnz}$ is the number of non-zero elements in the matrix and $n$ denotes the matrix dimension. We propose two schemes for estimating the matrix condition number using GNNs; one follows by decomposing the condition number and predicts the relatively more computationally intensive part $\|\mathbf{A}^{-1}\|$, without explicitly forming the inverse, while the other is to predict the whole condition number $κ$. Our approach can be extended to an arbitrary norm. Extensive experiments are conducted for the estimation of the 1-norm and 2-norm condition numbers, which show that our method achieves a significant speedup over the traditional numerical estimation methods. Our software for GNN condition number estimator is made publicly available at https://github.com/inEXASCALE/sparse-kappa.

Discrete graph generation has emerged as a powerful paradigm for modeling graph-structured data, yet state of the art models often rely on Graph Transformers or higher order architectures. We revisit this design assumption by introducing GenGNN, a modular message passing backbone for graph generation. GenGNN enables powerful generation by persisting edge fields through latent refinement of coupled node edge graph states, all without requiring global attention. Diffusion models integrating GenGNN achieve over 90 percent validity on standard benchmark datasets, performing within margins of Graph Transformer backbones and achieving up to 2x or even 5x faster inference. Systematic ablations isolate how GenGNN is resilient to oversmoothing during generative denoising, indicating each GenGNN component is necessary for downstream generation quality. Finally, representation-space analysis suggests GenGNN learns functionally similar representations to more theoretically-expressive architectures; even at deeper layers. As such, GenGNN uplifts local message-passing to challenge prevailing assumptions that performant discrete graph generation requires global attention or higher-order representations. Source Code Available Here

Micro-expression Action Unit (AU) detection identifies localized AUs from subtle facial muscle activations, providing a foundation for decoding affective cues. Previous methods face three key limitations: (1) heavy reliance on low-density visual information, rendering discriminative evidence vulnerable to background noise; (2) coarse-grained feature processing that misaligns with the demand for fine-grained representations; and (3) neglect of inter-AU correlations, restricting the parsing of complex expression patterns. We propose AULLM++, a reasoning-oriented framework leveraging Large Language Models (LLMs), which injects visual features into textual prompts as actionable semantic premises to guide inference. It formulates AU prediction into three stages: evidence construction, structure modeling, and deduction-based prediction. Specifically, a Multi-Granularity Evidence-Enhanced Fusion Projector (MGE-EFP) fuses mid-level texture cues with high-level semantics, distilling them into a compact Content Token (CT). Furthermore, inspired by micro- and macro-expression AU correspondence, we encode AU relationships as a sparse structural prior and learn interaction strengths via a Relation-Aware AU Graph Neural Network (R-AUGNN), producing an Instruction Token (IT). We then fuse CT and IT into a structured textual prompt and introduce Counterfactual Consistency Regularization (CCR) to construct counterfactual samples, enhancing the model's generalization. Extensive experiments demonstrate AULLM++ achieves state-of-the-art performance on standard benchmarks and exhibits superior cross-domain generalization.

This work formulates and solves optimization problems to generate input points that yield high errors between a neural network's predicted AC power flow solution and solutions to the AC power flow equations. We demonstrate this capability on an instance of the CANOS-PF graph neural network model, as implemented by the PF$Δ$ benchmark library, operating on a 14-bus test grid. Generated adversarial points yield errors as large as 3.7 per-unit in reactive power and 0.08 per-unit in voltage magnitude. When minimizing the perturbation from a training point necessary to satisfy adversarial constraints, we find that the constraints can be met with as little as an 0.04 per-unit perturbation in voltage magnitude on a single bus. This work motivates the development of rigorous verification and robust training methods for neural network surrogate models of AC power flow.

Estimating causal quantities traditionally relies on bespoke estimators tailored to specific assumptions. Recently proposed Causal Foundation Models (CFMs) promise a more unified approach by amortising causal discovery and inference in a single step. However, in their current state, they do not allow for the incorporation of any domain knowledge, which can lead to suboptimal predictions. We bridge this gap by introducing methods to condition CFMs on causal information, such as the causal graph or more readily available ancestral information. When access to complete causal graph information is too strict a requirement, our approach also effectively leverages partial causal information. We systematically evaluate conditioning strategies and find that injecting learnable biases into the attention mechanism, together with a graph-convolutional encoder, is a highly effective method to utilise full and partial causal information. Our experiments show that this conditioning allows a general-purpose CFM to match the performance of specialised models trained on specific causal structures. Overall, our approach addresses a central hurdle on the path towards all-in-one causal foundation models: the capability to answer causal queries in a data-driven manner while effectively leveraging any amount of domain expertise.

The Winner Determination Problem (WDP) in combinatorial auctions is NP-hard, and no existing method reliably predicts which instances will defeat fast greedy heuristics. The ML-for-combinatorial-optimization community has focused on learning to \emph{replace} solvers, yet recent evidence shows that graph neural networks (GNNs) rarely outperform well-tuned classical methods on standard benchmarks. We pursue a different objective: learning to predict \emph{when} a given instance is hard for greedy allocation, enabling instance-dependent algorithm selection. We design a 20-dimensional structural feature vector and train a lightweight MLP hardness classifier that predicts the greedy optimality gap with mean absolute error 0.033, Pearson correlation 0.937, and binary classification accuracy 94.7% across three random seeds. For instances identified as hard -- those exhibiting ``whale-fish'' trap structure where greedy provably fails -- we deploy a heterogeneous GNN specialist that achieves ${\approx}0\%$ optimality gap on all six adversarial configurations tested (vs.\ 3.75--59.24% for greedy). A hybrid allocator combining the hardness classifier with GNN and greedy solvers achieves 0.51% overall gap on mixed distributions. Our honest evaluation on CATS benchmarks confirms that GNNs do not outperform Gurobi (0.45--0.71 vs.\ 0.20 gap), motivating the algorithm selection framing. Learning \emph{when} to deploy expensive solvers is more tractable than learning to replace them.

Given a weighted undirected graph, a number of clusters $k$, and an exponent $z$, the goal in the $(k, z)$-clustering problem on graphs is to select $k$ vertices as centers that minimize the sum of the distances raised to the power $z$ of each vertex to its closest center. In the dynamic setting, the graph is subject to adversarial edge updates, and the goal is to maintain explicitly an exact $(k, z)$-clustering solution in the induced shortest-path metric. While efficient dynamic $k$-center approximation algorithms on graphs exist [Cruciani et al. SODA 2024], to the best of our knowledge, no prior work provides similar results for the dynamic $(k,z)$-clustering problem. As the main result of this paper, we develop a randomized incremental $(k, z)$-clustering algorithm that maintains with high probability a constant-factor approximation in a graph undergoing edge insertions with a total update time of $\tilde O(k m^{1+o(1)}+ k^{1+\frac{1}λ} m)$, where $λ\geq 1$ is an arbitrary fixed constant. Our incremental algorithm consists of two stages. In the first stage, we maintain a constant-factor bicriteria approximate solution of size $\tilde{O}(k)$ with a total update time of $m^{1+o(1)}$ over all adversarial edge insertions. This first stage is an intricate adaptation of the bicriteria approximation algorithm by Mettu and Plaxton [Machine Learning 2004] to incremental graphs. One of our key technical results is that the radii in their algorithm can be assumed to be non-decreasing while the approximation ratio remains constant, a property that may be of independent interest. In the second stage, we maintain a constant-factor approximate $(k,z)$-clustering solution on a dynamic weighted instance induced by the bicriteria approximate solution. For this subproblem, we employ a dynamic spanner algorithm together with a static $(k,z)$-clustering algorithm.

A collection of hyperplanes $\mathcal{H}$ slices all edges of the $n$-dimensional hypercube $Q_n$ with vertex set $\{-1,1\}^n$ if, for every edge $e$ in the hypercube, there exists a hyperplane in $\mathcal{H}$ intersecting $e$ in its interior. Let $S(n)$ be the minimum number of hyperplanes needed to slice $Q_n$. We prove that $S(n) \leq \lceil \frac{4n}{5} \rceil$, except when $n$ is an odd multiple of $5$, in which case $S(n) \leq \frac{4n}{5} +1$. This improves upon the previously known upper bound of $S(n) \leq \lceil\frac{5n}{6} \rceil$ due to Paterson reported in 1971. We also obtain new lower bounds on the maximum number of edges in $Q_n$ that can be sliced using $k<n$ hyperplanes. We prove the improved upper bound on $S(n)$ by constructing $8$ hyperplanes slicing $Q_{10}$ aided by the recently introduced CPro1: an automatic tool that uses reasoning LLMs coupled with automated hyperparameter tuning to create search algorithms for the discovery of mathematical constructions.

Credit exposure in Decentralized Finance (DeFi) is often implicit and token-mediated, creating a dense web of inter-protocol dependencies. Thus, a shock to one token may result in significant and uncontrolled contagion effects. As the DeFi ecosystem becomes increasingly linked with traditional financial infrastructure through instruments, such as stablecoins, the risk posed by this dynamic demands more powerful quantification tools. We introduce DeXposure-FM, the first time-series, graph foundation model for measuring and forecasting inter-protocol credit exposure on DeFi networks, to the best of our knowledge. Employing a graph-tabular encoder, with pre-trained weight initialization, and multiple task-specific heads, DeXposure-FM is trained on the DeXposure dataset that has 43.7 million data entries, across 4,300+ protocols on 602 blockchains, covering 24,300+ unique tokens. The training is operationalized for credit-exposure forecasting, predicting the joint dynamics of (1) protocol-level flows, and (2) the topology and weights of credit-exposure links. The DeXposure-FM is empirically validated on two machine learning benchmarks; it consistently outperforms the state-of-the-art approaches, including a graph foundation model and temporal graph neural networks. DeXposure-FM further produces financial economics tools that support macroprudential monitoring and scenario-based DeFi stress testing, by enabling protocol-level systemic-importance scores, sector-level spillover and concentration measures via a forecast-then-measure pipeline. Empirical verification fully supports our financial economics tools. The model and code have been publicly available. Model: https://huggingface.co/EVIEHub/DeXposure-FM. Code: https://github.com/EVIEHub/DeXposure-FM.

Entity alignment (EA) is critical for knowledge graph (KG) fusion. Existing EA models lack transferability and are incapable of aligning unseen KGs without retraining. While using graph foundation models (GFMs) offer a solution, we find that directly adapting GFMs to EA remains largely ineffective. This stems from a critical "reasoning horizon gap": unlike link prediction in GFMs, EA necessitates capturing long-range dependencies across sparse and heterogeneous KG structuresTo address this challenge, we propose a EA foundation model driven by a parallel encoding strategy. We utilize seed EA pairs as local anchors to guide the information flow, initializing and encoding two parallel streams simultaneously. This facilitates anchor-conditioned message passing and significantly shortens the inference trajectory by leveraging local structural proximity instead of global search. Additionally, we incorporate a merged relation graph to model global dependencies and a learnable interaction module for precise matching. Extensive experiments verify the effectiveness of our framework, highlighting its strong generalizability to unseen KGs.

Graph neural networks are usually treated as auxiliaries for combinatorial optimization: they imitate algorithms, guide search, or supply scores to classical procedures. We show that this auxiliary role is not intrinsic. A GNN can itself be a heuristic. For the Euclidean Travelling Salesman Problem, we train a non-autoregressive GNN with no labels, rewards, sequential decoding, search, or local improvement. A differentiable Hamiltonian-cycle objective is the only supervision. The trained model produces a complete tour in one forward pass, while dropout and snapshots from a single training trajectory provide solution diversity without engineered moves. The heuristic is therefore learned, not programmed. It is also fast: batched inference remains in the millisecond regime on GPUs. Experiments on TSP100, TSP200, and TSP500 show that the model consistently improves over nearest-neighbor greedy baselines. These results identify unsupervised GNNs as a class of fast learned heuristics for combinatorial optimization.

Multivariate data often exhibit complex dependencies that violate the assumption of isotropic residual noise. For such cases, we introduce Graph Regularized PCA (GR-PCA). It is a graph-based regularization of PCA that incorporates the dependency structure of the data features by learning a sparse precision graph and biasing loadings toward the low-frequency Fourier modes of the corresponding graph Laplacian. Consequently, high-frequency signals are suppressed, while graph-coherent low-frequency ones are preserved, yielding interpretable principal components aligned with conditional relationships. We evaluate GR-PCA on synthetic data spanning diverse graph topologies, signal-to-noise ratios, and sparsity levels. Compared to mainstream alternatives, it concentrates variance on the intended support, produces loadings with lower graph-Laplacian energy, and remains competitive in out-of-sample reconstruction. When high-frequency signals are present, the graph Laplacian penalty prevents overfitting, reducing the reconstruction accuracy but improving structural fidelity. The advantage over PCA is most pronounced when high-frequency signals are graph-correlated, whereas PCA remains competitive when such signals are nearly rotationally invariant. The procedure is simple to implement, modular with respect to the precision estimator, and scalable, providing a practical route to structure-aware dimensionality reduction that improves structural fidelity without sacrificing predictive performance.

Neural Combinatorial Optimization (NCO) has mostly focused on learning policies, typically neural networks, that operate on a single candidate solution at a time, either by constructing one from scratch or iteratively improving it. In contrast, decades of work in metaheuristics have shown that maintaining and evolving populations of solutions improves robustness and exploration, and often leads to stronger performance. To close this gap, we study how to make NCO explicitly population-based by learning policies that act on sets of candidate solutions. We first propose a simple taxonomy of population awareness levels and use it to highlight two key design challenges: (i) how to represent a whole population inside a neural network, and (ii) how to learn population dynamics that balance intensification (generating good solutions) and diversification (maintaining variety). We make these ideas concrete with two complementary tools: one that improves existing solutions using information shared across the whole population, and the other generates new candidate solutions that explicitly balance being high-quality with diversity. Experimental results on Maximum Cut and Maximum Independent Set indicate that incorporating population structure is advantageous for learned optimization methods and opens new connections between NCO and classical population-based search.

Large language models (LLMs) have demonstrated promising capabilities in Text-Attributed Graph (TAG) understanding. Recent studies typically focus on verbalizing the graph structures via handcrafted prompts, feeding the target node and its neighborhood context into LLMs. However, constrained by the context window, existing methods mainly resort to random sampling, often implemented via dropping node/edge randomly, which inevitably introduces noise and cause reasoning instability. We argue that graphs inherently contain rich structural and semantic information, and that their effective exploitation can unlock potential gains in LLMs reasoning performance. To this end, we propose Homophily-aware Structural and Semantic Compression for LLMs (HS2C), a framework centered on exploiting graph homophily. Structurally, guided by the principle of Structural Entropy minimization, we perform a global hierarchical partition that decodes the graph's essential topology. This partition identifies naturally cohesive, homophilic communities, while discarding stochastic connectivity noise. Semantically, we deliver the detected structural homophily to the LLM, empowering it to perform differentiated semantic aggregation based on predefined community type. This process compresses redundant background contexts into concise community-level consensus, selectively preserving semantically homophilic information aligned with the target nodes. Extensive experiments on 10 node-level benchmarks across LLMs of varying sizes and families demonstrate that, by feeding LLMs with structurally and semantically compressed inputs, HS2C simultaneously enhances the compression rate and downstream inference accuracy, validating its superiority and scalability. Extensions to 7 diverse graph-level benchmarks further consolidate HS2C's task generalizability.

Mixed-integer linear programming (MILP) is a foundational framework for combinatorial optimization across science and engineering, but remains hard to solve at scale due to NP-hardness. Recent learning-based methods typically model MILP instances as variable-constraint bipartite graphs and use Graph Neural Networks (GNNs) for representation learning, yet their locality limits representation power. We propose an attention-driven neural backbone that adopts an element-centric view of variables and constraints, with dual attention performing parallel intra-type self-attention and inter-type cross-attention. Across three representative tasks at the instance, element, and solving-state levels, our model consistently outperforms conventional GNN-based architectures, highlighting attention-based, element-centric modeling as a powerful foundation for learning-enhanced combinatorial optimization.

We consider the densest submatrix problem, which seeks the submatrix of fixed size of a given binary matrix that contains the most nonzero entries. This problem is a natural generalization of fundamental problems in combinatorial optimization, e.g., the densest subgraph, maximum clique, and maximum edge biclique problems, and has wide application the study of complex networks. Much recent research has focused on the development of sufficient conditions for exact solution of the densest submatrix problem via convex relaxation. The vast majority of these sufficient conditions establish identification of the densest submatrix within a graph containing exactly one large dense submatrix hidden by noise. The assumptions of these underlying models are not observed in real-world networks, where the data may correspond to a matrix containing many dense submatrices of varying sizes. We extend and generalize these results to the more realistic setting where the input matrix may contain \emph{many} large dense subgraphs. Specifically, we establish sufficient conditions under which we can expect to solve the densest submatrix problem in polynomial time for random input matrices sampled from a generalization of the stochastic block model. Moreover, we also provide sufficient conditions for perfect recovery under a deterministic adversarial. Numerical experiments involving randomly generated problem instances and real-world collaboration and communication networks are used empirically to verify the theoretical phase-transitions to perfect recovery given by these sufficient conditions.

Predictive machine learning models generally excel on in-distribution data, but their performance degrades on out-of-distribution (OOD) inputs. Reliable deployment therefore requires robust OOD detection, yet this is particularly challenging for irregular 3D graphs that combine continuous geometry with categorical identities and are unordered by construction. Here, we present a probabilistic OOD detection framework for complex 3D graph data built on a diffusion model that learns a density of the training distribution in a fully unsupervised manner. A key ingredient we introduce is a unified continuous diffusion over both 3D coordinates and discrete features: categorical identities are embedded in a continuous space and trained with cross-entropy, while the corresponding diffusion score is obtained analytically via posterior-mean interpolation from predicted class probabilities. This yields a single self-consistent probability-flow ODE (PF-ODE) that produces per-sample log-likelihoods, providing a principled typicality score for distribution shift. We validate the approach on protein-ligand complexes and construct strict OOD datasets by withholding entire protein families from training. PF-ODE likelihoods identify held-out families as OOD and correlate strongly with prediction errors of an independent binding-affinity model (GEMS), enabling a priori reliability estimates on new complexes. Beyond scalar likelihoods, we show that multi-scale PF-ODE trajectory statistics - including path tortuosity, flow stiffness, and vector-field instability - provide complementary OOD information. Modeling the joint distribution of these trajectory features yields a practical, high-sensitivity detector that improves separation over likelihood-only baselines, offering a label-free OOD quantification workflow for geometric deep learning.

Many learning problems are organized by group symmetries. While invariance is often imposed through architectures or group averaging, we ask when it can emerge from training on a finite random subset of an orbit. We study this question in classical Hopfield networks, where strict memorization can be expressed as a linear margin problem. Reparameterizing minimization of energy flow (MEF) as an exponential loss connects gradient descent to the corresponding minimum-norm hard-margin memorizer. Our main result shows that, for independent uniform samples from any finite permutation orbit, the exact sample hard-margin support vector machine (HSVM) concentrates exponentially around the invariant full-orbit HSVM. Consequently, an orbit-size-independent polynomial number of samples suffices both for approximate parameter invariance and for simultaneous memorization of every orbit element; directional convergence transfers this conclusion asymptotically to MEF gradient descent. For graph-isomorphism orbits, we characterize the invariant parameters as a three-dimensional subspace and show that every such orbit is memorizable. For cliques of fixed linear density, additional symmetry sharpens the uniform memorization bound to $O(v^4\log(1/δ))$, exponentially smaller than the orbit size. Together with experiments across several learning rules, these results give a finite-sample account of how optimization bias can recover symmetry from partial group-structured data.

Quantum circuit design is a key bottleneck for practical quantum machine learning on complex, real-world data. We present an automated framework that discovers and refines variational quantum circuits (VQCs) using graph-based Bayesian optimization with a graph neural network (GNN) surrogate. Circuits are represented as graphs and mutated and selected via an expected improvement acquisition function informed by surrogate uncertainty with Monte Carlo dropout. Candidate circuits are evaluated with a hybrid quantum-classical variational classifier on the next generation firewall telemetry and network internet of things (NF-ToN-IoT-V2) cybersecurity dataset, after feature selection and scaling for quantum embedding. We benchmark our pipeline against an MLP-based surrogate, random search, and greedy GNN selection. The GNN-guided optimizer consistently finds circuits with lower complexity and competitive or superior classification accuracy compared to all baselines. Robustness is assessed via a noise study across standard quantum noise channels, including amplitude damping, phase damping, thermal relaxation, depolarizing, and readout bit flip noise. The implementation is fully reproducible, with time benchmarking and export of best found circuits, providing a scalable and interpretable route to automated quantum circuit discovery.

Inspired by graph-based methodologies, we introduce a novel graph-spanning algorithm designed to identify changes in both offline and online data across low to high dimensions. This versatile approach is applicable to Euclidean and graph-structured data with unknown distributions, while maintaining control over error probabilities. Theoretically, we demonstrate that the algorithm achieves high detection power when the magnitude of the change surpasses the lower bound of the minimax separation rate, which scales on the order of $\sqrt{nd}$. Our method outperforms other techniques in terms of accuracy for both Gaussian and non-Gaussian data. Notably, it maintains strong detection power even with small observation windows, making it particularly effective for online environments where timely and precise change detection is critical.

Algorithmic reasoning -- the ability to perform step-by-step logical inference -- is a synthetic benchmark for evaluating multi-step reasoning abilities, designed for graph neural networks and also for transformer models. Prior work has evaluated reasoning for executing a single algorithmic task, whereas a more desirable objective is to perform multiple algorithmic reasoning tasks simultaneously. We start by noting that this is inherently difficult due to differences arising from the execution traces of the algorithms (such as depth- vs. breadth-first search), which cause interference when they are trained together. In this paper, we introduce {branching neural networks}, a new architecture for multitask algorithmic reasoning. The main idea is to search for a recursive tree-structured partition of $n$ algorithmic tasks into a $k$-ary tree (divided into $L$ layers). Naive search requires $O(k^{nL})$ complexity; we develop an algorithm that reduces this to $O(nL)$ by solving a convex relaxation at each layer to approximate an optimal partition. Our approach clusters these tasks using gradient-based affinity and can be used on top of any base model. We validate our approach on algorithmic reasoning benchmarks and their extensions with text descriptions. We show that gradient-based affinity scores help estimate true performance with less than 5% error, measured across eight different architectures with up to 34 billion parameters. On the CLRS benchmark, our approach outperforms existing graph neural networks by 3.7% and baselines by 1.2%, while reducing runtime by 48% and memory usage by 26%. The learned branching structure shows a hierarchical clustering of related algorithms. On three text-based graph reasoning benchmarks, our approach improves over baseline methods by 3.2%. Finally, we validate our approach for overlapping community detection.

We study the problem of learning an unknown graph via group queries on node subsets, where each query reports whether at least one edge is present among the queried nodes. In general, learning arbitrary graphs with $n$ nodes and $k$ edges is hard in the non-adaptive setting, requiring $Ω\big(\min\{k^2\log n,\,n^2\}\big)$ tests even when a small error probability is allowed. We focus on learning Erdős--Rényi (ER) graphs $G\sim\mathrm{ER}(n,q)$ in the non-adaptive setting, where the expected number of edges is $\bar{k}=q\binom{n}{2}$, and we aim to design an efficient testing--decoding scheme, namely, a non-adaptive test design together with a decoding algorithm, achieving asymptotically vanishing error probability. Prior work (Li--Fresacher--Scarlett, NeurIPS 2019) presents a testing--decoding scheme that attains an order-optimal number of tests $O(\bar{k}\log n)$ but incurs $Ω(n^2)$ decoding time, whereas their proposed sublinear-time algorithm incurs an extra $(\log \bar{k})(\log n)$ factor in the number of tests. We extend the binary splitting approach, recently developed for non-adaptive group testing, to the ER graph learning setting, and prove that the edge set can be recovered with high probability using $O(\bar{k}\log n)$ tests while attaining decoding time $O(\bar{k}^{1+δ}\log n)$ for any fixed $δ>0$.

Operational knowledge-graph (KG) pipelines in networking and cybersecurity increasingly need to refresh embeddings under strict time, memory, and audit budgets, especially as curated feeds and LLM-assisted extraction accelerate KG updates. A recurring per-step cost in mini-batch KG learning is neighborhood-context estimation: uniform neighbor sampling without replacement followed by mean aggregation. Common frameworks implement this estimator through sampled-subgraph materialization and intermediate feature gathers, adding kernel launches, allocator pressure, and transient memory spikes. We present One-Pass Neighborhood Estimation, a fused PyTorch CUDA operator that samples neighbors and directly emits the sampled-neighborhood mean, avoiding explicit block construction while preserving GraphSAGE-mean semantics for the same sampled neighbor IDs. It supports seed-controlled sampling and optional saved-index replay for reproducible validation and regression testing. Across large-graph mini-batch workloads, it improves FP32 end-to-end step latency by 2.24x-3.48x over tuned DGL baselines and reduces transient GPU memory by up to 160x in our measurements. On OGB KG completion benchmarks such as WikiKG2 and BioKG, it reduces step time and peak VRAM while matching ranking quality within seed variability, improving time-to-quality for budgeted KG refresh.

Graph neural networks (GNNs) have become an indispensable tool for analyzing relational data. Classical GNNs are broadly classified into three variants: convolutional, attentional, and message-passing. While the standard message-passing variant is expressive, its typical pair-wise messages only consider the features of the center node and each neighboring node individually. This design fails to incorporate contextual information contained within the broader local neighborhood, potentially hindering its ability to learn meaningful relationships within the entire set of neighboring nodes. To address this, the paper first refines the concept of neighborhood-contextualization within GNNs, leveraging ideas from set-based aggregation methods and a key property of the attentional variant. This then serves as the basis for generalizing the message-passing variant to the proposed neighborhood-contextualized message-passing (NCMP) framework. To demonstrate its utility, a simple, mathematically grounded method to parametrize and operationalize NCMP is presented, leading to the development of the proposed Soft-Isomorphic Neighborhood-Contextualized Graph Convolution Network (SINC-GCN). Across a diverse set of synthetic and benchmark datasets, SINC-GCN strikes a highly favorable balance between expressivity and efficiency. Notably, while more complex models incur significant computational overhead, SINC-GCN delivers substantial performance gains with considerable effect sizes over baseline GNN models while maintaining a highly efficient asymptotic runtime complexity, further underscoring the distinctive utility of neighborhood-contextualization. Overall, by integrating multiset neighborhood context, the proposed NCMP framework serves as a practical and scalable path toward enhancing the graph representational power of classical GNNs.

In this paper, we present DiRecGNN, an attention-enhanced entity recommendation framework for monitoring cloud services at Microsoft. We provide insights on the usefulness of this feature as perceived by the cloud service owners and lessons learned from deployment. Specifically, we introduce the problem of recommending the optimal subset of attributes (dimensions) that should be tracked by an automated watchdog (monitor) for cloud services. To begin, we construct the monitor heterogeneous graph at production-scale. The interaction dynamics of these entities are often characterized by limited structural and engagement information, resulting in inferior performance of state-of-the-art approaches. Moreover, traditional methods fail to capture the dependencies between entities spanning a long range due to their homophilic nature. Therefore, we propose an attention-enhanced entity ranking model inspired by transformer architectures. Our model utilizes a multi-head attention mechanism to focus on heterogeneous neighbors and their attributes, and further attends to paths sampled using random walks to capture long-range dependencies. We also employ multi-faceted loss functions to optimize for relevant recommendations while respecting the inherent sparsity of the data. Empirical evaluations demonstrate significant improvements over existing methods, with our model achieving a 43.1% increase in MRR. Furthermore, product teams who consumed these features perceive the feature as useful and rated it 4.5 out of 5.

Monocular 3D human pose estimation remains a fundamentally ill-posed inverse problem due to the inherent depth ambiguity in 2D-to-3D lifting. While contemporary video-based methods leverage temporal context to enhance spatial reasoning, they operate under a critical paradigm limitation: processing each sequence in isolation, thereby failing to exploit the strong structural regularities and repetitive motion patterns that pervade human movement across sequences. This work introduces the Pattern Reuse Graph Convolutional Network (PRGCN), a novel framework that formalizes pose estimation as a problem of pattern retrieval and adaptation. At its core, PRGCN features a graph memory bank that learns and stores a compact set of pose prototypes, encoded as relational graphs, which are dynamically retrieved via an attention mechanism to provide structured priors. These priors are adaptively fused with hard-coded anatomical constraints through a memory-driven graph convolution, ensuring geometrical plausibility. To underpin this retrieval process with robust spatiotemporal features, we design a dual-stream hybrid architecture that synergistically combines the linear-complexity, local temporal modeling of Mamba-based state-space models with the global relational capacity of self-attention. Extensive evaluations on Human3.6M and MPI-INF-3DHP benchmarks demonstrate that PRGCN establishes a new state-of-the-art, achieving an MPJPE of 37.1mm and 13.4mm, respectively, while exhibiting enhanced cross-domain generalization capability. Our work posits that the long-overlooked mechanism of cross-sequence pattern reuse is pivotal to advancing the field, shifting the paradigm from per-sequence optimization towards cumulative knowledge learning.

Novel Markov Chain Monte Carlo (MCMC) methods have enabled the generation of large ensembles of redistricting plans modeled as a graph partitioning problem. However, existing algorithms such as Reversible Recombination (RevReCom) and Metropolized Forest Recombination (MFR) have strong preferences for distributions related to the spanning tree measure. In this paper we introduce the Marked Edge Walk (MEW), a novel Markov chain proposal for sampling from the space of graph partitions. The walk operates on the space of spanning trees with marked edges, allowing for calculable transition probabilities for use in the Metropolis-Hastings algorithm. Empirical results on real-world dual graphs show convergence under a broad class of target distributions less constrained by spanning tree counts, including policy-based distributions, such as competitiveness on New Hampshire that are independent of spanning trees, and compactness and partisan symmetry distributions on New Hampshire and Texas that, while related to spanning trees, can now be properly targeted with a smaller degree of spanning tree bias, which represents an advancement in flexible ensemble generation.

Limited-Area Models (LAMs) enable weather forecasting over regional domains at higher resolutions than what is computationally feasible for global models. At such high resolutions, machine learning approaches for weather prediction increasingly rely on ensemble methods to produce probabilistic forecasts. However, existing machine learning LAMs are not scalable due to relying on computationally costly diffusion models or inefficient graph neural networks. We tackle this by introducing a new hybrid CNN/GNN architecture, tailored to the LAM weather forecasting problem. Using this architecture, we construct the DET-LAM deterministic model, producing LAM forecasts both more efficiently and accurately than its graph-based competitor. We then tackle the ensemble forecasting problem, by using this architecture as a backbone for the generative model CRPS-LAM. CRPS-LAM is trained using a Continuous Ranked Probability Score (CRPS) objective, enabling efficient training and sampling in a single forward pass. This yields a speedup of $\approx \times 39$ compared to diffusion-based baselines. We evaluate our approach on regional domains in northern Europe, demonstrating that CRPS-LAM produces skillful and well-calibrated forecasts across a range of atmospheric variables.

Learning on temporal graphs has become a central topic in graph representation learning, with numerous benchmarks indicating the strong performance of state-of-the-art models. However, recent work has raised concerns about the reliability of benchmark results, noting issues with commonly used evaluation protocols and the surprising competitiveness of simple heuristics. This contrast raises the question of which characteristics of the underlying graphs temporal graph learning models actually use to form their predictions. We address this by systematically evaluating eight models on their ability to capture eight fundamental characteristics related to the link structure of temporal graphs. These include structural characteristics such as density, temporal patterns such as recency, and edge formation mechanisms such as homophily. Using both synthetic and real-world datasets, we analyze how well models learn these characteristics. Our findings reveal a mixed picture: models capture some characteristics well but fail to reproduce others. With this, we expose important limitations. Overall, we believe that our results provide practical insights for the application of temporal graph learning models and motivate more interpretability-driven evaluations in graph learning research.

We propose refined GRFs (GRFs++), a new class of Graph Random Features (GRFs) for efficient and accurate computations involving kernels defined on the nodes of a graph. GRFs++ resolve some of the long-standing limitations of regular GRFs, including difficulty modeling relationships between more distant nodes. They reduce dependence on sampling long graph random walks via a novel walk-stitching technique, concatenating several shorter walks without breaking unbiasedness. By applying these techniques, GRFs++ inherit the approximation quality provided by longer walks but with greater efficiency, trading sequential, inefficient sampling of a long walk for parallel computation of short walks and matrix-matrix multiplication. Furthermore, GRFs++ extend the simplistic GRFs walk termination mechanism (Bernoulli schemes with fixed halting probabilities) to a broader class of strategies, applying general distributions on the walks' lengths. This improves the approximation accuracy of graph kernels, without incurring extra computational cost. We provide empirical evaluations to showcase all our claims and complement our results with theoretical analysis.

We study the propagation of outliers in cyclic causal graphs with linear structural equations, tracing them back to one or several "root cause" nodes. We show that it is possible to identify a short list of potential root causes provided that the perturbation is sufficiently strong and propagates according to the same structural equations as in the normal mode. This shortlist consists of the true root causes together with those of its parents lying on a cycle with the root cause. Notably, our method does not require prior knowledge of the causal graph and yields encouraging results on simulated data and real data from biology and cloud computing.

Balancing resource efficiency and fairness is critical in networked systems that support modern learning applications. We introduce the \emph{Fair Minimum Labeling} (FML) problem: the task of designing a minimum-cost temporal edge activation plan that ensures each group of nodes in a network has sufficient access to a designated target set, according to specified coverage requirements. FML captures key trade-offs in systems where edge activations incur resource costs and equitable access is essential, such as distributed data collection, update dissemination in edge-cloud systems, and fair service restoration in critical infrastructure. We first give a structural characterisation of the single-terminal case, showing that it is equivalent to the rooted Covering Steiner problem. We prove that FML is NP-hard and admits no $((1-ε)\ln |\mathcal{C}|)$-approximation for $|\mathcal{C}|$ groups, already on a star, while for any fixed number of groups it inherits a constant-factor approximation and remains APX-hard. We then present probabilistic approximation algorithms for the two-group, single-terminal case: an algorithm whose tree subroutine is exact, hence optimal on tree-structured networks and $\mathcal{O}(\log |V|)$ in expectation on general graphs, together with a faster bicriteria variant whose coverage violation degrades gracefully with the merge depth of the tree computation. For practical scalability, we additionally introduce a graph-native variant based on a shortest-path-tree reduction. Empirical results show that FML enforces group-level fairness, while the graph-native variant substantially improves scalability and achieves competitive activation cost.

The pretrain-transfer paradigm, which underpins the success of large language models (LLMs), has demonstrated the immense power of creating foundation models that learn generalizable representations from vast datasets. However, extending this paradigm to Operations Research (OR) problems on graph structures remains challenging due to the fundamental conflict between the statistical flexibility of language and the strict combinatorial constraints of graphs. To bridge this gap, we introduce the Graph Foundation Model (GFM), the first framework capable of solving all distance-based optimization problems on graph structures. By introducing the LLM-like self-supervised pre-training paradigm on the paths generated from random walks in the graph, GFM is compelled to internalize the graph's complex topological and combinatorial rules, where the connectivity of the structure itself can be treated as the supervisory signal. Unlike existing neural methods that learn complex and task-specific solving policies, our approach leverages the pre-trained GFM as a foundational model of the graph's intrinsic structure, which in turn enables a simple generative heuristic to tackle a diverse range of optimization challenges effectively. Comprehensive experiments on networks ranging from 20 to 893 nodes demonstrate that GFM achieves competitive performance against specialized solvers across a variety of distinct optimization task classes, while maintaining significantly faster inference times. Our work establishes a new paradigm of adapting the pretrain-transfer framework to graph optimization, opening the door for applying foundation model innovations to OR.

Pipeline parallelism is widely used to train large language models (LLMs). However, increasing heterogeneity in model architectures exacerbates pipeline bubbles, thereby reducing training efficiency. Prior approaches typically optimize a single phase of the pipeline schedule (i.e., partitioning, placement, or scheduling), leaving substantial pipeline bubbles. While promising, co-optimization poses three key challenges: (1) complex performance modeling, (2) a combinatorial search space, and (3) irregular execution orders. To address these challenges, we propose OctoPipe, a pipeline parallelism system to jointly optimize partitioning, placement, and scheduling. First, we build a graph-based pipeline simulator to model heterogeneous pipeline execution for co-optimization. Second, on top of the simulator, we develop an iterative bubble-aware tuner to efficiently explore the combinatorial search space. Third, we implement a unified pipeline executor that dynamically orchestrates computation and communication to support irregular execution orders without deadlocks while maximizing communication-computation overlap. Experiments show that OctoPipe achieves 1.09--1.49$\times$ throughput improvement over the state-of-the-art pipeline parallelism approaches across various heterogeneous model configurations and GPU cluster scales.

The class imbalance problem refers to the disproportionate distribution of samples across different classes within a dataset, where the minority classes are significantly underrepresented. This issue is also prevalent in graph-structured data. Most graph neural networks (GNNs) implicitly assume a balanced class distribution and therefore often fail to account for the challenges introduced by class imbalance, which can lead to biased learning and degraded performance on minority classes. We identify a quality inconsistency problem in synthesized nodes, which leads to suboptimal performance under graph imbalance conditions. To mitigate this issue, we propose GraphIFE (Graph Invariant Feature Extraction), a novel framework designed to mitigate quality inconsistency in synthesized nodes. Our approach incorporates two key concepts from graph invariant learning and introduces strategies to strengthen the embedding space representation, thereby enhancing the model's ability to identify invariant features. Extensive experiments demonstrate the framework's efficiency and robust generalization, as GraphIFE consistently outperforms various baselines across multiple datasets. The code is publicly available at https://github.com/flzeng1/GraphIFE.

Mixed bundle pricing is a classic revenue management problem arising in industries such as e-commerce, tourism, and video games. It refers to designing product combinations (i.e., bundles) and determining their prices to maximize expected profit. Exact mixed-bundling formulations capture this structure but are computationally intractable because the number of possible bundles grows exponentially with the number of products. We propose a graph neural network (GNN)-guided pruning framework for scalable (non-)additive bundle pricing. Instead of learning on the exponential bundle-level formulation, we encode each instance as a compact customer-product graph and train an edge-output GNN to learn the product-assignment probabilities from optimal mixed-bundling solutions. The predicted probabilities are then converted into restricted candidate bundle families through fixed cutoff pruning and progressive cutoff pruning; the final prices and assignments are obtained by solving the mixed bundling formulation over the retained bundles. We further introduce a GNN-guided local search and an iterative self-improvement procedure for larger instances. The local search refines the retained bundle family by prioritizing high-confidence add/drop moves, while the iterative self-improvement procedure generates high-quality solutions on larger instances for retraining. Theoretically, we show that under mild distinguishability conditions the proposed edge-output GNN class is expressive enough to recover the optimal product-assignment mapping. Experiments show that the proposed policies recover over 98% of the optimal profit on small instances and outperform bundle-size pricing on larger instances with substantial runtime savings.

Graph foundation models face several fundamental challenges including transferability across diverse domains and data scarcity, which calls into question the very feasibility of creating such models. However, despite similar challenges, the tabular domain has recently witnessed the emergence of the first successful foundation models such as TabPFN. These models are based on the prior-data fitted networks (PFN) framework, in which models are pretrained on carefully designed synthetic datasets to make predictions in an in-context learning setting. Recently, G2T-FM, a framework that converts graph node-level tasks into tabular tasks, has made the first step towards adopting PFNs for graphs, yet it is limited to hand-crafted features and was never pretrained on graph data. In this work, we make the next step by proposing GraphPFN, a PFN-based model designed and pretrained specifically for graph node-level tasks. Following the PFN framework, we first design a prior distribution of synthetic attributed graphs by using a novel combination of multi-level stochastic block models and a preferential attachment process for structure generation and graph-aware structured causal models for attribute generation. Then, we augment the tabular foundation model LimiX with attention-based graph neighborhood aggregation layers and train it on millions of synthetic graphs sampled from our prior. On diverse real-world graph datasets with node-level tasks, GraphPFN achieves state-of-the-art results in both in-context learning and finetuning regimes, outperforming G2T-FM, prior GFMs, and task-specific GNNs trained from scratch. More broadly, GraphPFN shows the potential of PFN-based models for building graph foundation models.

When different objectives conflict with each other in multi-task learning, gradients begin to interfere and slow convergence, thereby potentially reducing the final model's performance. To address this, we introduce SON-GOKU, a scheduler that computes gradient interference, constructs an interference graph, and then applies greedy graph-coloring to partition tasks into groups that align well with each other. At each training step, only one group (color class) of tasks are activated, and the grouping partition is constantly recomputed as task relationships evolve throughout training. By ensuring that each mini-batch contains only tasks that pull the model in the same direction, our method improves the effectiveness of any underlying multi-task learning optimizer without additional tuning. Since tasks within these groups will update in compatible directions, multi-task learning will improve model performance rather than impede it. Empirical results on six different datasets show that this interference-aware graph-coloring approach consistently outperforms baselines and state-of-the-art multi-task optimizers. We provide extensive theory showing why grouping and sequential updates improve multi-task learning, with guarantees on descent, convergence, and the ability to accurately identify what tasks conflict or align.

This paper presents GraphMend, a compiler technique that automatically fixes FX graph breaks in PyTorch 2 programs. Although PyTorch 2 introduced TorchDynamo and TorchInductor to enable just-in-time graph compilation, certain code patterns still cause graph breaks that force execution to fall back to Python eager mode, introducing costly CPU-GPU synchronization and reducing optimization opportunities. Our investigation of 195 Hugging Face models reveals that 13.8% of models exhibit graph breaks. GraphMend automatically eliminates fixable breaks through source-level program analysis and transformations. It analyzes AST-level program structure to identify graph-break patterns and applies transformations only when their semantic preservation can be statically established. These transformations enable PyTorch to capture larger, uninterrupted FX graphs without manual refactoring by developers. We evaluate GraphMend on all 27 models found to exhibit graph breaks in our investigation. GraphMend eliminates 107 of 147 graph breaks (73%), fully fixing all breaks in 21 models. In our experiments on NVIDIA GPUs, GraphMend achieves up to 26x cold-start speedup, 5x on average, and up to 1.39x steady-state forward pass speedup. These results demonstrate that semantics-aware source-level analysis and transformation are effective complements to PyTorch's dynamic JIT compilation pipeline, substantially improving both usability and performance.

We present a learnable physics-based model that predicts motion of the robot end effector and reaction force-torque in contact-rich manipulation. The model represents the end effector and the environment as interacting meshes in a graph structure, and conditions its prediction explicitly on the applied control input. It predicts object-level pose update directly, while the reaction torque emerges from a per-vertex force field. Training is self-supervised using only joint encoder and force-torque data while the robot is randomly touching the environment without task context. In simulation, our model transfers to peg insertion with unseen concave geometry, where an MPC agent using it reaches up to 98% success rate, and after fine-tuning on self-collected data matches an agent planning with the ground truth dynamics at the tightest 1 mm clearance. In the real world, it outperforms the system-identified MuJoCo model by 45% in position and by 74% and 63% in force and torque error.

Generalized extreme value models capture dependence among choice alternatives in discrete choice modeling, but require this dependence to be predefined, symmetric, and shared uniformly across individuals. Recent efforts to synergize discrete choice models with deep neural networks have improved predictive performance but still cannot explicitly represent alternative dependence within neural architectures. To address these gaps, we introduce the alternative graph -- a graph in which nodes represent choice alternatives and edges encode their dependence -- and propose Alternative Graph Neural Networks (Alt-GNNs), a family of GNN-based discrete choice models that embed alternative dependence within a unified framework. Theoretically, Alt-GNNs incorporate multinomial logit, nested logit, and ASU-DNN as special cases and enable innovative model designs, including Nested Alt-GNN, Complete Alt-GNN, and Attention Alt-GNN. Alt-GNNs are consistent with random utility maximization theory, enforce behavioral constraints through alternative graphs, and offer a novel graph-based interpretation of utility functions. Empirically, on two travel mode choice datasets from London and Chicago, Alt-GNNs significantly improve predictive performance over all benchmark models in mode choice modeling because of their flexible alternative graph design and vast hyperparameter space. Even the simplest Alt-GNN variant -- Nested Alt-GNN -- generalizes the nested logit model while preserving its unique two-layer substitution properties, enabling graph-based behavioral constraints over otherwise unconstrained behavioral patterns from deep neural networks.

While foundation models have revolutionized fields such as natural language processing and computer vision, their potential in graph machine learning remains largely unexplored. One of the key challenges in designing graph foundation models (GFMs) is handling diverse node features that can vary across different graph datasets. While many works on GFMs have focused exclusively on text-attributed graphs, the problem of handling arbitrary features of other types in GFMs has not been fully addressed. However, this problem is not unique to the graph domain, as it also arises in the field of machine learning for tabular data. In this work, motivated by the recent success of tabular foundation models (TFMs) like TabPFNv2 and LimiX, we propose G2T-FM, a simple framework that allows tabular foundation models to be applied to graph node-level tasks. Specifically, G2T-FM augments the original node features with neighborhood feature aggregation, adds structural embeddings, and then applies a TFM to the constructed node representations. Even in the in-context learning setting, our model achieves strong results when combined with a strong TFM, outperforming both prior GFMs and well-tuned GNNs trained from scratch. Moreover, after finetuning, G2T-FM consistently surpasses well-tuned GNN baselines, often by a significant margin. In summary, our paper reveals the potential of a previously overlooked direction: utilizing tabular foundation models for graph machine learning tasks.

Accurately predicting the performance of active radio frequency (RF) circuits is essential for modern wireless systems but remains challenging due to highly nonlinear behavior and the high computational cost of traditional simulation tools. Existing machine learning (ML) surrogates often require large datasets to generalize across various topologies or are not accurate on held-out circuits. This work presents a lightweight, data-efficient, and topology-aware graph neural network (GNN) framework for predicting key performance metrics of active RF circuit classes, such as low-noise amplifiers (LNAs), mixers, voltage-controlled oscillators (VCOs), power amplifiers (PAs), and voltage amplifiers (VAs). The proposed framework employs RFIC domain-informed feature indexing to enable cross-topology adaptability by cheap encoding of functional device semantics (e.g., differential pair and varactor transistors) and efficient knowledge transfer. The surrogate model represents circuits using device-terminal graph abstractions to preserve fine-grained connectivity and transistor-level symmetry. The final model is generalized to a wide variety of classes by being trained in parallel. Experimental results demonstrate accurate modeling of multimodal and heavy-tailed RF performance distributions, achieving an average mean relative error (MRE) of 2.71% across nineteen topologies, an improvement of 3.3x and 20x faster in training over prior art, and the generalization to held-out topologies is improved by ~26.2x. Furthermore, this work shows ~36x training data efficiency compared to state-of-the-art, demonstrating its effectiveness for scalable and deployment-ready RF design automation.

Although the Maximum Clique Problem (MCP) has been extensively studied and features a rich ecosystem of exact solvers, empirical evidence shows that solver performance varies substantially across graph families. Consequently, selecting an appropriate algorithm for a given instance remains an open and practically important challenge that has received little systematic attention. We address this gap by developing an instance-aware selection framework that systematically combines global statistical descriptors with learned topological representations. We construct a comprehensive benchmark by evaluating four state-of-the-art exact solvers on a diverse collection of graph instances and deriving both global statistical and local structural features. An evaluation of conventional classifiers establishes Random Forest as a strong baseline and reveals that connectivity and topological features are key predictors of performance. Motivated by these observations, we introduce a dual-channel architecture that jointly leverages a Graph Attention Network for capturing local neighborhood patterns and a Multilayer Perceptron for modeling global statistical features. Extensive experiments show that the proposed dual-channel model consistently surpasses classical baselines and the single-best solver, achieving 90.43% test accuracy. These findings demonstrate the value of integrating local topological encoding with global statistical cues for combinatorial algorithm selection. Code and models are available at: https://anonymous.4open.science/r/GAT-MLP-7E5F.

While graph-based Android malware classifiers report strong benchmark accuracy of over 94%, their performance sharply decreases up to 45% when exposed to previously unseen variants of known malware families. In this work, we systematically investigate this critical yet overlooked challenge for real-world deployment by introducing a benchmarking suite designed to simulate two prevalent scenarios: MalNet-Tiny-Common for covariate shift, and MalNet-Tiny-Distinct for domain shift. We further identify an inherent limitation of existing benchmarks where input representation is limited to structure-only function call graphs, discarding the semantic signals needed for robust cross-distribution reasoning. To verify this, we propose a semantic enrichment framework that extends raw graph topology with function-level attributes, combining lightweight metadata with LLM-based code embeddings. Empirical evaluations confirm the effectiveness of our data-centric methodology, with which classification performs better under distribution shift compared to model-based approaches, and consistently further enhances robustness when used in conjunction. We release our precomputed datasets alongside an extensible pipeline implementation, laying the groundwork for more resilient malware detection systems in evolving threat environments.

Federated Graph Learning (FGL) is a distributed learning paradigm that enables collaborative training over large-scale subgraphs located on multiple local systems. However, most existing FGL approaches rely on synchronous communication, which leads to inefficiencies and is often impractical in real-world deployments. Meanwhile, current asynchronous federated learning (AFL) methods are primarily designed for conventional tasks such as image classification and natural language processing, consequently failing to account for the unique topological properties of graph data. Directly applying these methods to graph learning frequently results in semantic drift and representational inconsistency within the global model. To address these challenges, we propose FedSA-GCL, a semi-asynchronous federated framework that leverages both inter-client label distribution divergence and graph topological characteristics through a novel ClusterCast mechanism for efficient training. We evaluate FedSA-GCL on multiple real-world graph datasets using the Louvain and Metis algorithms and conduct comparative analysis against 10 baselines. Extensive experiments demonstrate that our method achieves superior robustness and outstanding efficiency, outperforming the baselines by an average margin of 1.9% with Louvain and 3.0% with Metis.

Explainable artificial intelligence approaches accelerate drug discovery by improving molecular representation learning, identifying key molecular structures, and rationalizing drug property prediction. However, developing end-to-end explainable models for target-specific structure-activity relationship modeling remains challenging because compound-protein interaction data are often limited for individual targets, and small changes in chemical substituents or local structural motifs can cause large differences in molecular properties. Therefore, effectively leveraging structural and property information to identify key moieties associated with compound-protein affinity is essential. We propose a graph neural network (GNN) framework that uses property and structural information from activity-cliff molecule pairs targeting specific proteins to predict compound-protein affinity, measured by half-maximal inhibitory concentration (IC50), and explain property differences. To improve explainability, we trained GNNs with structure-aware loss functions using group lasso and sparse group lasso regularization, which prune and highlight molecular subgraphs relevant to activity differences. We applied this framework to activity-cliff data from molecules targeting six tyrosine-protein kinases across the Src, Abl, and Tec families, as well as anaplastic lymphoma kinase. Integrating common- and uncommon-node information with sparse group lasso improved target-specific molecular property prediction, producing lower root mean square errors and higher Pearson correlation coefficients. Regularization also enhanced GNN feature attribution by improving graph-level global direction scores and atom-level coloring accuracy. These results support more interpretable drug discovery pipelines, particularly for identifying critical molecular substructures during lead optimization.

Graph-based multi-task learning at billion-scale presents a significant challenge, as different tasks correspond to distinct billion-scale graphs. Traditional multi-task learning methods often neglect these graph structures, relying solely on individual user and item embeddings. However, disregarding graph structures overlooks substantial potential for improving performance. In this paper, we introduce the Macro Graph of Experts (MGOE) framework, the first approach capable of leveraging macro graph embeddings to capture task-specific macro features while modeling the correlations between task-specific experts. Specifically, we propose the concept of a Macro Graph Bottom, which, for the first time, enables multi-task learning models to incorporate graph information effectively. We design the Macro Prediction Tower to dynamically integrate macro knowledge across tasks. MGOE has been deployed at scale, powering multi-task learning for a leading billion-scale recommender system, Alibaba. Extensive offline experiments conducted on three public benchmark datasets demonstrate its superiority over state-of-the-art multi-task learning methods, establishing MGOE as a breakthrough in multi-task graph-based recommendation. Furthermore, online A/B tests confirm the superiority of MGOE in billion-scale recommender systems.

Signed graphs are equipped with both positive and negative edge weights, encoding pairwise correlations as well as anti-correlations in data. A balanced signed graph is a signed graph with no cycles containing an odd number of negative edges. Laplacian of a balanced signed graph has eigenvectors that map via a simple linear transform to ones in a corresponding positive graph Laplacian, thus enabling reuse of spectral filtering tools designed for positive graphs. We propose an efficient computation method to learn a balanced signed graph Laplacian directly from data. Specifically, extending a previous linear programming (LP) based sparse inverse covariance estimation method called CLIME, we formulate a new LP problem for each Laplacian column $i$, where the linear constraints restrict weight signs of edges stemming from node $i$, so that nodes of same / different polarities are connected by positive / negative edges. We derive a feasible CLIME parameter $ρ_i$ for each sign-constrained column problem. We solve the LP problem efficiently by tailoring a sparse LP method based on ADMM. We theoretically prove that the row / column updates produce a non-increasing objective sequence, and show that the iterations are terminated in a finite number of steps. Extensive experimental results on synthetic and real-world datasets show that our balanced graph learning method outperforms competing methods and enables reuse of spectral filters, wavelets, and graph neural nets (GNN) constructed for positive graphs.

Prompt tuning has become a key mechanism for adapting pre-trained Graph Neural Networks (GNNs) to new downstream tasks. However, existing approaches are predominantly supervised, relying on labeled data to optimize the prompting parameters and typically fine-tuning a task-specific prediction head -- practices that undermine the promise of parameter-efficient adaptation. We propose Unsupervised Graph Prompting Problem (UGPP), a challenging new setting where the pre-trained GNN is kept entirely frozen, labels on the target domain are unavailable, the source data is inaccessible, and the target distribution exhibits covariate shift. To address this, we propose UGPrompt, the first fully unsupervised GNN prompting framework. UGPrompt leverages consistency regularization and pseudo-labeling to train a prompting function, complemented with diversity and domain regularization to mitigate class imbalance and distribution mismatch. Our extensive experiments demonstrate that UGPrompt consistently outperforms state-of-the-art supervised prompting methods with access to labeled data, demonstrating the viability of unsupervised prompting as a practical adaptation paradigm for GNNs.

We propose a novel benchmarking methodology for graph neural networks (GNNs) based on the graph alignment problem, a combinatorial optimization task that generalizes graph isomorphism by aligning two unlabeled graphs to maximize overlapping edges. We frame this problem as a self-supervised learning task and present several methods to generate graph alignment datasets using synthetic random graphs and real-world graph datasets from multiple domains. For a given graph dataset, we generate a family of graph alignment datasets with increasing difficulty, allowing us to rank the performance of various architectures. Our experiments prove that there is an optimal task difficulty for having a statistically relevant ranking of different models and that, even on a structure-only task, anisotropic models perform better compared to isotropic ones. To further prove that our synthetic task capture meaningful information, we show its effectiveness for self-supervised GNN pre-training: the learned node embeddings can be leveraged as positional encodings by transformers for graph regression or can be used to reconstruct the full structure of the graph with $98\%$ accuracy. To support reproducibility and further research, we provide an open-source Python package to generate graph alignment datasets and benchmark new GNN architectures. The source code is available at https://github.com/adrien-lagesse/graph-alignment-benchmark.