Graph Neural Networks

Understanding how large-scale brain networks represent visual categories is fundamental to linking perception and cortical organization. Using high-resolution 7T fMRI from the Natural Scenes Dataset, we construct parcel-level functional graphs and train a signed Graph Neural Network that models both positive and negative interactions, with a sparse edge mask and class-specific saliency. The model accurately decodes category-specific functional connectivity states (sports, food, vehicles) and reveals reproducible, biologically meaningful subnetworks along the ventral and dorsal visual pathways. This framework bridges machine learning and neuroscience by extending voxel-level category selectivity to a connectivity-based representation of visual processing.

Graph condensation (GC) has become a vital strategy for scaling Graph Neural Networks by compressing massive datasets into small, synthetic node sets. While current GC methods effectively maintain predictive accuracy, they are primarily designed for utility and often ignore fairness constraints. Because these techniques are bias-blind, they frequently capture and even amplify demographic disparities found in the original data. This leads to synthetic proxies that are unsuitable for sensitive applications like credit scoring or social recommendations. To solve this problem, we introduce FairGC, a unified framework that embeds fairness directly into the graph distillation process. Our approach consists of three key components. First, a Distribution-Preserving Condensation module synchronizes the joint distributions of labels and sensitive attributes to stop bias from spreading. Second, a Spectral Encoding module uses Laplacian eigen-decomposition to preserve essential global structural patterns. Finally, a Fairness-Enhanced Neural Architecture employs multi-domain fusion and a label-smoothing curriculum to produce equitable predictions. Rigorous evaluations on four real-world datasets, show that FairGC provides a superior balance between accuracy and fairness. Our results confirm that FairGC significantly reduces disparity in Statistical Parity and Equal Opportunity compared to existing state-of-the-art condensation models. The codes are available at https://github.com/LuoRenqiang/FairGC.

Graph anomaly detection (GAD) aims to identify irregular nodes or structures in attributed graphs. Neighbor information, which reflects both structural connectivity and attribute consistency with surrounding nodes, is essential for distinguishing anomalies from normal patterns. Although recent graph neural network (GNN)-based methods incorporate such information through message passing, they often fail to explicitly model its effect or interaction with attributes, limiting detection performance. This work introduces NeiGAD, a novel plug-and-play module that captures neighbor information through spectral graph analysis. Theoretical insights demonstrate that eigenvectors of the adjacency matrix encode local neighbor interactions and progressively amplify anomaly signals. Based on this, NeiGAD selects a compact set of eigenvectors to construct efficient and discriminative representations. Experiments on eight real-world datasets show that NeiGAD consistently improves detection accuracy and outperforms state-of-the-art GAD methods. These results demonstrate the importance of explicit neighbor modeling and the effectiveness of spectral analysis in anomaly detection. Code is available at: https://github.com/huafeihuang/NeiGAD.

Graph neural networks (GNNs) have achieved strong performance across various real-world domains. Nevertheless, they suffer from oversquashing, where long-range information is distorted as it is compressed through limited message-passing pathways. This bottleneck limits their ability to capture essential global context and decreases their performance, particularly in dense and heterophilic regions of graphs. To address this issue, we propose a novel graph learning framework that enriches node embeddings via cross-attentive cohesive subgraph representations to mitigate the impact of excessive long-range dependencies. This framework enhances the node representation by emphasizing cohesive structure in long-range information but removing noisy or irrelevant connections. It preserves essential global context without overloading the narrow bottlenecked channels, which further mitigates oversquashing. Extensive experiments on multiple benchmark datasets demonstrate that our model achieves consistent improvements in classification accuracy over standard baseline methods.

Graph Neural Networks (GNNs) show strong promise for circuit analysis, but scaling to modern large-scale circuit graphs is limited by GPU memory and training cost, especially for deep models. We revisit deep GNNs for circuit graphs and show that, when trainable, they significantly outperform shallow architectures, motivating an efficient, domain-specific training framework. We propose Grouped-Sparse-Reversible GNN (GSR-GNN), which enables training GNNs with up to hundreds of layers while reducing both compute and memory overhead. GSR-GNN integrates reversible residual modules with a group-wise sparse nonlinear operator that compresses node embeddings without sacrificing task-relevant information, and employs an optimized execution pipeline to eliminate fragmented activation storage and reduce data movement. On sampled circuit graphs, GSR-GNN achieves up to 87.2% peak memory reduction and over 30$\times$ training speedup with negligible degradation in correlation-based quality metrics, making deep GNNs practical for large-scale EDA workloads.

Optimal dispatch of energy storage systems (ESSs) in distribution networks involves jointly improving operating economy and voltage security under time-varying conditions and possible topology changes. To support fast online decision making, we develop a topology-aware Reinforcement Learning architecture based on Twin Delayed Deep Deterministic Policy Gradient (TD3), which integrates graph neural networks (GNNs) as graph feature encoders for ESS dispatch. We conduct a systematic investigation of three GNN variants: graph convolutional networks (GCNs), topology adaptive graph convolutional networks (TAGConv), and graph attention networks (GATs) on the 34-bus and 69-bus systems, and evaluate robustness under multiple topology reconfiguration cases as well as cross-system transfer between networks with different system sizes. Results show that GNN-based controllers consistently reduce the number and magnitude of voltage violations, with clearer benefits on the 69-bus system and under reconfiguration; on the 69-bus system, TD3-GCN and TD3-TAGConv also achieve lower saved cost relative to the NLP benchmark than the NN baseline. We also highlight that transfer gains are case-dependent, and zero-shot transfer between fundamentally different systems results in notable performance degradation and increased voltage magnitude violations. This work is available at: https://github.com/ShuyiGao/GNNs_RL_ESSs and https://github.com/distributionnetworksTUDelft/GNNs_RL_ESSs.

We introduce the Geometric Evolution Graph Convolutional Network (GEGCN), a novel framework that enhances graph representation learning through explicit modeling of geometric evolution on graph structures. Specifically, GEGCN leverages a Long Short-Term Memory (LSTM) network to capture the dynamic structural sequence generated by discrete Ricci flow, and infuses the learned dynamic representations into a graph convolutional network. Extensive experiments demonstrate that GEGCN achieves excellent performance on classification tasks across various benchmark datasets, including homophilic/heterophilic graphs, filtered graphs, and large-scale graphs.

Graph Neural Networks (GNNs) face two fundamental challenges when scaled to deep architectures: oversmoothing, where node representations converge to indistinguishable vectors, and oversquashing, where information from distant nodes fails to propagate through bottlenecks. Both phenomena are intimately tied to the underlying graph structure, raising a natural question: can we optimize the graph topology to mitigate these issues? This paper provides a theoretical investigation of the computational complexity of such graph structure optimization. We formulate oversmoothing and oversquashing mitigation as graph optimization problems based on spectral gap and conductance, respectively. We prove that exact optimization for either problem is NP-hard through reductions from Minimum Bisection, establishing NP-completeness of the decision versions. Our results provide theoretical foundations for understanding the fundamental limits of graph rewiring for GNN optimization and justify the use of approximation algorithms and heuristic methods in practice.

Message Passing Neural Networks (MPNNs) have achieved strong performance on tasks involving relational data. However, small perturbations to graph structure can significantly alter their outputs, raising concerns about their robustness in real-world deployment in security critical environments. In this work, we study a core vulnerability in MPNNs that explicitly consume graph topology via the adjacency matrix or Laplacian as part of their message passing mechanism. We show that this design choice exposes an extremely vulnerable attack surface, with significant effects even under minimal perturbation. Building on this observation, we propose PEA, a simple, gradient-free, black-box injection attack that requires only a single query to the target model, capitalizing on this vulnerability by constructing a perturbation aligned with a specific significant eigenvector to induce large output deviations. Unlike graph modification attacks, PEA operates under the realistic assumption that adversaries cannot alter the original graph and are limited to injecting new nodes at inference time. PEA requires no iterative optimization, parameter learning, or surrogate models---which require additional training and remain susceptible to differences in model priors and generalization capabilities---thereby avoiding significant computational overhead and the associated transferability challenges. We evaluate PEA on popular benchmark datasets across three graph learning tasks, showing consistent performance degradation under realistic attack constraints despite its simplicity. Our results reveal a fundamental security weakness in topology-driven message passing architectures and urge an implementation shift, as the worst effects of such attacks can be substantially mitigated through appropriate input filtering.

Large Language Models (LLMs) have advanced Graph Neural Networks (GNNs) by enriching node representations with semantic features, giving rise to LLM-enhanced GNNs that achieve notable performance gains. However, the robustness of these models against poisoning attacks, which manipulate both graph structures and textual attributes during training, remains unexplored. To bridge this gap, we propose a robustness assessment framework that systematically evaluates LLM-enhanced GNNs under poisoning attacks. Our framework enables comprehensive evaluation across multiple dimensions. Specifically, we assess 24 victim models by combining eight LLM- or Language Model (LM)-based feature enhancers with three representative GNN backbones. To ensure diversity in attack coverage, we incorporate six structural poisoning attacks (both targeted and non-targeted) and three textual poisoning attacks operating at the character, word, and sentence levels. Furthermore, we employ four real-world datasets, including one released after the emergence of LLMs, to avoid potential ground truth leakage during LLM pretraining, thereby ensuring fair evaluation. Extensive experiments show that LLM-enhanced GNNs exhibit significantly higher accuracy and lower Relative Drop in Accuracy (RDA) than a shallow embedding-based baseline across various attack settings. Our in-depth analysis identifies key factors that contribute to this robustness, such as the effective encoding of structural and label information in node representations. Based on these insights, we outline future research directions from both offensive and defensive perspectives, and propose a new combined attack along with a graph purification defense. To support future research, we release the source code of our framework at~https://github.com/CyberAlSec/LLMEGNNRP.

The identification and reconstruction of charged particles, such as muons, is a main challenge for the physics program of the ATLAS experiment at the Large Hadron Collider. This task will become increasingly difficult with the start of the High-Luminosity LHC era after 2030, when the number of proton-proton collisions per bunch crossing will increase from 60 to up to 200. This elevated interaction density will also increase the occupancy within the ATLAS Muon Spectrometer, requiring more efficient and robust real-time data processing strategies within the experiment's trigger system, particularly the Event Filter. To address these algorithmic challenges, we present two machine-learning-based approaches. First, we target the problem of background-hit rejection in the Muon Spectrometer using Graph Neural Networks integrated into the non-ML baseline reconstruction chain, demonstrating a 15 % improvement in reconstruction speed (from 255 ms to 217 ms). Second, we present a proof-of-concept for end-to-end muon tracking using state-of-the-art Vision Transformer architectures, achieving ultra-fast approximate muon reconstruction in 2.3 ms on consumer-grade GPUs at 98 % tracking efficiency.

Machine-learned interatomic potentials (MLIPs), particularly graph neural network (GNN)-based models, offer a promising route to achieving near-density functional theory (DFT) accuracy at significantly reduced computational cost. However, their practical deployment is often limited by the large volumes of expensive quantum mechanical training data required. In this work, we introduce a transfer learning framework, Transfer-PaiNN (T-PaiNN), that substantially improves the data efficiency of GNN-MLIPs by leveraging inexpensive classical force field data. The approach consists of pretraining a PaiNN MLIP architecture on large-scale datasets generated from classical molecular simulations, followed by fine-tuning (dubbed autotuning) using a comparatively small DFT dataset. We demonstrate the effectiveness of autotuning T-PaiNN on both gas-phase molecular systems (QM9 dataset) and condensed-phase liquid water. Across all cases, T-PaiNN significantly outperforms models trained solely on DFT data, achieving order-of-magnitude reductions in mean absolute error while accelerating training convergence. For example, using the QM9 data set, error reductions of up to 25 times are observed in low-data regimes, while liquid water simulations show improved predictions of energies, forces, and experimentally relevant properties such as density and diffusion. These gains arise from the model's ability to learn general features of the potential energy surface from extensive classical sampling, which are subsequently refined to quantum accuracy. Overall, this work establishes transfer learning from classical force fields as a practical and computationally efficient strategy for developing high-accuracy, data-efficient GNN interatomic potentials, enabling broader application of MLIPs to complex chemical systems.

Graph Neural Networks (GNNs) deliver strong performance on graph tasks, but their accuracy drops significantly under out-of-distribution (OOD) scenarios. Under distribution shifts, GNNs often fit environmental noise and spurious correlations instead of stable causal mechanisms, leading to weak OOD robustness and unstable predictive representations. Existing solutions based on environment invariance or causal reasoning are insufficient for node classification, as they do not explicitly model the fine-grained latent geometry required by the task. We further observe a training instability named Info-Jitter, where the mutual information between predictive representations and ground-truth labels fluctuates throughout training. To address these issues, we construct a node-classification-specific causal graph derived from the task's geometric objective. Using do-calculus to block non-causal paths caused by environmental noise, we derive a deconfounded interventional objective and a variational lower bound to disentangle representations into intra-class and inter-class components. We then propose Causal-Guided Representation Learning (CGRL), a framework with two core modules. First, a multi-branch re-weighted representation learning (RRL) module learns a causal modulation matrix to amplify causal signals and suppress environmental noise during message passing. Second, an optimization strategy combining intra-class aggregation, inter-class separation, energy-based reconstruction and supervised prediction regularizes the latent space for robust node-level generalization. Experiments on multiple benchmark datasets show that CGRL outperforms strong baselines across various distribution shifts and effectively mitigates the Info-Jitter phenomenon.

Recent work distinguishes two heterophily regimes: adversarial, where cross-class edges dilute class signal and harm classification, and informative, where the heterophilous structure itself carries useful signal. We ask: when does per-edge message routing help, and when is a uniform spectral channel sufficient? To operationalize this question we introduce Cost-Sensitive Neighborhood Aggregation (CSNA), a GNN layer that computes pairwise distance in a learned projection and uses it to soft-route each message through concordant and discordant channels with independent transformations. Under a contextual stochastic block model we show that mean aggregation can reverse the label-aligned signal direction under heterophily, and that cost-sensitive weighting with $w_+/w_- > q/p$ preserves the correct sign. On six benchmarks with uniform tuning, CSNA is competitive with state-of-the-art methods on adversarial-heterophily datasets (Texas, Wisconsin, Cornell, Actor) but underperforms on informative-heterophily datasets (Chameleon, Squirrel) -- precisely the regime where per-edge routing has no useful decomposition to exploit. The pattern is itself the finding: the cost function's ability to separate edge types serves as a diagnostic for the heterophily regime, revealing when fine-grained routing adds value over uniform channels and when it does not. Code is available at https://github.com/eyal-weiss/CSNA-public .

Mesh-free numerical methods provide flexible discretisations for complex geometries; however, classical meshless discrete differential operators typically trade low computational cost for limited accuracy or high accuracy for substantial per-stencil computation. We introduce a parametrised framework for learning mesh-free discrete differential operators using a graph neural network trained via polynomial moment constraints derived from truncated Taylor expansions. The model maps local stencils relative positions directly to discrete operator weights. The current work demonstrates that neural networks can learn classical polynomial consistency while retaining robustness to irregular neighbourhood geometry. The learned operators depend only on local geometry, are resolution-agnostic, and can be reused across particle configurations and governing equations. We evaluate the framework using standard numerical analysis diagnostics, showing improved accuracy over Smoothed Particle Hydrodynamics, and a favourable accuracy-cost trade-off relative to a representative high-order consistent mesh-free method in the moderate-accuracy regime. Applicability is demonstrated by solving the weakly compressible Navier-Stokes equations using the learned operators.

Message passing is a core mechanism in Graph Neural Networks (GNNs), enabling the iterative update of node embeddings by aggregating information from neighboring nodes. Graph Convolutional Networks (GCNs) exemplify this approach by adapting convolutional operations for graph structures, allowing features from adjacent nodes to be combined effectively. However, GCNs encounter challenges with complex or dynamic data. Capturing long-range dependencies often requires deeper layers, which not only increase computational costs but also lead to over-smoothing, where node embeddings become indistinguishable. To overcome these challenges, reservoir computing has been integrated into GNNs, leveraging iterative message-passing dynamics for stable information propagation without extensive parameter tuning. Despite its promise, existing reservoir-based models lack structured convolutional mechanisms, limiting their ability to accurately aggregate multi-hop neighborhood information. To address these limitations, we propose RGC-Net (Reservoir-based Graph Convolutional Network), which integrates reservoir dynamics with structured graph convolution. Key contributions include: (i) a reimagined convolutional framework with fixed-random reservoir weights and a leaky integrator to enhance feature retention; (ii) a robust, adaptable model for graph classification; and (iii) an RGC-Net-powered transformer for graph generation with application to dynamic brain connectivity. Extensive experiments show RGC-Net achieves state-of-the-art performance in classification and generative tasks, including brain graph evolution, with faster convergence and mitigated over-smoothing. Our source code is available at https://github.com/basiralab/RGC-Net.

Digital circuits representation learning has made remarkable progress in the electronic design automation domain, effectively supporting critical tasks such as testability analysis and logic reasoning. However, representation learning for analog circuits remains challenging due to their continuous electrical characteristics compared to the discrete states of digital circuits. This paper presents a direct current (DC) electrically equivalent-oriented analog representation learning framework, named KCLNet. It comprises an asynchronous graph neural network structure with electrically-simulated message passing and a representation learning method inspired by Kirchhoff's Current Law (KCL). This method maintains the orderliness of the circuit embedding space by enforcing the equality of the sum of outgoing and incoming current embeddings at each depth, which significantly enhances the generalization ability of circuit embeddings. KCLNet offers a novel and effective solution for analog circuit representation learning with electrical constraints preserved. Experimental results demonstrate that our method achieves significant performance in a variety of downstream tasks, e.g., analog circuit classification, subcircuit detection, and circuit edit distance prediction.

Sensor placement for leakage detection in water distribution networks is an important and practical challenge for water utilities. Recent work has shown that graph neural networks can estimate and predict pressures and detect leaks, but their performance strongly depends on the available sensor measurements and configurations. In this paper, we investigate how sensor placement influences the performance of GNN-based leakage detection. We propose a novel PageRank-Centrality-based sensor placement method and demonstrate that it substantially impacts reconstruction, prediction, and leakage detection on the EPANET Net1.

Anti-money laundering (AML) systems are important for protecting the global economy. However, conventional rule-based methods rely on domain knowledge, leading to suboptimal accuracy and a lack of scalability. Graph neural networks (GNNs) for digraphs (directed graphs) can be applied to transaction graphs and capture suspicious transactions or accounts. However, most spectral GNNs do not naturally support multi-dimensional edge features, lack interpretability due to edge modifications, and have limited scalability owing to their spectral nature. Conversely, most spatial methods may not capture the money flow well. Therefore, in this work, we propose LineMVGNN (Line-Graph-Assisted Multi-View Graph Neural Network), a novel spatial method that considers payment and receipt transactions. Specifically, the LineMVGNN model extends a lightweight MVGNN module, which performs two-way message passing between nodes in a transaction graph. Additionally, LineMVGNN incorporates a line graph view of the original transaction graph to enhance the propagation of transaction information. We conduct experiments on two real-world account-based transaction datasets: the Ethereum phishing transaction network dataset and a financial payment transaction dataset from one of our industry partners. The results show that our proposed method outperforms state-of-the-art methods, reflecting the effectiveness of money laundering detection with line-graph-assisted multi-view graph learning. We also discuss scalability, adversarial robustness, and regulatory considerations of our proposed method.

Graph foundation models (GFMs) have recently attracted interest due to the promise of graph neural network (GNN) architectures that generalize zero-shot across graphs of arbitrary scales, feature dimensions, and domains. While existing work has demonstrated this ability empirically across diverse real-world benchmarks, these tasks share a crucial hidden limitation: they admit a narrow set of effective GNN architectures. In particular, current domain-agnostic GFMs rely on fixed architectural backbones, implicitly assuming that a single message-passing regime suffices across tasks. In this paper, we argue that architecture adaptivity is a necessary requirement for true GFMs. We show that existing approaches are non-robust to task-dependent architectural attributes and, as a case study, use range as a minimal and measurable axis along which this limitation becomes explicit. With theoretical analysis and controlled synthetic experiments, we demonstrate that fixed-backbone GFMs provably under-reach on tasks whose architectural requirements differ from those seen at training time. To address this issue, we introduce a framework that adapts effective GNN architecture at inference time by discovering and mixing task-specific linear graph operators, enabling zero-shot generalization across tasks with heterogeneous architectural requirements, without retraining. We validate our approach on arbitrary-range synthetic tasks and a suite of real-world benchmarks, demonstrating improved performance and robustness over existing domain-agnostic GFMs.

Deep learning techniques for rumor detection typically utilize Graph Neural Networks (GNNs) to analyze post relations. These methods, however, falter due to over-smoothing issues when processing rumor propagation structures, leading to declining performance. Our investigation into this issue reveals that over-smoothing is intrinsically tied to the structural characteristics of rumor propagation trees, in which the majority of nodes are 1-level nodes. Furthermore, GNNs struggle to capture long-range dependencies within these trees. To circumvent these challenges, we propose a Pre-Trained Propagation Tree Transformer (P2T3) method based on pure Transformer architecture. It extracts all conversation chains from a tree structure following the propagation direction of replies, utilizes token-wise embedding to infuse connection information and introduces necessary inductive bias, and pre-trains on large-scale unlabeled datasets. Experiments indicate that P2T3 surpasses previous state-of-the-art methods in multiple benchmark datasets and performs well under few-shot conditions. P2T3 not only avoids the over-smoothing issue inherent in GNNs but also potentially offers a large model or unified multi-modal scheme for future social media research.

The core of molecular dynamics simulation fundamentally lies in the interatomic potential. Traditional empirical potentials lack accuracy, while first-principles methods are computationally prohibitive. Machine learning interatomic potentials (MLIPs) promise near-quantum accuracy at linear cost, but existing models still face challenges in efficiency and stability. We presents Machine Learning Advances Neural Network (MLANet), an efficient and robust graph neural network framework. MLANet introduces a dual-path dynamic attention mechanism for geometry-aware message passing and a multi-perspective pooling strategy to construct comprehensive system representations. This design enables highly accurate modeling of atomic environments while achieving exceptional computational efficiency, making high-fidelity simulations more accessible. Tested across a wide range of datasets spanning diverse systems, including organic molecules (e.g., QM7, MD17), periodic inorganic materials (e.g., Li-containing crystals), two-dimensional materials (e.g., bilayer graphene, black phosphorus), surface catalytic reactions (e.g., formate decomposition), and charged systems, MLANet maintains competitive prediction accuracy while its computational cost is markedly lower than mainstream equivariant models, and it enables stable long-time molecular dynamics simulations. MLANet provides an efficient and practical tool for large-scale, high-accuracy atomic simulations.

Automated classification of clinical transcriptions into medical specialties is essential for routing, coding, and clinical decision support, yet prior work on the widely used MTSamples benchmark suffers from severe data leakage caused by applying SMOTE oversampling before train test splitting. We first document this methodological flaw and establish a leakage free benchmark across 40 medical specialties (4966 records), revealing that the true task difficulty is substantially higher than previously reported. We then introduce CLiGNet (Clinical Label Interaction Graph Network), a neural architecture that combines a Bio ClinicalBERT text encoder with a two layer Graph Convolutional Network operating on a specialty label graph constructed from semantic similarity and ICD 10 chapter priors. Per label attention gates fuse document and label graph representations, trained with focal binary cross entropy loss to handle extreme class imbalance (181 to 1 ratio). Across seven baselines ranging from TF IDF classifiers to Clinical Longformer, CLiGNet without calibration achieves the highest macro F1 of 0.279, with an ablation study confirming that the GCN label graph provides the single largest component gain (increase of 0.066 macro F1). Adding per label Platt scaling calibration yields an expected calibration error of 0.007, demonstrating a principled trade off between ranking performance and probability reliability. We provide comprehensive failure analysis covering pairwise specialty confusions, rare class behaviour, document length effects, and token level Integrated Gradients attribution, offering actionable insights for clinical NLP system deployment.

The standard in LLM-based prediction is to use the final-layer representation as the input to a downstream predictor. However, intermediate layers may encode complementary task-relevant signals. Existing approaches therefore either search for the best layer for each task or apply expensive attention-based mechanisms to learn inter-layer aggregation. In this work, we first show that such complexity is unnecessary: a lightweight Graph Neural Network over a fully connected graph of LLM layers is more efficient and achieves significantly stronger predictive performance than existing approaches. We then introduce the Cayley-Encoder, which further improves both efficiency and predictive performance by replacing the fully connected graph with a Cayley graph over SL(2, Zn). These Cayley graphs provide a mathematically grounded topology that is sparse, regular by construction, and has low diameter. This enables effective communication across layers while constraining the aggregation structure and reducing the risk of GNN overfitting. In an evaluation of Cayley-Encoder across 13 tasks and 9 LLMs, Cayley-Encoder consistently outperforms baselines, achieving improvements of up to 40 percentage points in accuracy, while introducing at most 0.1% additional parameters relative to the LLM size. We further show that Cayley-Encoder is effective in few-shot regimes. Finally, we show that Cayley-Encoder outperforms LoRA fine-tuning while operating on the frozen LLM. We conclude with an explainability analysis showing that multiple layers contribute meaningfully to the final prediction, supporting our hypothesis.

Data-driven discovery of partial differential equations (PDEs) offers a promising paradigm for uncovering governing physical laws from observational data. However, in practical scenarios, measurements are often contaminated by noise and limited by sparse sampling, which poses significant challenges to existing approaches based on numerical differentiation or integral formulations. In this work, we propose a Symbolic Graph Network (SGN) framework for PDE discovery under noisy and sparse conditions. Instead of relying on local differential approximations, SGN leverages graph message passing to model spatial interactions, providing a non-local representation that is less sensitive to high frequency noise. Based on this representation, the learned latent features are further processed by a symbolic regression module to extract interpretable mathematical expressions. We evaluate the proposed method on several benchmark systems, including the wave equation, convection-diffusion equation, and incompressible Navier-Stokes equations. Experimental results show that SGN can recover meaningful governing relations or solution forms under varying noise levels, and demonstrates improved robustness compared to baseline methods in sparse and noisy settings. These results suggest that combining graph-based representations with symbolic regression provides a viable direction for robust data-driven discovery of physical laws from imperfect observations. The code is available at https://github.com/CXY0112/SGN

Predicting the next mobile app a user will launch is essential for proactive mobile services. Yet accurate prediction remains challenging in real-world settings, where user intent can shift rapidly within short sessions and user-specific historical profiles are often sparse or unavailable, especially under cold-start conditions. Existing approaches mainly model app usage as sequential behavior or local session transitions, limiting their ability to capture higher-order structural dependencies and evolving session intent. To address this issue, we propose MISApp, a profile-free framework for next app prediction based on multi-hop session graph learning. MISApp constructs multi-hop session graphs to capture transition dependencies at different structural ranges, learns session representations through lightweight graph propagation, incorporates temporal context and similarity-based spatial categorization to characterize session conditions, and captures intent evolution from recent interactions. Experiments on two real-world app usage datasets show that MISApp consistently outperforms competitive baselines under both standard and cold-start settings, while maintaining a favorable balance between predictive accuracy and practical efficiency. Further analyses show that multi-hop relations capture higher-hop-specific predictive signals beyond direct 1-Hop adjacency, and that the learned hop-level attention weights align well with structural relevance, providing both empirical and interpretable evidence for the effectiveness of the proposed multi-hop modeling strategy.

Multimodal emotion recognition in conversations (MERC) aims to identify and understand the emotions expressed by speakers during utterance interaction from multiple modalities (e.g., text, audio, images, etc.). Existing studies have shown that GCN can improve the performance of MERC by modeling dependencies between speakers. However, existing methods usually use fixed parameters to process multimodal features for different emotion types, ignoring the dynamics of fusion between different modalities, which forces the model to balance performance between multiple emotion categories, thus limiting the model's performance on some specific emotions. To this end, we propose a dynamic fusion-aware graph convolutional neural network (DF-GCN) for robust recognition of multimodal emotion features in conversations. Specifically, DF-GCN integrates ordinary differential equations into graph convolutional networks (GCNs) to {capture} the dynamic nature of emotional dependencies within utterance interaction networks and leverages the prompts generated by the global information vector (GIV) of the utterance to guide the dynamic fusion of multimodal features. This allows our model to dynamically change parameters when processing each utterance feature, so that different network parameters can be equipped for different emotion categories in the inference stage, thereby achieving more flexible emotion classification and enhancing the generalization ability of the model. Comprehensive experiments conducted on two public multimodal conversational datasets {confirm} that the proposed DF-GCN model delivers superior performance, benefiting significantly from the dynamic fusion mechanism introduced.

Neuronal morphology encodes critical information about circuit function, development, and disease, yet current methods analyze topology or graph structure in isolation. We introduce GraPHFormer, a multimodal architecture that unifies these complementary views through CLIP-style contrastive learning. Our vision branch processes a novel three-channel persistence image encoding unweighted, persistence-weighted, and radius-weighted topological densities via DINOv2-ViT-S. In parallel, a TreeLSTM encoder captures geometric and radial attributes from skeleton graphs. Both project to a shared embedding space trained with symmetric InfoNCE loss, augmented by persistence-space transformations that preserve topological semantics. Evaluated on six benchmarks (BIL-6, ACT-4, JML-4, N7, M1-Cell, M1-REG) spanning self-supervised and supervised settings, GraPHFormer achieves state-of-the-art performance on five benchmarks, significantly outperforming topology-only, graph-only, and morphometrics baselines. We demonstrate practical utility by discriminating glial morphologies across cortical regions and species, and detecting signatures of developmental and degenerative processes. Code: https://github.com/Uzshah/GraPHFormer

Graph neural network (GNN) is a powerful tool for analyzing graph-structured data. However, their vulnerability to adversarial attacks raises serious concerns, especially when dealing with sensitive information. Local Differential Privacy (LDP) offers a privacy-preserving framework for training GNNs, but its impact on adversarial robustness remains underexplored. This paper investigates adversarial attacks on LDP-protected GNNs. We explore how the privacy guarantees of LDP can be leveraged or hindered by adversarial perturbations. The effectiveness of existing attack methods on LDP-protected GNNs are analyzed and potential challenges in crafting adversarial examples under LDP constraints are discussed. Additionally, we suggest directions for defending LDP-protected GNNs against adversarial attacks. This work investigates the interplay between privacy and security in graph learning, highlighting the need for robust and privacy-preserving GNN architectures.

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.