Graph Neural Networks

Text-Attributed Graphs (TAGs), endowed with abundant textual content along with topological structures, have emerged as a versatile backbone for real-world anomaly detection spanning large language model security, social network moderation, and cyber threat identification. Unlike conventional Graph Anomaly Detection (GAD), which relies primarily on structural irregularities, TAG anomaly detection must jointly leverage both topological patterns and fine-grained textual semantics to capture nuanced anomalous behaviors. The current GNN-based anomaly detectors adopt holistic message-passing schemes that indiscriminately fuse structural proximity and textual semantics during propagation, leading to deep cross-modality coupling. This entanglement acts as a noise amplifier, obscuring subtle anomalous signals and directly giving rise to the Blurred-Anomaly-Boundary (BAB) issue by rendering normal-anomalous decision boundaries poorly separable. This challenge is further amplified for graph foundation models that require robust cross-domain generalization. To bridge this gap, we introduce a novel foundation model for TAG anomaly detection featuring decoupled topological and textual prototypes. Our framework constructs dual prototype banks to independently model structural normality and semantic consistency, effectively isolating anomaly cues that are otherwise diluted during coupled aggregation. Extensive experiments across 14 diverse benchmark datasets demonstrate that our method consistently achieves state-of-the-art performance in cross-domain settings. Notably, the ablation studies further corroborate the prevalence of the BAB issue in conventional coupled TAG anomaly detectors, and show that our decoupled prototype design effectively mitigates this challenge.

Message-passing neural networks (MPNNs) often struggle when task-relevant information is distributed across distant regions of a graph, since local propagation must compress remote signals through limited structural interfaces. Graph rewiring provides a structural response to over-squashing. Most existing methods rely on edge-level bottleneck scores or graph-level connectivity surrogates. With a limited rewiring budget, the key question is which pairwise communications most need structural support. This paper proposes PairAlign, a pair-centric graph rewiring framework that makes this question explicit through demand-support shortage. Specifically, PairAlign combines original-graph structural demand with current-graph finite-hop propagation support; their ratio highlights interactions whose communication demand is poorly supported by topology, and our theory shows that this score provides a computable proxy for the corresponding Jacobian-based shortage with a pair-level interpretation of over-squashing. Our theory reveals a two-sided effect of edge insertion: a new edge can create useful walks and simultaneously dilute existing normalized transition mass. Guided by this observation, PairAlign optimizes shortage to favor edge additions that alleviate over-squashing. Beyond selecting useful additions, PairAlign further introduces an Optimal Transport-guided rewiring mechanism to coordinate the finite edge budget for pair-level structural compatibility and shortage-target coverage. It formulates communication alignment between the candidate edge budget and the shortage targets, and the theory shows that this allocation covers shortage targets more broadly and effectively than a greedy-local assignment. Experiments on standard graph benchmarks show PairAlign's improvement across message-passing backbones, validating pair-level repair as an effective route for alleviating over-squashing.

The Large Language Model from Power Law Decoder Representations (PLDR-LLM) and its attention, Power Law Graph Attention (PLGA), replace the fixed bilinear form of scaled dot-product attention (SDPA) with a learned, input-generated bilinear operator $G_{LM}$, built from a positive tensor $A_{LM}$ by elementwise power laws. The architecture is fully specified, verified against pinned reference releases; claims are labeled theorem, conditional theorem, measurement, or conjecture. Unconditionally: PLGA contains SDPA exactly at $G_{LM}=I$; $A_{LM}$ and $A_P$ are strictly entrywise positive, with Perron-Frobenius structure on $A_{LM}$; the DAG regularizer has the NOTEARS walk-counting form and positivity obstructs exact acyclicity; and, under nonresonance (satisfied by standard rotary frequencies), a commutant criterion identifies which operators preserve relative-position dependence. An inference-collapse theorem: exact input invariance of deductive outputs collapses inference to generalized SDPA with a constant operator. Measured invariance: relative fluctuations of $10^{-6}$ and below; perturbation bounds quantify but do not certify cached inference; the assembled proxy misses the decoding margin. A conditional three-stage mechanism (rotary twirl, concentration, row-map contraction) is measured on a released checkpoint. Blockwise training and scoring under the global Gram are stated with explicit target exposure; on tested samples, block and sequential scoring select identical answers and agree on the published TruthfulQA probability-mass metric within $5\times 10^{-5}$ per item. Self-organized criticality enters as a phenomenological framework with an intrinsic order parameter; open claims become falsifiable conjectures. Selected proof cores are machine-checked in Lean 4.

Graph Neural Networks (GNNs) suffer from two fundamental limitations: over-smoothing, where node representations become indistinguishable with depth, and over-squashing, where long-range information is compressed through limited message-passing channels. Existing metrics such as Dirichlet energy provide global characterizations of over-smoothing but lack the resolution to analyze node-level behavior and guide architectural improvements. In this paper, we propose LEED (Local Embedding Evolution Distance), a novel local metric that quantifies over-smoothing by tracking the evolution of individual node embeddings across layers. By operating at the node level, LEED enables fine-grained analysis of representation dynamics during training, revealing heterogeneous over-smoothing patterns that are invisible to global energy-based measures. This locality induces informative node importance scores, interpreted as embedding-driven centrality measures. We leverage LEED to design a more efficient strategy for virtual node selection. Unlike existing approaches that depend on multiple heuristic centrality measures, our method uses LEED as a unique criterion to guide the construction of Local Virtual Nodes to mitigate over-squashing. Experiments show that LEED provides more informative diagnostics than Dirichlet energy while preserving global evaluation, and enables more effective virtual node integration, improving GNN performance across datasets.

Global medium-range weather forecasting requires modeling structured yet state-dependent interactions among heterogeneous atmospheric fields. Existing data-driven models largely learn these interactions implicitly, whereas equation-level physical constraints may inherit approximation and model-form biases. We present VeinCast, a physics-guided dynamic field graph and graph-conditioned fusion framework that jointly forecasts 69 surface and upper-air fields. Within each local window, its Physics-Guided Dynamic Field Graph combines predefined atmospheric relations with state-dependent Top-K residual edges and adapts Earth-window attention using the resulting graph context. Graph-Conditioned Latent Fusion further employs graph context and source-node centrality to guide field-to-latent aggregation, while bounded feedback preserves field-specific information. On the $1.5^\circ$ ERA5 benchmark, VeinCast demonstrates competitive forecasting performance across all 69 meteorological fields at lead times of up to 14 days, compared with representative global weather forecasting models including FuXi, Pangu-Weather, GraphCast, FengWu, and ARROW. Ablations confirm that the two modules provide complementary gains, demonstrating the effectiveness of relational-level physical guidance for data-driven weather forecasting.

Industrial processes are complex systems composed of multiple interacting sensors that generate multivariate time series (MTS). Detecting anomalies in such systems is critical for reliability and safety, yet understanding their origin is equally important. Existing Graph Neural Network (GNN)based methods for anomaly detection primarily focus on sensor-level deviations and either attribute anomalies directly to the deviating sensors. When diagnosis is attempted, generally, the most deviated sensor is identified as a root cause of a system fault. However, in many industrial systems, anomalies do not arise from faulty sensors but from disruptions in the influences governing the system dynamics. We propose an explainable GNN-based anomaly detection framework that shifts the perspective from sensor-level anomalies to component-level diagnosis, hypothesizing that anomalous measurements are symptoms of altered inter-sensor influences. Experiments show that the method effectively identifies and prioritizes the true faulty components, providing interpretable insights into system failures.

Quantitative estimation of protein-ligand binding affinity from three-dimensional complex structures is a fundamental task in structure-based computational chemistry and molecular modeling. Reliable prediction remains challenging because available structure-affinity data are limited, experimentally heterogeneous, conformation-dependent, and sensitive to dataset partitioning. RAVEN (Randomized Atomistic Views with Ensemble Neural Reservoirs) utilizes a multihead reservoir of independently initialized and fully frozen atomistic graph encoders to generate diverse structural projections without end-to-end optimization of the graph representation. These projections are integrated with a deterministic physicochemical interaction fingerprint and processed by heterogeneous supervised readers, including neural and tree-based regressors, whose outputs are combined through validation-based nonnegative fusion. The random reservoir expands structural feature coverage across independent encoder realizations, whereas the explicit physicochemical descriptors and heterogeneous readers contribute complementary information and distinct inductive biases. Evaluation on a similarity-isolated PDBbind 2020R1 split reconstructed using GEMS similarity resources, together with the protected CASF-2016 subset, demonstrated strong predictive performance. The results indicate that frozen multi-view graph representations, explicit physicochemical statistics, and heterogeneous model fusion provide a robust and flexible framework for protein-ligand binding-affinity prediction.

Spatiotemporal prediction on graph-structured data is central to traffic forecasting and environmental monitoring, yet decentralized and heterogeneous data complicate both sequence modeling and collaborative training. We propose F$^2$STNet, a federated forecasting framework that combines truncated graph-Fourier features, a lightweight diagonal state-space temporal encoder, graph convolution, and Fairness-aware Federated Aggregation (FFA). The spectral branch exposes graph-frequency structure, while the state-space layer models long temporal dependencies with linear complexity in the sequence length. FFA adjusts the FedAvg prior using client validation losses and an increasing fairness schedule. Experiments on PeMS04, HZMetro, and KnowAir show favorable forecasting accuracy relative to the evaluated baselines; federated experiments on PeMS04 additionally improve worst-client and client-dispersion metrics.

Graph neural networks typically propagate information through repeated message-passing layers, coupling the distance over which information travels with the number of nonlinear transformations applied. This coupling can make deep architectures difficult to optimize and can lead to over-smoothing, over-squashing, and the loss of long-range information. Linearized Graph Sequence Models (LGSMs) address this issue by separating information depth from processing depth and treating the successive propagation states of each node as a sequence. However, existing LGSMs construct these sequences using fixed graph operators, limiting their ability to adapt propagation to the input graph, node features, and downstream task. We introduce HOPPER, an end-to-end learnable extension of LGSM that learns how hop sequences should be extracted before they are processed by a modern state-space model. Our framework supports feature-conditioned, structure-aware, graph- and hop-adaptive propagation mechanisms while preserving permutation equivariance. Standard adjacency-based and non-backtracking LGSM sequences arise as special cases of our proposed extractor family. We show that HOPPER is state-of-the-art or competitive across the ECHO-Synth benchmark, and that varying the maximum neighborhood size of message backtracking cancellation (i.e. structural memory window) can optimize accuracy on the LRIM physics-based long-range dependency benchmark. These results demonstrate that learnable sequence extraction provides a flexible and effective approach to long-range graph representation learning.

Multi-agent systems (MAS) built on Large Language Models (LLMs) are proliferating rapidly, but their heterogeneous execution traces provide no common basis for evaluation across methods. Outcome-only benchmarks discard collaborations, whereas LLM-as-Judge evaluation requires additional, model-dependent inference and can vary with the LLM and rubric. We introduce a generalizable evaluation framework that maps native MAS traces into a shared space of unified collaboration graphs, enabling different methods to be evaluated under the same representation, reference set, and metric panel. Candidate graphs are compared with a query-specific reference forest. Each forest is a benchmark-provided collection of verified-success graphs: it records diverse ways in which representative MAS methods can complete the task, rather than prescribing a unique optimal process. Instantiating the framework as ForestBench, we filter $844$ collaboration-necessary queries from seven public datasets, precompute ten successful target-conditioned reference graphs per query, and evaluate six representative MAS frameworks. Controlled backbone, reference-construction, and perturbation studies test the stability and scope of evaluation. Once the benchmark forests are built, ForestBench scores a trace in milliseconds without further LLM inference, providing a reusable structural basis for comparing diverse MAS collaboration traces.

A central obstacle in building graph foundation models is the input heterogeneity in terms of feature space dimensionality, semantics, and structure. Such heterogeneity limits the capability of graph neural networks to generalize to new graphs with unseen feature spaces. We address the transferability challenge with SIGIL, a framework that maps any attributed graph to a unified representation space of fixed dimension. Given a graph, SIGIL lifts it to a structural interaction graph, where nodes are the input feature dimensions and weighted, typed edges encode feature alignment across multiple orders of the graph's connectivity. A relational message-passing network embeds each feature dimension into a shared space, transforming the original node features, of arbitrary dimensionality, into representations transferable to any downstream graph. By construction, SIGIL is equivariant to permutations of nodes, feature dimensions, and labels. Additionally, when the input features are one-hot indicators of discrete relations, SIGIL recovers and strictly generalizes existing foundation models for knowledge graph reasoning. A single SIGIL model, pretrained on one graph, delivers strong fully-inductive link prediction. Also, SIGIL can be used to implement existing knowledge graph foundation models. As such, SIGIL unifies several existing regimes in graph foundation model design under a single framework

Circuit localization is a mechanistic interpretability task whose goal is to identify a sparse subgraph of a transformer's computation graph sufficient to reproduce a particular behavior. Most established methods localize circuits independently for each model--task pair. We instead frame circuit localization as a graph machine learning problem in which the edges of a computation graph represent computational pathways, and graph neural networks (GNNs) model interactions among these pathways. We introduce Graph Circuit Learning (GCL), a supervised, amortized framework that trains a GNN across multiple model--task pairs and applies it to unseen cases. To provide sufficient data, we augment the InterpBench benchmark with additional cases derived from the TracrBench programs. Of the 14 evaluated GCL configurations, the highest scored a median edge AUROC of $0.902$ (interquartile interval $[0.861, 0.942]$) on the 16 original held-out InterpBench cases. This is close to the published InterpBench median of $0.910$ for EAP-IG while remaining below ACDC's $0.959$. Removing all message-passing edges reduces the median to $0.825$. We also adapt PGExplainer, a GNN explainability method, to circuit localization, obtaining a median edge AUROC of $0.858$ on the same cases. These preliminary results suggest that graph machine learning offers a natural and potentially powerful perspective on circuit localization, and we hope this perspective encourages closer exchange between the two communities.

The Zarankiewicz number Z(m,n,s,t) is the maximum number of edges in a bipartite graph with parts of orders m and n containing no copy of Ks,t. We give one combined, certificate-based computer-assisted proof for two finite slices and a corrected neighboring frontier: Z(12,n,3,3) = 6n (18 <= n <= 22), Z(13,22,3,3) = 137, Z(13, 18, 3, 3) = 116, Z(14, 18, 3, 3) = 124, Z(15,18,3,3) = 132, Z(14, 17, 3, 3) = 118, Z(15, 17, 3, 3) = 126, 132 <= Z(16,17,3,3) <= 133. The load-bearing new upper bounds are the exact 12 x 18 and 13 x 18 certificate packages. Their orbit certificates exclude every hypothetical matrix at the next edge count. Deletion lemmas and explicit witnesses close four neighboring cells, while the 16 x 17 entry is deliberately reported as an interval because only its 132-edge lower witness and the published 133 upper bound are certified here. Separately, the 13 x 22 proof excludes 138 ones by reducing to 83 degree profiles, rationally separating 77 of them, and eliminating the remaining six by marked-row congruences, leave enumeration, modular Gram tests, and exact Farkas certificates. All accepted claims are replayed by standard-library Python and exact integer/rational arithmetic; floating-point optimization is used only to discover certificates.

There are several methods for searching for graphs with prescribed properties, such as SAT solvers and specialized generators. These methods return the result as raw data: an adjacency matrix or a string encoding. The raw data certifies that the graph exists, but it does not reveal any structural properties of the graph. We ask whether one can automatically discover a short algebraic description if only this raw data is provided. We look for a description such as a Cayley graph $\mathrm{Cay}(Γ, S)$ or a lexicographic product $C_5[K_3]$. We address this question with a neurosymbolic approach. We propose an agent that runs on a general-purpose large language model with no fine-tuning or per-target training. The model interleaves reasoning with calls to the computer algebra system SageMath: it analyzes the target graph, proposes and tests candidate constructions, and revises them until the output matches the target. The agent communicates with SageMath through a Model Context Protocol (MCP) server, which we release as a general-purpose bridge. Whether a construction matches the target is checked by a single exact isomorphism test, and therefore rests on the symbolic side and not on the model. We test the approach on a benchmark of 100 highly symmetric graphs, namely two-orbit graphs on up to 25 vertices; the benchmark was fixed in advance. Our agent could find verified algebraic constructions for all of them, without falling back to raw encodings. A strong template-enumeration baseline reaches only about $20\%$, and a catalog lookup could not identify any of these graphs. However, construction quality declines when symmetry is removed. As a concrete application, we identify the smallest known counterexample to the Bernhart-Kainen dispersability conjecture, a $16$-vertex graph that enumeration found as raw data. For this graph, our agent found an explicit algebraic construction.

Large language models can answer knowledge-intensive questions more reliably when they are grounded with knowledge graphs, but systems such as Think-on-Graph and Reasoning-on-Graph repeatedly query the same graph neighborhoods across different questions. In this work, we study this repeated retrieval in Knowledge Graph Question Answering~(KGQA) workloads and propose KGCache, an in-memory cache for one-hop knowledge graph neighborhoods. KGCache is designed to be compatible with both iterative traversal (ToG) and one shot planning (RoG) KGQA paradigms. KGCache is placed between the KGQA engine and the backend serving the KG, so repeated entity requests can be served from cache instead of issuing new KG queries. We evaluate KGCache on WebQSP and CWQ using LRU, LFU, and a trace-aware Oracle policy. Our analysis shows that both datasets contain substantial entity reuse among starting entities and entities reached during traversal. We also explore semantic caching for similar queries, which shows additional hit-rate gains on WebQSP and needs further accuracy testing on CWQ. Entity caching accelerates KG retrieval by up to $1.91\times$, while semantic-context caching achieves up to $1.06\times$ full-system speedup in the evaluated WebQSP configurations, with each hit being up to $3.73\times$ faster.

Graph Neural Networks (GNNs) are widely used across domains such as natural sciences, social network analysis, chip design, and recommendation systems. However, as graph sizes grow, storing and processing them entirely on a single-node CPU-GPU system becomes increasingly impractical. A promising approach is to distribute the graph across multiple remote memory nodes, though this introduces a major bottleneck: inter-node network congestion during training. To address this, we propose LGNNIC, a novel inter-node system architecture that leverages SmartNICs co-located with remote memory nodes-a configuration already available in modern systems-to reduce communication overhead in distributed GNN training. LGNNIC offloads key preprocessing tasks to SmartNICs, reducing the volume of data transferred to computational (training) nodes and alleviating network congestion. We introduce two complementary techniques executed on the SmartNICs during the preprocessing phase: Neighbor Sampling, which performs mini-batch sampling, and Quantization of the sampled batches. To evaluate LGNNIC under different communication infrastructures, we designed both an optimized low-overhead DMA-based synchronization mechanism and a high-overhead socket-based alternative used as a benchmark. We evaluate the core SmartNIC offloading mechanisms across standard GNN workloads and sampling hyperparameters using a proof-of-concept (PoC) system comprising one remote-memory node with an NVIDIA BlueField-2 SmartNIC and one compute node with an A100 GPU. Both Neighbor Sampling and Quantization on the remote node demonstrated substantial training speedups in most configurations. Neighbor Sampling achieved up to 62.4x and 17.5x speedups with Sockets and DOCA-DMA, respectively, primarily due to reduced data transaction time. Quantization provided additional speedups of up to 3.6x and 1.3x, respectively, by reducing data transfer.

Modeling multivariate time series by representing them as graphs, where individual series act as nodes and pairwise temporal corre- lations serve as edges, has gained significant traction. Recent advances in Graph Neural Networks (GNNs) have demonstrated strong perfor- mance by assuming a static graph topology and aggregating information from neighboring series. In this work, we investigate the representa- tional power of GNNs for forecasting under both static and dynamic settings (i.e., when pairwise correlations evolve drastically over time) and identify critical limitations in current architectures. To formalize this, we first propose Temporal Correlation Volatility (TCV), a model- agnostic metric designed to quantify the distributional evolution of these latent structures. We establish a clear connection between TCV and performance degradation, demonstrating that many popular models, including Transformers, generalize poorly in high-TCV settings and are often outperformed by simple structure-agnostic baselines. To address these limitations, we propose Graph Layer for Inference in Dynamic En- vironments (GLIDE), a novel GNN layer enhanced by two theoretically grounded design mechanisms: (D1) Path-based Message Passing, which captures path-based neighborhoods and (D2) Static and Dynamic Propagation Separation, which identifies optimal dynamics via local static approximation. These components significantly improve learning under dynamic topology while preserving robustness in static scenarios. Ex- tensive experiments on synthetic and real-world benchmarks show that GLIDE improves average performance by up to 45.6% across static and dynamic settings, with the largest gain reaching 85.7%. The source code is available at https://github.com/ChenS676/GLIDE.

Small businesses often have only 12-24 months of accounting history, yet planning and risk workflows require coordinated forecasts across financial statements. We study joint 12-month forecasting of 13 income-statement, balance-sheet, cash-flow, and working-capital key performance indicators (KPIs) from 71 monthly ledger series. We introduce the Accounting Graph Transformer (AGT), which represents each ledger series as a masked token, exchanges information through typed attention on a fixed accounting-relation graph, pools target-specific context, and fuses it with a gated three-month recency path. Across 11,993 forecast origins from 1,060 unseen companies, AGT achieves sample-weighted KPI-macro mean absolute error (MAE) $0.6990 \pm 0.0013$ over three independent seeds, compared with $0.7378 \pm 0.0014$ for the strongest baseline, LightGBM. At the pre-specified seed 42, a paired company-clustered bootstrap gives a LightGBM-minus-AGT difference of 0.0395 with 95% confidence interval (CI) $[0.0350,0.0439]$. AGT is best on all 13 KPIs against LightGBM, TimeMixer, and SOFTS in the matched seed-42 comparison, while final-architecture ablations show that relational attention, accounting topology, and the recency path each improve validation and test accuracy. On 7,094 additional unseen companies with origins sampled from January-May 2025, AGT obtains 0.7548 MAE versus 0.7694 for SOFTS. A single 5.3M-parameter model produces 156 aligned forecasts without company-specific fitting, providing one forecasting layer for integrated planning, liquidity, and working-capital analysis.

Clustering is a fundamental data mining technique for pattern recognition through unsupervised learning. Among various clustering methods, hierarchical clustering, density-based clustering, and graph clustering stand out as representative approaches. For hierarchical clustering, it can be categorized into agglomerative and divisive modes to construct clusters in a recursive manner. The key aspect of both modes is the calculation of inter-cluster similarity, which determines whether to merge the sub-clusters into one cluster or divide a current cluster into sub-clusters. Traditionally, the similarity is derived from pairwise distances, often overlooking density variations and structural connectivity in graphs. To address this, we propose a density-aware hierarchical clustering method based on element-categorized connection subgraphs (DHC-ECS), which effectively integrates the hierarchical clustering, density-based clustering, and graph clustering. Particularly, a novel inter-cluster similarity metric is introduced that considers not only distances but also the element categorization in the KNN connection subgraphs, kernel density estimation, and local connectivity within sub-clusters. Extensive evaluations on heterogeneous benchmark datasets demonstrate that DHC-ECS exhibits superior overall performance in terms of clustering accuracy and parameter robustness compared with the baseline methods (including AChameleon, RNN-DBSCAN, McDPC, and G-RMS). The work indicates the great potential of the proposed clustering algorithm for low-dimensional datasets by leveraging local density and graph-structured connectivity (i.e., the duality of vertices and edges), as well as the possibility to determine an intrinsic threshold, reducing the reliance on manual parameter tuning.

Recent Large Multimodal Models (LMMs) have achieved impressive performance in recipe generation from food images.However, cooking is a structured transformation process in which ingredients undergo state changes through ordered actions,while free-form recipe language leaves the corresponding entities, intermediate states, and dependencies largely implicit and entangled.A graph representation makes this procedural knowledge explicit and compositional, providing a structured basis for assessing whether model outputs encode process-level knowledge rather than merely presenting plausible textual descriptions. To address this limitation, we present ReGraph, a large-scale recipe graph dataset that represents ingredients, cooking actions, and tools as entities, uses entity attributes to describe ingredient state changes, and employs typed relations to encode manipulation targets, destinations, and procedural ordering. ReGraph further incorporates explicit Recipe Reasoning Chain-of-Thought (RR-CoT) traces, providing auxiliary supervision for procedural decomposition and structured graph generation. Building on ReGraph, we propose Recipe Graph Learning (RGL), a two-stage framework that enables LMMs to generate a plausible fine-grained cooking workflow from a food image in the form of a structured recipe graph. Under a deterministic, schema-aware matching protocol, our experiments reveal a substantial gap between text-generation quality and recoverable procedural structure: recipes produced by existing approaches achieve competitive text-generation scores yet yield limited reference-aligned entity and relation structure under the ReGraph schema. In contrast, across two representative LMM backbones, RGL consistently improves the generation of cooking entities and procedural relations, while our analysis further shows that fine-grained ingredient-state capture remains the most challenging dimension.

Transformers provide a powerful architecture for global content-based matching, but reasoning problems may benefit from a stronger inductive bias toward iterative traversal of latent relations. We introduce Graph Machine, an architecture with two explicit edge-based mechanisms: Edge-augmented attention, in which edges modulate attention between nodes, and edge-centric referral, in which nodes exchange addresses to update their edges. Conceptually, this enables the model to dynamically and differentiably construct and revise relational graphs across layers. We study this inductive bias using Sudoku under controlled settings and find that Graph Machine outperforms Transformer baselines, with ablation studies and mechanistic analysis attributing the gains to the edge mechanisms. Surprisingly, we found that the model discovers a compact edge-based construction for Sudoku geometry. Our results support explicit edge mechanisms as a promising architectural design, motivating broader evaluation.

Cognitive distortion detection is a key task in computational mental health, yet existing approaches often overlook the psychological structure of distorted thoughts. We propose MTI-GNN (Multi-Perspective Triad Interaction Graph Neural Network), which models Beck's cognitive triad---negative views of the self, world, and future---as complementary perspectives for classification. An LLM decomposes each utterance into the three perspectives, from which perspective-specific similarity graphs are constructed and encoded by a Multi-Perspective GNN. A Triad Interaction module models cross-perspective dependencies through sequential source-conditioned updates and feature-wise gating, while Prototype-Guided Perspective Fusion performs label-conditioned aggregation. Label-expanded supervision incorporates all available distortion annotations during training. We evaluate MTI-GNN on 9,764 samples from four Korean, English, and Chinese datasets spanning ten distortion categories. MTI-GNN significantly outperforms all supervised variants and exceeds eight prompted generative models under zero-shot and few-shot settings. Leave-one-perspective-out ablations show that all three perspectives contribute significantly, while human expert evaluation provides preliminary evidence of their alignment with the intended cognitive dimensions.

Accurate estimation of building energy use is essential for achieving carbon neutral and sustainable buildings. To better understand the influence of design decisions on building energy use and calibrate machine learning models that can give architects and engineers rapid design feedback, large-scale datasets are needed that explicitly map building geometry to performance. We present ArchEGraph, a large-scale benchmark dataset that represents buildings as heterogeneous graphs with aligned geometry, topology, weather, and zone-level thermal loads. The dataset contains 5,481 buildings and 49,326 validated building-weather simulation cases. In total, it includes over 133,000 space nodes and 1.44 million face nodes, reflecting substantial geometric and topological complexity. Based on ArchEGraph, we define two benchmark tasks: (i) graph reconstruction from polygonal meshes, aiming to recover topological structure from geometric representations; and (ii) topology-informed load prediction, which leverages graph structure and temporal weather conditions to forecast zone-level response time series. We further introduce standardized evaluation protocols for both tasks and conduct cross-building and cross-climate generalization experiments to assess model robustness. ArchEGraph provides a unified testbed for studying geometry-topology-physics coupling in building energy modeling, enabling the development and evaluation of scalable and generalizable surrogate models.

Lightweight connectors make frozen multimodal encoders composable at the representation level. Deployment exposes a second problem at the level of task decisions. A connected route can expand cross-modal reach while changing an established native retrieval capability. We introduce CertBind, a multiscale theory of certifiable composition for frozen multimodal connector graphs. At the node scale, native anchors establish the exact task identification boundary under the stated chart model. At the edge scale, contract-aware conformal ranks provide graph-wide family-wise error control. At the path scale, an overlap-aware budget and clean calibration yield a finite-sample recovery radius under declared conditions. At the query scale, this radius yields a covered top-k candidate set that becomes a point certificate when its size equals k. CertBind therefore retains supported routes as Direct, sends only flagged routes to recovery, returns Certified for decisive recovery, and returns Abstain for unresolved queries. The evaluated C-MCR shared route reduced native CLIP R@1 from 0.524 to 0.290. The production fallback recovered 0.963 +- 0.002 of clean retrieval, while the passing branch recorded a no-harm value of 1.000. CertBind extends multimodal composability from connected representations to certifiable task decisions.

Relational inductive biases are essential for capturing structural dependencies among data. This study investigates a dual-level relational framework for image classification, bridging the gap between implicit representation learning and explicit structural modelling. We begin by establishing a baseline using an EfficientNetB3 architecture. To move beyond standard convolutional biases, we adopt a patch-based strategy, employing a convolutional masked autoencoder to learn implicit inter-patch relationships through self-supervised reconstruction. We then extend this approach by incorporating explicit relational modelling, organizing the learned embeddings into various graph topologies, including grid-based, random, and k-nearest neighbour structures. Experimental results on the ISIC-2018 and ISIC-2019 skin lesion diagnosis benchmarks show that combining implicit inter-patch modelling with explicit graph-based message passing yields the best performance. On the ISIC-2018 test set, the baseline model achieves a balanced accuracy of 76.17%, which improves to 77.12% with implicit patch-based relational modelling. The fully integrated grid-structured Graph Attention Network further increases performance to 79.27%. Similarly, on ISIC-2019, the implicit approach reaches 59.84% balanced accuracy, while the combination of implicit and explicit modelling yields 60.67%.

Full-graph GNN training delivers high accuracy but scales poorly on multi-server clusters due to heavy, irregular inter-node embedding exchanges. We present SNI-GNN, a SmartNIC-assisted full-graph training system that reduces communication while preserving accuracy by predicting remote embeddings in-network. SNI-GNN deploys a lightweight linear-trend predictor on SmartNICs to refine cached historical embeddings, coupled with an importance-based boundary-node sampling policy and an asynchronous DPU--GPU data pipeline with intermediate-result reuse. We provide error and convergence bounds showing that predictor bias remains controlled under bounded second-order dynamics and yields standard non-convex convergence with inexact gradients. Implemented on NVIDIA BlueField-3, SNI-GNN integrates with state-of-the-art full-graph systems, cuts communication by 21--45%, achieves 1.3--3.6$\times$ end-to-end speedups over BNS-GCN and up to 1.29$\times$ over baseline SANCUS, with accuracy loss $\leq 0.01$, and scales efficiently to 16 GPUs on graphs with up to tens of millions of edges. These results indicate SmartNIC-based in-network prediction is a practical complement to partitioning and compression techniques for communication-efficient full-graph GNN training at scale.

Predicting how a subcortical structure's shape will evolve from a few prior scans could support prognosis and clinical-trial enrichment. Existing longitudinal mesh predictors either extrapolate shape trajectories via high-dimensional embeddings or regress vertex deformations directly. We instead predict the surface's intrinsic geometry in continuous time: a single per-structure graph network predicts the future per-vertex first fundamental form (metric tensor) for an arbitrary causal multiple-visit history and an arbitrary prediction horizon, conditioned on a Fourier encoding of the lead time. The predicted metric is decoded into a surface by a differentiable As-Rigid-As-Possible solver, and the model is trained end-to-end on the rigid-aligned vertex error. Training through the reconstruction keeps the decoded prediction a valid surface and consistently improves it. On 14 subcortical structures from the ADNI dataset, the proposed mesh evolution model (MT-GNN) predicts best among the evaluated methods at every horizon ($-2.29\%$ mean vertex error vs. the temporal mean, $p{=}6.1{\times}10^{-5}$, beating it on 14/14 structures), ahead of geodesic shape regression (DCM, $-0.19\%$) and a mesh transformer (TransforMesh, $-0.45\%$; $p{=}1.2{\times}10^{-4}$), with the lead widening as the horizon grows.

Agents for long term reasoning require a memory that can be efficiently and effectively updated over time, as new facts and external feedback continue to arrive. Recently, graph memory has been adopted to offer structural organization for multi-hop retrieval and reasoning. However, existing methods store all memories in a flat graph, and accumulated historical memories can introduce irrelevant contexts and increase the cost of evidence selection during retrieval. Moreover, they typically update memory units independently, requiring repeated unit-wise rewrite to cover related changes. To address these issues, we propose HiGram, an evolving hierarchical graph memory framework with path-level localization and rewriting. Specifically, we first propose a hierarchical graph memory, which organizes the memory into coarse-to-fine architecture composed of upper-level nodes and MemoryUnits, thereby reducing the amount of irrelevant information during retrieval. We further propose MicroGraph-based path-level localization, which leverages query and update conditioned MicroGraphs to identify support subgraph and evidence path before rewrite. Finally, we propose a coordinated rewriting method that jointly revises intra-unit memory and inter-unit dependencies, enable valid dependency structures updating in the localized evidence path. Experiments on benchmarks for long-term conversational question answering and conflict-aware memory evaluation demonstrate that our method demonstrate substantial improvements over baselines in answer quality and token efficiency. Besides, our method improves answer accuracy and query-valid evidence selection under dynamic, static, and conditional conflicts.

We investigate the transferability of Earth weather foundation models to planetary atmospheres by adapting the GraphCast graph neural weather forecasting model to Mars. While GraphCast achieves state-of-the-art performance for terrestrial forecasting, its applicability to non-Earth environments remains unexplored. Using the Mars Climate Database (MCD), which provides global atmospheric fields across vertical altitude levels (similar to Earth pressure levels), we evaluate zero-shot and fine-tuned GraphCast predictions of Martian temperature and wind fields. Zero-shot forecasts produce a surprisingly accurate depiction of current conditions but fail to reproduce diurnal variability and rapidly decay toward climatological mean states. To address this limitation, we fine-tune GraphCast using MCD variables and top-of-atmosphere solar radiation forcing while holding humidity constant. Fine-tuning enables rapid learning of Martian thermal variability. Within as few as 10 training epochs, the model begins to capture the diurnal cycle and forecasts up to 10 days reproduce seasonal and vertical temperature structure. Prediction quality improves with training sample size and exhibits sensitivity to seasonal initialization. These results demonstrate that Earth-trained AI weather models can be adapted to simulate Martian atmospheric dynamics, providing a pathway toward rapid planetary weather prediction to support mission operations, dust storm risk mitigation, and future human exploration.

Sparse matrix computation performance on GPU depends on how representation and execution schedule match the input structure and target hardware. No single implementation consistently dominates across sparsity patterns, operators, and hardwares. Existing sparse compilers and specialized systems cannot cover all of them simultaneously. We present SparseDitto, an agentic sparse compilation framework for sparse matrix computation on GPUs. It jointly synthesizes representation, execution schedule, and hardware mapping in a unified compilation plan. Structural analysis and a learned template-ranking prior guide architecture-aware synthesis. LLM-guided lowering realizes each plan as CUDA code, while target-GPU profiling drives plan refinement. SparseDitto covers multiple operators, e.g., SpMV, SpMM, and SpGEMM, and various representations within one framework. It can also automatically adapt to different hardwares. Across various SuiteSparse matrices, SparseDitto achieves geometric-mean speedups over cuSPARSE of $2.68\times$ on an NVIDIA RTX PRO 6000 and $2.79\times$ on an NVIDIA H200 (up to 146.61$\times$). Its generated SpMM kernels accelerate full-batch GCN training by up to $3.39\times$.

Predicting the existence and type of links (edges) between nodes in a multi-relational graph is key for applications from social interaction prediction to knowledge relationship identification. Enhancing local features with relevant global information is crucial for accurate link prediction, yet it remains challenging. We address this by modeling the relationship between node pairs as node influence. That is, whether the node influence can be propagated and what type of influence is propagated indicates where and what type the edge is, which will be the most relevant local and global information to predict the edges. To this end, we extend the Susceptible-Infectious-Recovered (SIR) epidemic model to capture the influence propagation of nodes on a large scale through sub-graph structures. Subsequently, these sub-graphs are compressed using virtual edges, thereby substantially reducing the computation associated with utilizing the global graph structure. Finally, we propose the Influential Graph Neural Predictor, referred to as IGNP, a link prediction framework guided by influence propagation. Extensive experiments demonstrate the superiority of the proposed method, which outperforms strong baselines by a large margin on the widely used and real-world datasets.

The quantitative analysis of 3D neuronal morphologies requires capturing both graph topology and spatial geometry. Current message-passing Graph Neural Networks (GNNs) are bounded by the 1-Weisfeiler-Lehman (1-WL) test, limiting their ability to capture cycles induced by spatial proximities. To address this, we propose a training-free geometric prior based on tropical algebraic geometry. We apply the recently established tropical Abel-Jacobi transform and polarization distances to machine learning on tree-structured data. We introduce a structural transformation pipeline, comprising cycle space augmentation and quotient space construction, to convert spatial trees into cyclic metric graphs suitable for embedding into the Tropical Jacobian. Computing exact tropical polarization distances requires solving the NP-Hard Closest Vector Problem (CVP) on integer lattices. Instead of relying on explicit approximations with quantization errors (e.g., Babai's rounding), we adopt a continuous relaxation on the universal cover of the Albanese torus. We show that the discrete Arakelov-Green measure, computed in closed form via the graph Laplacian's generalized inverse, decomposes exactly into the intrinsic path metric minus the unquantized polarization distance on this cover, avoiding integer lattice searches. This metric yields two descriptors: eigenvectors provide node-level structural coordinates, and the permutation-invariant eigenvalue spectrum provides a graph-level signature. On the BREC benchmark, the eigenvector formulation demonstrates expressivity beyond the 1-WL limit. On 3D morphology datasets (ACT-4, JML-4, BIL-6), the spectrum seamlessly integrates into standard architectures (VAEs, GNNs, Tree-LSTMs) without additional trainable parameters, outperforming explicit lattice approximations and improving classification accuracy over existing spatial models.

High-resolution pixels and crop or zoom tools give multimodal large language models the ability to inspect an image, but they do not provide a reliable task-conditioned policy for deciding where to inspect. Q-CueGraph makes this decision explicit. It maps a question and an image representation to budgeted, coordinate-level observations for a frozen reader. Text-rich images use a reusable OCR/layout graph; natural-image search instantiates query-conditioned visual nodes behind the same selection, composition, and budgeting interface. Optional utility refinement learns which candidate crops the frozen reader can use from training-answer correctness, without region-box supervision. With a frozen Qwen2.5-VL-7B reader, Q-CueGraph reaches 0.833 accuracy on V*Bench versus 0.696 for full-image inference from a 19% image-area budget, and reaches 92% of full-image ANLS on InfographicVQA from about half the image area. Across six benchmarks, explicit observation is most valuable when evidence is localizable, the question discriminates its location, and resolution limits full-image reading.

Self-supervised learning on graphs is largely shaped by contrastive methods that depend on carefully designed augmentations, and by generative methods that reconstruct node attributes in the input space. Both paradigms can entangle representations with low-level input statistics rather than with relational structure. Joint-embedding predictive architectures (JEPA) instead learn by predicting latent targets rather than reconstructing inputs. Recent work has explored this idea for graph-level representation learning, but how to design JEPA-style objectives for node-level tasks, and which structural signals the predictor should condition on, remains less clear. We present NodeJEPA, a joint-embedding predictive architecture for node-level graph self-supervised learning. NodeJEPA masks structure-aware k-hop ego-subgraphs and trains a context encoder to predict the latent representations of the masked nodes. These targets come from an EMA-updated target encoder with stop-gradient. A structure-conditioned predictor integrates spectral and centrality descriptors through cross-attention. Variance, covariance, and Laplacian spectral regularizers help stabilize the embedding geometry, and an optional curriculum gradually increases masking difficulty during training. Because prediction occurs in latent space, NodeJEPA does not rely on input reconstruction or hand-crafted graph augmentations. We evaluate NodeJEPA on standard node classification benchmarks under linear probing and fine-tuning protocols, and conduct ablations on masking, prediction, and regularization design choices. Our study offers a practical recipe for node-level JEPA-style latent prediction on graphs, and clarifies when structural conditioning helps representation learning. Code, configurations, and evaluation scripts are publicly available at https://github.com/OliverZ-dot/Node-Jepa.

Coding agents increasingly work across sessions, but prose notes can preserve a conclusion without the program state that supported it. After an upstream change, a repository may still build even though earlier verification claims are no longer valid. EA-Graph is an artifact-anchored memory for verification claims. It represents artifacts at sub-path granularity, resolves aliases to leaf definitions, anchors each claim to the content used to establish it, and keeps evidence strength separate from freshness. When replacement content is unavailable, the claim becomes unprovable rather than guessed. EA-Graph is evaluated on generated repositories whose behavior-to-artifact ground truth is known by construction. The task is to classify prior claims as unaffected, affected, or unprovable after value drift, logic drift, and deliberately withheld upstream content. The analysis covers 42 sessions across seven clean worlds, 14 model-world instances, three memory conditions, and two model tiers. In the Haiku round, artifact-anchored memory outscored prose notes and no persistent memory in all seven worlds; each exact paired Wilcoxon comparison yielded p = 0.0156. In the Sonnet round, the anchored condition was perfect, but frequent control ceilings left the preregistered contrasts non-significant. No session fabricated withheld content. These results support a bounded claim: artifact-anchored memory improved the smaller model's provability judgments in this testbed. An exploratory comparison further suggests that structured claim memory may narrow a capability gap by externalizing in-session re-derivation, but it does not establish cross- model equivalence. The study makes no claim about efficiency or repair quality.

Blood-brain barrier permeability (BBBP) prediction is a critical screening task in central nervous system drug discovery, where candidate molecules must be assessed for whether they can cross, or should be prevented from crossing, the blood-brain barrier. However, this task remains challenging because of limited, class-imbalanced datasets and sensitivity to molecular structure. Recent advances in deep learning have established graph neural networks (GNNs) as a powerful approach for molecular representation learning, while pre-trained molecular GNNs provide transferable knowledge for downstream tasks. However, full fine-tuning is often parameter-inefficient and prone to overfitting, whereas existing parameter-efficient fine-tuning (PEFT) methods mainly adapt node features or the two-dimensional covalent graph, limiting their ability to capture three-dimensional geometry and second-order interactions. To address these limitations, we propose BBBP-GeoPEFT, a geometry-informed PEFT framework for pre-trained molecular GNNs. BBBP-GeoPEFT constructs distance-based graphs at multiple cutoffs and their corresponding line graphs from molecular conformers to capture spatial atom and second-order edge interactions. Lightweight auxiliary geometric graph encoders generate cutoff-specific representations, which are incorporated into each pre-trained layer through node-wise cutoff attention and gated residual connections. This design preserves pre-trained knowledge while incorporating permeability-relevant geometric information with a small trainable-parameter budget. Experiments on a curated BBBP dataset show that BBBP-GeoPEFT achieves competitive performance compared with full fine-tuning and representative PEFT baselines. Under both random and scaffold splitting, BBBP-GeoPEFT achieves competitive or improved ROC-AUC and accuracy in most experiments while updating only 10.1% of the model parameters.

Graph inference over relational data can expose sensitive edge information, and this risk becomes more severe in dynamic graphs, where repeated model updates cause privacy loss to accumulate. We formulate Edge-level Differentially Private Dynamic Graph Inference (EDG) and propose PriDyG, a private inference framework that combines GNN-based structural learning with LLM-based semantic reasoning. PriDyG introduces incremental private multi-hop aggregation, which buffers newly arrived edges and processes each edge exactly once. By parallel composition, the total privacy cost equals that of a single static release, independent of the number or schedule of model updates. Compared with geometrically decaying budget allocation, incremental aggregation avoids exponentially increasing noise while preserving exact one-hop signals and at least half of two-hop information transfers. PriDyG further complements privatized GNN outputs with LLM predictions derived solely from node text, incurring no additional edge-level privacy cost. Experiments on four benchmarks for node classification and link prediction show that PriDyG consistently outperforms geometrically decaying baselines under the same privacy budget and matches the utility of naive per-update retraining while reducing cumulative privacy cost by up to three orders of magnitude.

The dynamical Lie algebraic (DLA) theory of variational quantum algorithms (VQAs) predicts commonplace exponentially vanishing loss and gradient variances for sufficiently deep parametrized circuits. In this work, we show that these predictions fail dramatically in the shallow-circuit (and particularly constant-depth) regime for the Quantum Approximate Optimization Algorithm (QAOA) applied to the maximum independent set (MIS) problem. In a large-scale numerical study across $\sim$23,000 problem instances, we find that barren plateaus are rare, while landscapes whose variances polynomially increase with system size---which we term "cragged terrains"---are common across graph families. This aggregate polynomial growth persists both for generic, low-symmetry random graphs and for highly symmetric vertex-transitive graphs, indicating that DLA-based variance predictions do not describe landscape scaling in this regime. As a stopgap alternative to the theory, we train empirical hardness models to predict instance-wise hardness metrics for QAOA-MIS. While these models generalize poorly, they nonetheless recover the correct landscape scaling class (barren plateau vs. cragged terrain) with high fidelity. Taken together, our results identify shallow QAOA for MIS as a prototypical setting in which asymptotic, unitary-design-centric predictions may be fundamentally insufficient to describe shallow variational quantum algorithms more broadly, emphasizing the need for more empirically-informed models of VQA loss landscapes.

Language models (LMs) offer strong textual representations for electronic health records (EHRs), but they encode patient sequences in isolation and provide limited explainability. Graph neural networks (GNNs) complement LMs by incorporating inter-patient relationships and enabling reference-patient attribution, yet they rely on high-quality patient representations. We propose Patients-like-me (PLM), a unified LM--GNN framework that integrates local patient semantics with global cohort structure. To train PLM efficiently, we introduce a Variational Expectation-Maximization algorithm that alternates LM and GNN updates under a supervised variational objective. Extensive experiments on MIMIC-III and MIMIC-IV show that PLM consistently outperforms state-of-the-art methods, with improvements generalizing across encoder-only and decoder-only LM backbones. These gains are achieved with only modest additional computational overhead. PLM also provides reference-patient explanations by retrieving influential similar patients, while edge-masking experiments confirm that the highest-ranked references have the greatest impact on model predictions.

This work focuses on the problem of learning on temporal graphs, with particular emphasis on the task of clustering: obtaining coarse-grained representations by aggregating information from nodes, edges, and temporal dynamics - a task related to pooling in machine learning on graphs, or community detection in network science. Although graph neural networks reach state-of-the-art performance across many downstream graph tasks, their advantage over established descriptive and inferential clustering algorithms is far less settled, especially under demands of efficiency and recovery accuracy. We frame this tension through three linked perspectives: principles, connecting graph learning and community detection through shared spectral foundations and detectability thresholds in stochastic block model regimes; primitives, making spectral clustering and multislice modularity optimization tractable through GPU-accelerated temporal backends; and pooling, viewing principled community detection as a theory-grounded coarse-graining operator for temporal graphs. Our results indicate that algorithmic methods remain the appropriate tool where attributes are absent or weak - scalability rather than accuracy being the binding obstacle - while neural models are most compelling when structural, temporal, and attribute signals align. By making temporal clustering scalable, GPU-accelerated primitives suggest a route toward theory-grounded pooling, while raising a central question: when does community-based coarse-graining preserve the dynamics needed for downstream learning tasks?

This work addresses community detection in temporal networks through GPU-accelerated extensions of spectral clustering and modularity-based algorithms originally designed for static graphs. Built on the NVIDIA RAPIDS ecosystem, the framework enables the characterization and tracking of communities in snapshot-based dynamic graphs, either by Leiden greedy optimization with multi-GPU support via Dask-based workload distribution, or eigendecomposition of a symmetric Bethe-Hessian operator. Our multislice modularity backend achieves up to roughly three orders of magnitude speedup over the CPU reference under an equal-work budget, depending on graph density and snapshot count, while preserving compatibility with existing graph analytics pipelines. We demonstrate its applicability on real-world and synthetic datasets, facilitating exploratory analysis of structural network properties over time. Such capabilities are relevant across several application domains, such as epidemic spreading, financial systems, cybersecurity, and trajectory and mobility analysis. We release our implementation as free and open-source software, including Python bindings through the NetworkX-Temporal library for ease of use and zero-code acceleration with existing codebases.

We study fair allocations of indivisible goods among agents with heterogeneous monotone valuations. As fair we consider the allocations that are envy-free-up-to-any-good (EFX). Finding if EFX alloca- tions always exist, even for agents with additive valuations, is a major open problem in Fair Division. Christodoulou et al. (2023) introduced the (multi-hyper)graph setting, where agents and goods are represented by vertices and edges of a graph, respectively, and only the endpoints of an edge may have non-zero marginal value for it. We show that for hypergraphs with girth at least 4 and agents with general monotone valuations there always exists an EFX allocation and can be constructed in polynomial time. We generalize our approach to also show that multi-hypergraphs with girth (on the simple hypergraph) at least 4 always admit an EFX allocation, as long as there exists a single vertex whose incident edges have multiplicity at most the size of that edge minus 2; our construction in this case needs pseudo-polynomial time.

Pretrained large language models (LLMs) have demonstrated in-context learning (ICL) capabilities for numerical inference over sequences serialized as text. Prior work has identified and characterized this form of numerical inference primarily through output-level evaluations such as prediction error. However, how numerical information is organized within LLM representations remains much less understood. To study this internal organization, we adopt a graph signal processing perspective in which attention induces a weighted graph over tokens, while token hidden states define signals on its nodes. Quantitative graph-spectral diagnostics and qualitative token-graph visualizations reveal that representations become more clearly differentiated by input dynamical complexity as context length increases. Simpler inputs produce attention-induced token graphs with stronger global connectivity and smoother, spectrally concentrated hidden-state signals, whereas more complex inputs produce more localized graphs and hidden-state signals with broader spectral support and greater high-frequency energy. Together, these findings point to systematic, context-dependent internal signatures associated with numerical ICL that are conserved across model families.

Graph attention normalizes neighborhood scores with softmax, the maximum-entropy choice under Shannon statistics. But homophilic and heterophilic graphs want different attention shapes, and one fixed normalization cannot serve both. We propose \textbf{LTGA} (\textbf{L}earnable \textbf{T}sallis \textbf{G}raph \textbf{A}ttention), a graph attention layer whose Tsallis entropic index $q$ is learned jointly with the weights, interpolating continuously between heavy-tailed ($q\!<\!1$), softmax ($q\!=\!1$) and compact-support ($q\!>\!1$) attention at four granularities from a global scalar to a per-edge index, under a bounded reparameterization that starts every model at the GAT baseline. Across eight benchmarks at ten seeds, LTGA-Edge takes the best average rank ($2.75$), but the omnibus test does not reject ($p\!=\!0.199$) and learning $q$ does not beat searching it: a validation-tuned frozen grid reaches $61.4\%$, tuned $α$-entmax $62.2\%$ and a capacity-matched $q\!\equiv\!1$ control $62.0\%$, against $61.7\%$ for LTGA-Edge. What the learned index buys is one run instead of a grid, and an interpretable mechanism: where $q$ leaves $1$, it prunes $42\%$ of attention coefficients to exactly zero, and those edges are selectively the wrong ones, restoring them costs $7.1$ points, while random pruning at the same rate costs $13.0$ more. Project page: https://kleyt0n.github.io/ltga

Multimodal supervised learning seeks to leverage multiple heterogeneous data sources to improve predictive performance. A central challenge is determining the fusion granularity across modalities: over-integration may amplify noise while under-integration fails to exploit cross-modal dependence. Existing approaches rely on pre-specified fusion architectures, from early to late fusion, that may not adapt to the underlying dependence structure among modalities. We propose DAIF, a data adaptive intermediate fusion framework that combines random matrix theory and non-parametric dependence measures to learn fusion structure directly from data. We operate under a Bayesian multimodal factor model where the prior on the latent factors determines the cross-modal dependence. Our method clusters modalities based on estimated intermodal dependence, then performs clusterwise empirical Bayes estimation of the priors. These estimated priors are used to construct denoisers within an approximate message passing (AMP) framework, yielding denoised low-dimensional features that borrow strength across related modalities while preserving modality-specific signal. The resulting embeddings are used for downstream supervised prediction. We evaluate the framework through simulations under varying dependence structures and signal regimes, comparing against several benchmark methods, and demonstrate its practical utility on two multimodal datasets, namely a trimodal TEA-seq dataset (Swanson et al., 2021) and TCGA-BRCA dataset (Goldman et al., 2020). In the first example, we predict the expression level of a T-cell differentiation marker protein and in the second case we analyze patient survival prediction based on multimodal information. Our method competes with or outperforms the state-of-the-art techniques in both prediction problems, demonstrating its versatility across diverse supervised learning tasks.

Virtual nodes give message-passing neural networks a simple global communication route, but the standard node--VN--node pipeline compresses the graph into one homogeneous state and broadcasts it identically to every node. Building on the Two-Radius analysis of Mishayev et al., we ask how auxiliary virtual memory can relieve this finite-capacity bottleneck without self-attention. We identify two requirements. First, the global memory should be factorized into independently writable and readable states: this can be achieved using addressable cross-attention slots. Second, addressability alone does not preserve multiplicity, because softmax attention is invariant to uniform replication. Inserting each slot query as a private key/value anchor recovers the discarded normalization mass and yields, on bounded color domains, an injective multiset representation able to implement a 1-WL refinement. Experiments on multiplicity-aware Two-Radius, motif counting, and constrained link-set prediction support this addressable and cardinality-preserving virtual memory at (O(nMd)) arithmetic cost.

Sheaf Neural Networks (SNNs) generalize message passing by replacing scalar edge weights of standard Graph Neural Networks (GNNs) with learnable, edge-dependent restriction maps between node stalks. Despite their strong theoretical foundations and promising transductive results, SNNs have been evaluated almost exclusively on transductive node classification, leaving their behaviour under inductive protocols unknown. We address this gap through the first systematic benchmark of the sheaf design space, evaluating three diffusion mechanisms (neural sheaf diffusion, sheaf attention, and sheaf attention with Graph Attention Network v2), three restriction-map parameterizations, three stalk dimensions, and six modern GNN architectural components, within a message-passing reformulation that never assembles the heavy sheaf Laplacian, making the full design space trainable under cross-graph batching. Across $1{,}890$ controlled experiments on 14 inductive datasets, multiple insights emerge: restriction maps are the dominant design choice and general maps are preferable, larger stalks add capacity but not long-range reach, architectural components explain more performance variation than the entire sheaf-specific design space itself. Under a matched protocol, SNNs transfer to inductive settings but do not reach the strongest baselines, with gaps being dataset-dependent. Practically, a single sheaf configuration can generalize across datasets, so effort is better spent tuning the surrounding architectural recipe than the sheaf operator itself.

We construct unambiguous DNFs having width $O(n)$ but $0$-certificate complexity $Ω(n^2)$. By utilizing the special structure of these DNFs, we prove a lifting theorem with a constant-sized gadget that lifts the DNF to a communication problem, while losslessly translating the separation in certificate complexity to a separation in communication complexity. This leads to an optimal refutation of the Alon-Saks-Seymour conjecture, as well as an optimal communication lower bound for the Clique versus Independent Set problem, improving the previous results of Balodis, Ben-David, Göös, Jain and Kothari (FOCS 2021, SICOMP 2023) by several doubly logarithmic factors. As further applications of our construction to query complexity and learning theory, we exhibit: (a) a family of Boolean functions that has an optimal quartic separation between certificate complexity and approximate degree, and (b) a sample compression lower bound of $Ω(\sqrt{\log c})$ for multiclass concept classes over $c$ labels.

Content-based detection of unreliable news is increasingly difficult, as low-reliability sources mimic credible journalism and generative AI makes fabricated content harder to flag. We ask whether network structure can improve news reliability classification, taking a domain-level approach that shifts the focus from individual articles to source reliability. From URL-sharing patterns in Telegram chats, we build a statistically validated domain co-sharing network and find assortative mixing by reliability: low-reliability domains group together, as do reliable ones. Exploiting this structure, we compare Graph Neural Networks against network-unaware baselines using both content-aware features (multilingual text embeddings) and content-agnostic features (spreading dynamics). GNNs consistently outperform Multi-Layer Perceptrons on identical features, with GraphSAGE best in both settings (accuracy 0.63 with content, 0.53 without), a 13-14% relative gain over the network-unaware baseline. Network topology thus systematically improves domain reliability assessment, and remains effective even when content analysis is infeasible.

Graph functional dependencies (GFD) are a recently-developed concept aimed at capturing both topological structures in graphs and functional dependencies between attributes. The process of verifying whether a given GFD holds over a particular graph is referred to as GFD validation. In this very computationally expensive problem, locating suitable subgraphs accounts for about 99% of the total run time. The concept's authors originally proposed a parallel scheme (algorithm), targeting specifically clusters of high-performance servers. The goal of this study is to open GFD validation to a broader public by making it possible to run it on a consumer class PC. Our initial experiments demonstrated that the existing algorithm may not be optimal for these purposes. Therefore, we propose FastGFDs - a GFD validation algorithm that employs a recently developed graph matching technique. In contrast to the parallel scheme, it is sequential and operates on the entire graph. Its novelty lies in the use of Core-First Decomposition and the Compact Path Index (CPI). We compare it with the naive sequential algorithm and the parallel scheme, evaluating run times and memory consumption. The current study is the first step towards designing an efficient algorithm for GFD validation in low-end single-node environments. We also provide an open-source implementation of GFD validation over large data graphs. To the best of our knowledge, this is the only publicly available implementation of an algorithm for this problem. It is developed in Desbordante - an open-source high-performance data profiler aimed at science-intensive tasks. Finally, our experiments on a real-life graph demonstrated up to three times performance (2.6x on average) improvement over the parallel scheme. Employing the new subgraph matching algorithm also reduced memory consumption by five times.

Credit risk detection, particularly mitigating individual fraud, is crucial for maintaining the stability of digital financial ecosystems. Accurately identifying credit fraud among billions of users is critical for minimizing financial losses and safeguarding the sustainability of inclusive financial services. Given that credit fraud risks are often concealed within heterogeneous user-risk graphs, Graph Neural Networks (GNNs) have emerged as an effective tool for risk mining by capturing complex dependencies. To address the scalability bottleneck of industrial GNNs, distributed training based on subgraphs is indispensable. However, existing strategies often compromise topological integrity for load balancing. This can be catastrophic for risk detection, as it indiscriminately severs the long-tail evidence chains essential for risk propagation. Overlapping subgraphs can restore severed risk contexts but inevitably introduce redundancy and noise, while overlooking the representation alignment across different local subgraphs. In this paper, we propose a risk-aware overlapping subgraph learning framework for large-scale credit risk detection. We first construct base partitions to ensure load balance. Then, we perform budget-constrained sampling that selects informative long-tail nodes, thereby preserving critical risk diffusion patterns while filtering out noise. To mitigate representation inconsistency, we design a cross-subgraph consistency alignment mechanism. By enforcing alignment constraints on the overlapping nodes, we harmonize the local representations into a globally consistent latent space. Extensive experiments on Weixin Pay's production dataset demonstrate that our model significantly outperforms existing strategies for risk detection, offering a scalable and effective solution for industrial graph learning.

Training Graph Neural Networks on large graphs is challenged by the memory cost of storing all node representations across layers. We show that several existing scalable approaches can be written as structured modifications of the GNN propagation matrix, providing a unified perspective that exposes their respective limitations. In particular, graph coarsening replaces it by a low-rank approximation that enables spectral guarantees but assigns uniform representations to clustered nodes, while Cluster-GCN restricts the propagation matrix to intra-cluster connections that allow efficient batching but sever long-range information. These are complementary failures of the \emph{same} decomposition of the graph into groups of nodes. To obtain the best of both worlds, we propose \textbf{CoRe-GNN}, which performs both propagations in parallel at each layer: a coarsened inter-cluster term capturing long-range structure, and a local intra-cluster term preserving per-node discriminability. We prove that CoRe-GNN inherits analogous approximation guarantees to those of graph coarsening, and introduce a natural cluster-based \emph{batching scheme} that scales to graphs with millions of nodes. On node classification benchmarks spanning homophilic, heterophilic, large-scale, and long-range graphs, CoRe-GNN outperforms both graph coarsening and Cluster-GCN baselines. Notably, CoRe-GNN reaches competitive accuracy on \emph{long-range} tasks, while remaining memory-efficient through batching.

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

Large language models are increasingly used to reason about software vulnerabilities, but their outputs can silently violate domain knowledge, limiting their reliability in safety-critical settings such as medical devices. Prior work either treats that output as a prediction to be scored or constrains it to walks within a single knowledge graph; neither checks whether reasoning over a binary is consistent with an independent body of domain knowledge. We present EntailLLM, which validates each LLM-proposed analyst path by entailment: the path is a traversal of the binary's function call graph, the domain knowledge is represented in a separate graph, and verification aligns the two under temporal annotated logic. Across three CWE classes, four LLMs, three prompting strategies, and seven binaries varying in size from 405 to 12,696 function call-graph nodes, domain knowledge raises pooled entailment from 78% to 98%, with entailment decreasing in only 3% of the experiments. EntailLLM is deployed end-to-end on real medical-device binaries, reaching 98% pooled entailment without per-device tuning. Our system inherits the formal guarantees of generalized annotated logic, providing logical verification of LLM output that is both explainable and grounded in well-defined semantics.

Large language model (LLM) agents are increasingly capable of planning, using tools, and interacting with external environments. They are typically supported by harnesses, which manage state and coordinate multi-step execution. Graph analysis provides a promising setting for evaluating their agentic capabilities, because it requires agents to access data and execute operations in a graph environment. However, existing graph benchmarks for LLMs provide limited coverage of graph tasks and graph types, making it difficult to comprehensively evaluate LLM agents. Moreover, they typically formulate graph analysis as text-based question answering, where graph information is directly provided in the prompt, limiting the evaluation of end-to-end agentic capabilities. To address these limitations, we introduce GABench, a comprehensive benchmark for agentic graph analysis. GABench spans three graph types and covers four graph analysis task categories: graph retrieval, graph theory, graph machine learning, and graph open-ended question answering. GABench also provides 84 executable tools for accessing graph data and performing diverse graph operations. Building on these tools, we develop an agentic graph analysis task generation pipeline and construct 10,400 tasks with verifiable ground truth.Using GABench, we evaluate a range of frontier LLMs and agent harnesses. Our experiments reveal three key findings: (1) Existing LLM agents still struggle with complex graph analysis tasks. (2) Harness choice significantly affects performance, yet existing harnesses remain limited on complex graph tasks. (3) Graph analysis depends more on tool-call quality than quantity. Our findings provide practical insights into the development and evaluation of LLM agents for graph analysis.

Large language models (LLMs) enable neural architecture search (NAS) directly over executable neural network programs. However, code-level flexibility does not provide the architecture state needed for effective mutation: LLMs must infer tensor dependencies, editable components, and compatibility constraints from implementation details. To address this representation mismatch, we propose GraphIR, an architecture-aware intermediate representation that supplements executable programs with a mutation-aligned candidate state. GraphIR organizes each candidate through three complementary views: a computation skeleton describing tensor flow, a mutation surface exposing editable modules and operations, and a validity envelope capturing interface contracts, propagated shapes, and downstream dependencies. To evaluate our method, we construct NAS-Dependency, a 120-question benchmark covering six complementary dependency-reasoning dimensions. The diagnostic shows that GraphIR is particularly effective at identifying exact producer occurrences, tracing dependency propagation, and diagnosing interface and failure risks. Across six downstream benchmarks including CLRS, GraphIR achieves the best overall search performance while maintaining comparable model size and favorable end-to-end NAS efficiency when integrated into OpenEvolve. These results show that a mutation-oriented architecture state provides an effective interface between executable neural programs and LLM-guided architecture evolution.

Selecting a complete 3D object from a reconstructed scene with minimal user effort is essential for practical scene editing and embodied interaction. Existing 3DGS-based methods either retrain the Gaussian representation to embed per-object labels, or build dense multi-view SAM observations, both requiring heavy computation and dense viewpoint coverage that is rarely available in practice. We present GaussianSelector, a training-free framework for interactive 3D object selection from sparse views and sparse scribble guidance. Operating directly on native Gaussian primitives, we coarsen dense Gaussians into geometrically coherent superpoints and construct a continuity-weighted graph using appearance and spatial cues. Sparse user scribbles are lifted into 3D via visibility-aware transmittance coverage, and selection is solved as a global graph-cut energy minimization that propagates sparse evidence to a complete 3D object. This design naturally supports multi-round refinement, where users iteratively correct the selection from additional viewpoints to progressively improve the result. Experiments demonstrate that GaussianSelector achieves competitive selection quality against state-of-the-art multi-view SAM-based methods, while requiring significantly fewer interaction views and substantially lower computational overhead. These properties make it well suited for human-in-the-loop 3D scene editing and 3D asset extraction in real-world deployment scenarios.

Topological neural networks (TNNs) enable leveraging high-order structures on graphs (e.g., cycles and cliques) to boost the expressive power of message-passing neural networks. In turn, however, these structures are typically identified a priori through an unsupervised graph lifting operation. Notwithstanding, this choice is crucial and may have a drastic impact on a TNN's performance on downstream tasks. To circumvent this issue, we propose $\partial$lift (DiffLift), a general framework for learning graph liftings to hypergraphs and cellular- and simplicial complexes in an end-to-end fashion. In particular, our approach leverages learned vertex-level latent representations to identify and parameterize distributions over candidate higher-order cells for inclusion. This results in a scalable model which can be readily integrated into any TNN. Our experiments show that $\partial$lift outperforms existing lifting methods on multiple benchmarks for graph and node classification across different TNN architectures. Notably, our approach leads to gains of up to 45% over static liftings, including both connectivity- and feature-based ones.

Kinematic models provide reliable motion constraints for odometry estimation in featureless environments, where exteroceptive sensing degrades and IMU integration drifts. Learning-based kinematic models can achieve more accurate odometry estimation than model-based methods by capturing nonlinear effects; however, most existing learning-based models are trained on a single embodiment and generalize poorly to new embodiments. This generalization is difficult because the meanings and structures of proprioceptive measurements vary across embodiments, including the number of joints and ground-contact elements (e.g., wheels, feet). To address this challenge, we propose KING, a Graph Neural Network (GNN)-based kinematic model that explicitly incorporates robot embodiments by representing them as a common graph. We show that wheel and leg kinematic models can be expressed by a unified representation, enabling a single model for both wheeled and legged robots. Trained on datasets spanning diverse embodiments, KING provides a unified representation of wheeled and legged kinematics and achieves high-accuracy odometry estimation in real environments. KING estimates accurate odometry using only an embodiment description (e.g., a URDF file) and on-board proprioception (encoders and an IMU) and can be adapted to new robot embodiments through few-shot learning with only one minute of data, avoiding retraining from scratch on a new dataset for each robot. The project page is available at: https://smrg-aist.github.io/king_project_page/

Community detection is a fundamental task in graph analytics that aims to identify cohesive groups of entities with similar behaviors or interests. Classic objective-driven methods struggle with complex graph structures, while deep-learning approaches improve performance at the expense of interpretability and rely on labeled data and training. Large language models (LLMs), with strong reasoning capabilities and world knowledge, are promising for interpretable, label-free community detection. To leverage these strengths, we propose LUCID, an LLM-guided, interpretable, training-free, and unsupervised community detection method. Inspired by phase-transition kinetics in natural systems, where complex structures emerge through initialization, merging, refinement, and selection, LUCID is designed as a four-stage pipeline. Within this pipeline, the LLM induces formal rules that translate implicit knowledge into explicit and interpretable logical structures. Specifically, (1) the Local-View Community Initialization stage encodes local graph structures using k-ego contexts and unsupervised node roles; (2) the Multi-factor Community Merge stage uses LLM-induced rules to iteratively merge local communities; (3) the Multi-grain Community Refinement stage applies LLM-induced coarse-to-fine rules in parallel to reduce boundary noise; and (4) the Global-view Community Selection stage identifies high-quality communities based on topological compactness and boundary clarity. Extensive experiments on real-world datasets demonstrate that LUCID, as an unsupervised approach, achieves state-of-the-art performance and consistently outperforms leading unsupervised and semi-supervised baselines.