Graph Structure

Large language models (LLMs) and vision-language models (VLMs) have significantly advanced zero-shot task planning for embodied agents. However, most LLM- and VLM-driven methods struggle to generate safe high-level actions due to a lack of physical risk awareness, particularly under partial observability, where hazards lie outside the immediate field of view. To address this challenge, we propose a novel safe task-planning framework, SafeMem, which constructs and maintains a long-term semantic graph memory of the open and dynamic environment. Based on egocentric observations, the proposed framework incrementally accumulates knowledge about surrounding objects and their relationships with a graph. Then, an LLM-based risk predictor evaluates candidate actions using the graph memory, triggering a conservatism-modulated replanning loop with explanations for detected hazards. Extensive experiments on the IS-Bench benchmark and a real-world robot platform demonstrate that the SafeMem framework substantially improves safe success rates compared to state-of-the-art VLM-driven task planners. Video results are available on our webpage: https://sites.google.com/view/safemem.

Graph modeling, a crucial task for representing complex relationships in graph-structured data, has achieved significant success in recent years. However, current graph modeling methods rely on traditional Graph Neural Networks and pre-training approaches to implicitly learn the underlying relational structure of graph data. Thus, these prior methods cannot capture the complex graph structure and correlations among inputs. In this paper, we introduce a novel Attention-based Normalizing Flow-based Approach\footnote{Our implementation and models will be released publicly for research reproducibility.} (ANFA or $α$) that provides an explicit, interpretable, and tractable Graph Modeling ($α$-Graph). In particular, we propose a new Unconditional Graph Normalizing Flow with an Invertible Attention Mechanism to capture the complex relational structure of graph data. To further enhance the expressiveness of the model, we introduce Conditional Graph Normalizing Flow with Learnable Queries that enables efficient modeling of correlations in graph-structured data. We show that our Conditional Graph Normalizing Flows behave similarly to Unconditional Graph Normalizing Flows, enhancing expressiveness while maintaining training stability and efficiency. Our experimental results on three benchmarks will illustrate the effectiveness and the state-of-the-art (SoTA) performance of the proposed $α$-Graph method.

Learned graph simulators provide an efficient alternative to high-fidelity solvers for granular dynamics. However, granular motion depends strongly on inter-granular contact history, which is difficult to preserve when particle contacts form, break, and rearrange. Existing simulators mainly store temporal information in node features or node-level memory. Here we introduce TRACE, a graph-network simulator that stores interaction history directly on contact edges. Each edge maintains a persistent memory updated by attention-based message passing and a gated recurrent unit, while an edge-identity dictionary preserves this memory as the contact graph changes. A physics-structured decoder predicts inter-granular normal and tangential contact forces, enforces the Coulomb friction limit, and applies equal-and-opposite internal forces. The model is trained with single-step pretraining followed by autoregressive rollout fine-tuning. We evaluate TRACE on 2D and 3D granular column-collapse benchmarks. In both cases, TRACE produces stable, physically consistent long-horizon rollouts, closely reproducing the final deposit geometry and the kinetic energy released during collapse. Compared with graph network simulator (GNS) and node-memory graph neural simulator (NMGNS), TRACE reduces long-rollout position error by 31-62% and final-deposit error by 58-89% across the two benchmarks, while using fewer parameters and maintaining near-zero particle interpenetration. TRACE also achieves 12.2$\times$ and 8.9$\times$ speedups over the material point method (MPM) reference solver in 2D and 3D, respectively. Our code is available at https://github.com/Data-Driven-Computational-Geotechnics/TRACE.

The conventional approach to machine learning, that is, collecting data, training models, and performing inference in a single location, faces fundamental limitations, including scalability and privacy, that restrict its applicability. To address these challenges, recent research has explored collaborative learning approaches, including federated learning and decentralized learning, where individual agents perform training and inference locally, with limited collaboration. Most collaborative learning research focuses on Euclidean data with regular, grid-like structure (e.g., images, text). However, these approaches fail to capture the relational patterns in many real-world applications, best represented by graphs. Learning on graphs relies on message-passing mechanisms to propagate information between connected nodes, making it conceptually well-suited for collaborative environments where agents must exchange information. Yet, the opportunities and challenges of learning on graph-structured data in collaborative settings remain largely underexplored. This survey provides a comprehensive investigation of collaborative learning from Euclidean to graph-structured data, aiming to consolidate this emerging field. We begin by reviewing its foundational principles for Euclidean data, organizing them along three core dimensions: learning effectiveness, efficiency, and privacy preservation. We then extend the discussion to graph-structured data, introducing a taxonomy of graph distribution scenarios, characterizing associated statistical heterogeneities, and developing standardized problem formulations and algorithmic frameworks. Finally, we systematically identify open challenges and promising research directions.

Deep learning detectors for anomalies in dynamic graphs have reached strong accuracy, yet they remain opaque: when an edge is flagged, the analyst receives a score but no reason. This opacity is untenable in the cooperative, regulated information systems where such detectors are deployed, where automated decisions must be auditable and trustworthy. We address this gap for AddGraph, the foundational GCN+GRU framework for edge-level anomaly detection in dynamic graphs, which to our knowledge has never been equipped with any form of explainability. We present a strictly post-hoc explainability framework, X-AddGraph, built on a Dual Spatial-Temporal Attribution (DSTA) mechanism whose three components are each aligned with one of AddGraph's architectural modules: a gradient-based relevance attribution over the current adjacency structure (spatial), a direct reading of the contextual attention weights already computed during inference (short-term temporal, at zero additional cost), and a gradient rollback through the recurrent hidden states (long-term temporal). Because the detector is frozen, detection performance is preserved exactly (Delta AUC = 0, verified empirically to ten decimal places). On the UCI Message benchmark, our trained AddGraph baseline reaches an average per-snapshot AUC of 0.8705, exceeding the originally published result; X-AddGraph reproduces every score identically while adding explanations where none existed. Evaluated across four edge populations - confident true positives, low-confidence true positives, false positives, and random samples - the long-term attribution identifies historical snapshots carrying significantly more counterfactual signal than random selection (0.127 vs. 0.074), a capability that no spatially-blind explainer can provide. We release our implementation for full reproducibility.

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.

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.

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.

This work revealed a relationship between a multi-objective optimization problem and single-objective optimization problems that exist in the multi-objective problem. This work focused on combinatorial problems and investigated the relations between the local optima networks of the single-objective problems and the Pareto optima network of the multi-objective problem. Each of their networks has a graph structure. We divided the entire network into subgraphs. Each subgraph was called a component and characterized by overlapping relations between the single-objective local optima networks and the multi-objective Pareto optima network. Results on multi-objective landscape problems showed that most Pareto optimal solutions were reachable from the single-objective local optimal solutions. This tendency was emphasized by increasing the number of objectives and the objective correlation. The number of co-variables impacted the number of cross-link relations between the single-objective local optima networks and the multi-objective Pareto optima network. The results suggested that searching for single-objective problems is a clue to multi-objective optimization.

Reinforcement learning (RL) search agents commonly model retrieval as free-form natural-language query generation and optimize multi-turn interactions using final-answer rewards. Current studies mainly improve training with denser or more structured credit signals, but rarely examine whether retrieval is properly formulated at the policy-environment interface. We observe pronounced retrieval aliasing during Search-R1 training: rollouts for the same question continue to generate distinct query strings, yet their accumulated evidence sets increasingly overlap. We call this phenomenon retrieval-equivalence collapse; in this regime, trajectories approach utility equivalence with respect to retrieval decisions, leaving within-group returns with little effective retrieval contrast. To address this problem, we propose Harness-G, a graph-structured retrieval framework that redesigns this interface. It reformulates free-form query generation as finite action selection: the policy selects an evidence sentence or entity, or chooses to answer, while the environment constructs the menu, tracks retrieval state, and validates and executes each choice. This interface reduces linguistic aliasing and makes same-state alternatives directly comparable. Building on this interface, we introduce Structured Non-myopic Credit (SNC), which uses a frozen answer scorer to compare the selected action with its alternatives and assigns downstream gains to the earlier actions that enabled them. Across six QA benchmarks, Harness-G achieves the highest average F1 at both evaluated model scales, outperforming the strongest baseline, Graph-R1, by 10.74 points at 1.5B and 3.98 points at 3B.

We present the first implementation of a 3D Gaussian renderer on an Intelligence Processing Unit (IPU), comprising 1,472 independent tiles with only on-chip SRAM; constraints that approximate properties of efficient sensor-processor architectures. Our input scenes are 3D Gaussian maps from real-world sequences. Each tile 'owns' a screen-space region of the framebuffer; Gaussian primitives are routed to destination tiles via Manhattan-distance hops on a north-east-west-south (NEWS) grid, then distributed to overlapping neighbours in an expanding tree pattern. Computation follows the IPU's Bulk Synchronous Parallel (BSP) model, with inter-tile communication defined at compile time. We show this hardware allows us to exploit spatial and temporal locality by enabling local data transfer between cores. We evaluate the bottlenecks in this SRAM-only implementation: inter-tile bandwidth, per-tile SRAM capacity, and workload imbalance from non-uniform Gaussian density. We analyse how these constraints affect performance and render quality. This exploration raises broader questions for conventional GPUs and 3D representations, suggesting that direct inter-SM (streaming multiprocessor) communication might offer ways to reduce DRAM access in GPU kernels. We discuss these implications for the future of on-sensor and DRAM-free architectures. Project page: https://nmjfry.github.io/ipu-3dgs/

Like many optimization-driven domains, railway rescheduling relies on Mixed-Integer Linear Programming (MILP), yet the field's modeling knowledge is scattered across hundreds of papers in incompatible notations, and narrative surveys organize it subjectively: they classify models by vocabulary rather than by structure, and reproduce neither. We present LP Mining with LP2Graph, a method that mines the structure of published LP and MILP formulations into a reproducible dataset and an induced taxonomy. Its core, LP2Graph, represents each formulation admitted by its canonical grammar as a typed variable--equation graph derived from a single canonical model; once a source is extracted into that model, everything downstream is deterministic. Each source is parsed into this model, homologized, and clustered bottom-up (over variables, then constraints and the objective, then whole-model structure) and, separately, by application domain and solution approach; the resulting groups are labeled by a rule-seeded, self-updating classifier. We validate the representation rather than assume it: per-cluster representatives are regenerated as independent LaTeX and re-solved across CBC, HiGHS and Gurobi against the optimum reported in the source paper. The outcome is an objective, repeatable taxonomy of variables, constraints and model types: the principled foundation on which our raiLPminer line of automated railway-rescheduling model development builds.

For robots to work reliably in commercial and industrial applications, can recent advances in agentic coding systems combine interpretable robot programming with the open-world adaptability of model-free policies? We focus on "Variational Automation" (VA), a class of tasks that have larger variations in object geometry and pose than fixed automation. Model-free policies often struggle to close the reliability gap for VA tasks, which must be executed persistently and reliably in commercial and industrial applications. Motivated by prior work on Task and Motion Planning (TAMP) and the Robot Operating System (ROS), we introduce Graph-as-Policy (GaP), a multi-agent coding harness that generates directed computation graphs with perception, planning, and control nodes from a Modular Open Robot Skill Library (MORSL). GaP then generates an internal simulation environment to rehearse task instances with different graphs in parallel to iteratively refine the graph structure and parameters to improve success rates and throughput. Evaluation with 8 new open VA task benchmarks, 4 in-simulation and 4 in real-world, suggests that GaP can achieve success rates that significantly outperform baselines. Details, code, and data can be found online: https://graph-robots.github.io/gap

Neoadjuvant chemotherapy (NAC) response prediction is clinically important for treatment stratification in breast cancer. However, robust pre-treatment pathological complete response (pCR) prediction remains challenging due to insufficient cross-modal modeling, multicenter imaging heterogeneity, and weak evidence-grounded interpretability. We propose ClinRAG-GRAPH, a Clinically informed Retrieval-Augmented Generation Graph framework, for pre-treatment pCR prediction from DCE-MRI, structured clinical variables, and biopsy-derived pathological biomarkers. ClinRAG-GRAPH constructs an intra-patient clinical-prior graph and applies a prior-guided relation-aware graph convolutional network for structured multimodal representation learning. To improve cross-center robustness, we introduce a dual-branch domain-adversarial learning strategy to suppress protocol-related MRI bias while preserving pCR-relevant features. To enhance interpretability, we further incorporate large language model (LLM)-driven subgraph RAG module that retrieves clinically analogous historical cases and integrates retrieved evidence for pCR inference. We assemble a large-scale multicenter NAC breast cancer cohort for extensive validation, drawing from two public sources and three in-house centers.Results show that ClinRAG-GRAPH achieves AUCs of 0.815 on the internal test set and 0.774/0.712 on two external test sets, demonstrating robust pre-treatment pCR prediction across centers. The code is available at the anonymized https://github.com/miccai26-1181/ClinRAG-GRAPH.

Graph neural networks have moved from a niche representation-learning technique to the default model class wherever data carry relational structure. The interesting question is no longer whether message passing helps on a given dataset, but where graph structure earns its computational cost and where it does not. This survey organises the field around a single design space, derives the spectral and spatial formulations from shared first principles, and connects expressive power to the Weisfeiler-Leman hierarchy with explicit statements of what current architectures can and cannot separate. Against that methodological backbone we examine twelve application domains, among them recommendation and social networks, knowledge graphs and language-model integration, drug discovery and molecular property learning, healthcare and neuroscience, computer vision, traffic and urban computing, power and renewable-energy systems, wireless and sixth-generation networks, fraud and cybersecurity, industrial prognostics, materials science, and climate modelling. For each domain we specify the graph-construction choices and their costs, identify which architecture families dominate and why, and separate reported gains from artefacts of weak baselines or favourable splits. A cross-domain comparison exposes recurring patterns: heterophily and scale undercut the same models almost everywhere, temporal graphs remain harder than their static counterparts, and the architectures that top public leaderboards are seldom the ones that reach deployment. We treat over-smoothing, over-squashing, robustness, distribution shift, fairness, and explainability not as a closing checklist but as the constraints that decide adoption.

We introduce TabPFN-CFM, a causal foundation model that can handle multiple causal problems. TabPFN-CFM predicts both causal structure and outcomes from observational data, supports queries on all three levels of Pearl's Causal Hierarchy and uses known graph structure when available to improve predictions. TabPFN-CFM is trained on synthetic datasets, and generalises to real datasets, demonstrating improved performance over both structural and outcome prediction baselines.

Despite recent progress, LLM agents still struggle with reasoning over long interaction histories. While current memory-augmented agents rely on a static retrieve-then-reason paradigm, this rigid pipeline design prevents them from dynamically adapting memory access to intermediate evidence discovered during inference. To bridge this gap, we propose MRAgent, a framework that combines an associative memory graph with an active reconstruction mechanism. We represent memory as a Cue-Tag-Content graph, where associative tags serve as semantic bridges connecting fine-grained cues to memory contents. Operating on this structure, our active reconstruction mechanism integrates LLM reasoning directly into memory access, allowing the agent to iteratively explore and prune retrieval paths based on accumulated evidence. This ensures that memory retrieval is dynamically adapted to the reasoning context while avoiding combinatorial explosion caused by unconstrained expansion. Experiments on the LoCoMo benchmark and LongMemEval benchmark demonstrate significant improvements over strong baselines (up to 23%), while substantially reducing token and runtime cost, highlighting the effectiveness of active and associative reconstruction for long-horizon memory reasoning.

Generating realistic and diverse graphs is a key problem in machine learning, with applications in molecular discovery, circuit design, cybersecurity, and beyond. However, current graph generative models remain limited by scalability and novelty. Diffusion-based methods often require costly full-adjacency operations and long denoising chains, while many autoregressive and hybrid models have at least quadratic complexity. In addition, these models often imitate training graphs rather than generalize beyond them. We propose a lightweight autoregressive framework to address these issues. It uses a structure-guided topological ordering to serialize graphs into regular edge sequences, enabling near log-linear generation, and a two-phase training strategy that combines exploration-oriented augmentation with iterative refinement to reduce overfitting and promote controlled novelty. Experiments on molecular and non-molecular benchmarks show that our approach improves novelty while preserving high validity and uniqueness. The framework also supports both LSTM and Mamba-style causal sequence backbones, with large-memory accelerators enabling longer graph-sequence experiments beyond typical GPU limits.

Shapley values are a widely used tool for attributing importance and interactions among input variables in black-box models, but their computation involves a function defined over an exponentially large space of subsets. We propose TN-SHAP-G, a framework that exploits structure in graph-structured inputs to compute Shapley values and higher-order interaction indices efficiently. Given a predictor and a fixed masking scheme, TN-SHAP-G learns a compact, graph-aligned multilinear surrogate that approximates the masked-input behavior, represented as a tensor network whose topology mirrors the input graph. Once trained from a small number of oracle queries, the surrogate enables deterministic recovery of first- and higher-order Shapley indices via the multilinear extension, without additional model queries or Monte Carlo variance. Experiments on molecular benchmarks show that the learned factorization closely matches exact Shapley values on small graphs and scales efficiently to larger graphs where sampling-based methods become infeasible.

Relational reasoning lies at the heart of intelligence, but existing benchmarks are typically confined to formats such as grids or text. We introduce GraphARC, a benchmark for abstract reasoning on graph-structured data. GraphARC generalizes the few-shot transformation learning paradigm of the Abstraction and Reasoning Corpus (ARC). Each task requires inferring a transformation rule from a few input-output pairs and applying it to a new test graph, covering local, global, and hierarchical graph transformations. Unlike grid-based ARC, GraphARC instances can be generated at scale across diverse graph families and sizes, enabling systematic evaluation of generalization abilities. We evaluate state-of-the-art language models on GraphARC and observe clear limitations. Models can answer questions about graph properties but often fail to solve the full graph transformation task, revealing a comprehension-execution gap. Performance further degrades on larger instances, exposing scaling barriers. More broadly, by combining aspects of node classification, link prediction, and graph generation within a single framework, GraphARC provides a promising testbed for future graph foundation models.

Real-world information needs require access to structurally diverse knowledge sources, from unstructured text and relational tables to knowledge graphs and property graphs. Existing retrievers, however, operate over one source at a time under a fixed query language, leaving the broader landscape of available knowledge fragmented behind incompatible interfaces. A natural attempt at unification would collapse these sources into a shared space, but this erases the structural affordances (such as schemas, ontologies, compositional operators) that give each source its expressive power. Effective retrieval over diverse knowledge, therefore, requires not homogenization but an overarching layer that meets each source on its own terms. To achieve this, we present OmniRetrieval, a framework that takes any natural-language query, identifies appropriate knowledge sources, and dispatches source-native queries to their native execution engines. Across an extensive benchmark spanning 13 datasets and 309 distinct knowledge bases over text, relational, and graph-structured sources, OmniRetrieval exceeds single-source baselines, demonstrating that it can serve as a general-purpose interface to the heterogeneous sources while preserving the structural distinctions that make each source valuable.

Message-passing neural networks (MPNNs) are a powerful framework for learning representations of graph-structured domains. However, weights in MPNNs act on features only, limiting their ability to capture structural patterns. We introduce a novel structure-aware weight sharing principle that explicitly incorporates information inherent to the graph structure. Weights are indexed directly by user-chosen graph invariants, i.e., functions preserved under node permutations, enabling systematic reuse across structurally equivalent subgraphs. We present ShareGNNs, which instantiate this principle within a simple encoder-decoder architecture, resulting in an MPNN with learnable adjacency and transformer-like connectivity. We show that their expressivity is at least as strong as the discriminative power of the chosen invariants, providing explicit control over the model complexity. Experiments on synthetic and real-world data, as well as subgraph counting tasks, demonstrate consistent improvements over standard MPNNs, competitive expressivity beyond the 1-WL test, and scalability to large datasets.

While deep ensembles are widely considered to be the default method for uncertainty quantification in deep learning, their effectiveness for graph-structured data is often simply assumed based on successes in domains like computer vision. We investigate standard deep ensembles specifically for message-passing graph neural networks. Benchmarking across seven datasets representing varied tasks and complexities, we reveal that ensembles provide surprisingly little improvement over a single model. Instead, the observed marginal gains stem primarily from stabilizing optimization noise in point predictions rather than yielding meaningfully better uncertainty estimates. Through an aleatoric-epistemic decomposition, we identify epistemic collapse: independently trained networks consistently converge to overly similar predictions. Because disagreement is the fundamental mechanism through which ensembles capture epistemic uncertainty, this lack of diversity neutralizes their key advantage. Analyzing this phenomenon further, we suggest this collapse is driven by functional rather than weight-space convexity, where distinct parameter solutions induce almost identical behavior. Our results suggest that deep ensemble success does not seamlessly transfer to graph machine learning.

Relational prediction tasks are fundamental in many real-world applications, where data are naturally stored in relational databases (RDBs). Relational Deep Learning (RDL) addresses this problem by modeling RDBs as graphs and applying graph neural networks (GNNs) for end-to-end learning. However, the full-resolution property is commonly adopted as a design principle in graph construction for RDBs to preserve relational semantics, which leads most existing methods to rely on fixed graph structures. In this paper, we propose FROG, a Full-Resolution and Optimizable Graph Structure Learning} framework for RDL that formulates relational structure learning as a learnable table role modeling problem, allowing tables to contribute as nodes and edges in message passing. We further design role-driven message passing mechanisms to capture relational semantics, enabling joint optimization of graph structure and GNN representations. To ensure semantic consistency, we introduce functional dependency constraints that regularize representations across table and entity levels. Extensive experiments demonstrate that our method outperforms existing approaches and reveal how table roles impact downstream tasks, offering new insights into graph construction for RDL

Graph combinatorial optimization (GCO) has attracted growing interest, as many NP-hard problems naturally admit graph formulations, yet their combinatorial explosion renders exact methods computationally intractable. Recent advances in Reinforcement Learning (RL) combined with Graph Neural Networks (GNNs) have significantly improved learning-based GCO solvers. However, existing approaches face limitations in both generalization across diverse graph instances and computational scalability as action spaces grow. To address both challenges, we introduce projection agents, a novel RL-GCO approach that operates directly in a continuous GNN-based action embedding space, predicting a desired latent action in a single forward pass and subsequently decoding it into a valid discrete action. Additionally, we enable fair comparison across RL methods through a shared embedding space for both observations and actions. Across diverse benchmarks, our approach achieves up to 16.2x faster inference and up to 40% better generalization than existing solutions using only simple nearest-neighbor decoding, while opening the door to strong RL performance in super-linear decision spaces with multiple interdependent variables. Finally, we release LaGCO-RL, a Python library that automates latent action-space construction and supports existing RL-GCO solutions, promoting reproducibility and adaptation to new GCO benchmarks.

We introduce Graph-Augmented Sequence-to-Sequence (GA-S2S), a novel framework that integrates a T5-small encoder-decoder with a Relational Graph Attention Network (RGAT) to improve link prediction in knowledge graphs. While existing Seq2Seq models rely solely on surface-level textual descriptions of entities and relations and at best, flatten the neighborhoods of a query entity into a single linear sequence, thereby discarding the inherent graph structure, GA-S2S jointly encodes both textual features and the full $k$-hop subgraph topology surrounding the query entity. By integrating raw encoder outputs with RGAT's relation-aware embeddings, our model captures and leverages richer multi-hop relational patterns and textual information. Our preliminary experiments on the CoDEx dataset demonstrate that GA-S2S outperforms competitive Seq2Seq-based baseline models, achieving up to a 19% relative gain in link prediction accuracy.

Graph Neural Networks (GNNs) have advanced significantly in handling graph-structured data, but a comprehensive framework for evaluating explainability remains lacking. Existing evaluation frameworks primarily involve post-hoc explanations, and operate in the setting where multiple methods generate a suite of explanations for a single model. This makes comparison of explanations across models difficult. Evaluation of inherently interpretable models often targets a specific aspect of interpretability relevant to the model, but remains underdeveloped in terms of generating insight across a suite of measures. We introduce AIM, a comprehensive framework that addresses these limitations by measuring Accuracy, Instance-level explanations, and Model-level explanations. AIM is formulated with minimal constraints to enhance flexibility and facilitate broad applicability. Here, we use AIM in a pipeline, extracting explanations from inherently interpretable GNNs such as graph kernel networks (GKNs) and prototype networks (PNs), evaluating these explanations with AIM, identifying their limitations and obtaining insights to their characteristics. Taking GKNs as a case study, we show how the insights obtained from AIM can be used to develop an updated model, xGKN, that maintains high accuracy while demonstrating improved explainability. Our approach aims to advance the field of Explainable AI (XAI) for GNNs, providing more robust and practical solutions for understanding and improving complex models.

Graph neural networks (GNNs) have emerged as a fundamental tool for learning from graph-structured data, achieving strong performance across a wide range of applications. However, understanding their generalization capabilities remains challenging due to the complex structural dependencies inherent in such data. Existing generalization analyses largely follow the classical machine learning paradigm, focusing primarily on model complexity while overlooking the fundamental role of graph structure. Therefore, in this work, we systematically investigate this role by asking: does the graph structure actually influence generalization, and if so, by how much? To answer the first question and validate our intuition, we theoretically prove that incorporating more edges into the prediction process transforms the input representations to be overly accommodating to the output model, thereby inducing overfitting. To address the second question, we formulate a structural complexity measure based on the number of effective edges and derive a Rademacher complexity-based generalization bound. In doing so, we demonstrate that GNN generalization depends explicitly on structural complexity, alongside traditional parameter-dependent factors. Motivated by these theoretical findings, we propose a structural entropy regularization method. This approach controls structural complexity by regulating effective edges to balance underfitting and overfitting, ultimately improving the generalization performance of GNNs.

Long-term memory is becoming a central bottleneck for language agents. Exsting RAG and GraphRAG systems largely treat memory graphs as static retrieval middleware, which limits their ability to recover complete evidence chains from partial cues, exploit reusable graph-structrual roles, and improve the memory itself through downstream feedback. We introduce SAGE, a Self-evolving Agentic Graph-memory Engine that models graph memory as a dynamic long-term memory substrate. SAGE couples two roles: a memory writer that incrementally constucts structured graph memory from interaction histories, and a Graph Foundation Model-based memory reader to perform retrieval and provide feedback to the memory writer. We provide rigorooous theoretical annalyses supporting the framework. Across multi-hop QA, open-domain retireval, domain-specific review QA, and long-term agent-memory benchmarks, SAGE improves evidence recovery, answer grounding, and retrieval efficiency: after two self-evolution rounds, it achieves the best average rank on multi-hop QA; in zero-shot open-domain transfer, it reaches 82.5/91.6 Recall@2/5 on NQ. Further results on LongMemEval and HaluMem show that traning and reader-writer feedback improve multiple long-term memory and hallucination-diagnostic metrics, suggesting that self-evolving, structure-aware graph memory is a promising foundation for robust long-horizon language agents.

Graph Neural Networks (GNNs) have emerged as a powerful paradigm in Knowledge Graphs (KGs) due to their intrinsic ability to model graph-structured data. However, there remains a lack of a systematic review about GNN-based methodologies across the entire knowledge graph technologies pipeline. To address this gap, we first propose a novel two-level taxonomy framework for GNN-based knowledge graph technologies: the KG technologies pipeline and GNN-based perspective. Specifically, the knowledge graph technologies pipeline covers knowledge graph construction, knowledge graph embedding, knowledge reasoning and knowledge graph applications. Meanwhile, the GNN-based perspective provides a new categorization of knowledge graph technologies with GNN models, such as GCN, GAT, and HGNN. Then, we analyze the advantages of GNN technology based on the characteristics of different tasks in the knowledge graph lifecycle. Furthermore, we detailed review various GNN-based models for knowledge graph following the proposed taxonomy, and summarize strengths and limitations. Finally, we discuss unresolved challenges and outline promising directions for future research.

Epigenetic clocks based on DNA methylation have emerged as powerful tools for estimating biological age, with broad applications in aging research, age-related disease studies, and longevity science. Despite advances across machine learning approaches to epigenetic age prediction, spanning penalised linear regression, deep feedforward networks, residual architectures, and graph neural networks, no existing method jointly models co-methylation graph structure and site-specific DNA sequence context within a unified framework. We propose a unified sequence--graph integration framework for epigenetic age prediction that addresses this gap, integrating eight-dimensional DNA sequence statistical features through a lightweight gated modulation mechanism that adaptively scales each site's methylation signal according to its sequence-determined biological relevance prior to graph convolution. Evaluated on 3,707 blood methylation samples against a comprehensive set of baselines, our method achieves a test MAE of 3.149 years, a 12.8% improvement over the strongest graph-based baseline. Biologically informed statistical features outperform CNN-based sequence encoding, demonstrating that handcrafted sequence features are more effective than end-to-end learned representations in this data regime. Post-hoc interpretability analysis identifies CpG density and local adenine frequency as features with age-dependent importance shifts, consistent with known mechanisms of age-related hypermethylation at CpG-dense promoter regions. Our code is at https://github.com/yaoli2022/graphage-seq.

Large language models (LLMs) are increasingly used in K-12 education, yet existing benchmarks such as C-Eval, CMMLU, GaokaoBench, and EduEval mainly evaluate factual recall through exam-style question answering. Effective educational AI additionally requires curriculum cognition: understanding how knowledge is structured through prerequisite chains, concept taxonomies, experiment-concept links, and pedagogical sequencing. To address this gap, we introduce K12-KGraph, a curriculum-aligned knowledge graph extracted from official People's Education Press textbooks across mathematics, physics, chemistry, and biology from primary to high school. The graph contains seven node types (Concept, Skill, Experiment, Exercise, Section, Chapter, Book) and nine relation types covering taxonomy, prerequisite, association, verification, assessment, location, and order. Based on this graph, we construct two resources: (1) K12-Bench, a 23,640-question multi-select benchmark spanning five graph-derived task families (Ground, Prereq, Neighbor, Evidence, and Locate); and (2) K12-Train, a KG-guided supervised fine-tuning corpus of approximately 2,300 QA pairs synthesized from graph structure and node attributes. Experiments reveal substantial deficiencies in curriculum cognition: on K12-Bench, Gemini-3-Flash achieves only 57% exact match, while the best open-source model, Gemma-4-31B-IT, reaches 46%. Under a strictly matched 2,300-sample SFT budget on Qwen3-4B-Base and Llama-3.1-8B-Base, K12-Train consistently outperforms equally sized subsets from eight mainstream instruction-tuning corpora on both GaokaoBench and EduEval, demonstrating that curriculum-structured supervision is highly sample-efficient for educational tuning. We release the graph, benchmark, training data, and full construction pipeline.

Scene graphs (SGs) represent objects and their relationships as structured graphs, enabling applications in image generation, robotics, and 3D understanding. Recent work suggests that conditioning image generation on scene graphs improves compositional fidelity compared to text-only prompting. However, since users typically provide text rather than structured graphs, a key challenge is to generate scene graphs from natural language. Prior work on discrete diffusion has demonstrated success in generating generic graphs such as molecules and circuits, but fails to account for the hierarchical structure and strong dependencies between objects, edges, and relations in scene graphs. We address this limitation by introducing a dependency-aware, hierarchically constrained discrete diffusion model for scene graph generation. Our approach decouples structure and semantics across the forward and reverse processes, enabling the model to capture conditional dependencies. At inference time, we perform training-free conditioning to sample text-aligned scene graphs. We evaluate our method on standard SG benchmarks and demonstrate improvements over both continuous and discrete graph generation baselines across graph and layout metrics. When fed to downstream image generation, our approach yields improved compositional alignment compared to text-to-image models, particularly in multi-object scenarios.

Graph-based agent memory is increasingly used in LLM agents to support structured long-term recall and multi-hop reasoning, but it also creates a new poisoning surface: an attacker can inject a crafted relation into graph memory so that it is later retrieved and influences agent behavior. Existing agent-memory poisoning attacks mainly target flat textual records and are ineffective in graph-based memory because malicious relations often fail to be extracted, merged into the target anchor neighborhood, or retrieved for the victim query. We present SHADOWMERGE, a poisoning attack against graph-based agent memory that exploits relation-channel conflicts. Its key insight is that a poisoned relation can share the same query-activated anchor and canonicalized relation channel as benign evidence while carrying a conflicting value. To realize this, we design AIR, a pipeline that converts the conflict into an ordinary interaction that can be extracted, merged, and retrieved by the graph-memory system. We evaluate SHADOWMERGE on Mem0 and three public real-world datasets: PubMedQA, WebShop, and ToolEmu. SHADOWMERGE achieves 93.8% average attack success rate, improving the best baseline by 50.3 absolute points, while having negligible impact on unrelated benign tasks. Mechanism studies show that SHADOWMERGE overcomes the three key limitations of existing agent-memory poisoning attacks, and defense analysis shows that representative input-side defenses are insufficient to mitigate it. We have responsibly disclosed our findings to affected graph-memory vendors and open sourced SHADOWMERGE.

Bilevel graph structure learning is widely understood to improve graph neural networks by jointly optimizing model parameters and a learned graph structure, with the resulting performance gain attributed to the rewired adjacency. We find that this attribution may be overstated: training-dynamics effects in the inner loop, rather than the rewiring itself, capture a substantial share of the gain. To establish this, we introduce frozen-$φ$, a control that freezes the graph while retaining the inner-loop training schedule. This decomposes the bilevel gain into an inner channel of $T$-step training dynamics with implicit gradient regularization and a graph channel of the graph rewiring itself. On spatio-temporal flow forecasting the inner channel matches or exceeds the full bilevel pipeline, accounting for 78-101% of the gain; on node classification it accounts for 37-44% under a Bernoulli edge-level parameterization. We also verify that classical spectral diagnostics can dissociate from task gain. We propose frozen-$φ$ as a standardized diagnostic for bilevel graph structure learning, with graph distillation as a method-agnostic complement. A three-precondition framework further predicts the sign of the bilevel gain on all six benchmarks.

When a machine learning (ML) model forecasts an undesired event, one often seeks a decision to avoid it, known as the avoiding undesired future (AUF) problem. Many rehearsal learning methods have been proposed for AUF, but they rely on an underlying graph structure; learning such a graph from observational data is challenging and can incur substantial estimation error. In this work, we demonstrate that the order structure can be sufficient for AUF decision-making, and propose the first order-based rehearsal learning method. Although an order is less informative than a graph, it can be sufficient to identify the influence of decisions from observational data, suggesting that learning the entire graph is not always necessary. To learn the order, we develop an information-theoretic method that imposes no restrictions on the form of structural functions or the type of noise distributions. For AUF decision-making, we construct an order-based sampler to approximate the influence of decisions and, combined with a surrogate objective for maximizing the post-decision success probability, reduce the AUF task to a differentiable optimization problem. Experiments show that our order learning method outperforms existing methods, and that our AUF approach not only surpasses methods relying on learned graphs or learned orders, but also matches or even exceeds oracle baselines that are given the true graph.

Generative models can produce individual game facets, but whole-game generation remains an orchestration problem: narrative, level structure, encounters, objectives, rewards, and visuals must express shared intent. We present Forking Garden, a branching game generation system that uses narrative archetype as a persistent semantic signal across the generation pipeline. Narrative progression is represented as soft Rise/Fall states; candidate plot nodes are generated before structural constraints assemble archetype-conforming graphs. The same state then conditions encounter composition, objectives, rewards, and runtime difficulty adaptation, while a shared symbolic schema preserves narrative entities and gameplay configurations through content instantiation. Across 10 storylines, generated paths exhibit distinguishable archetypal trajectories, narrative threat predicts damage taken by a threat-blind combat agent, and generate-first-constrain-later yields 2.6 times the entity diversity of a hierarchical baseline. A 16-participant study further suggests that propagated Rise/Fall distinctions can remain meaningful during play, while also supporting narrative understanding and creator-oriented interpretation.

Heterogeneous graphs with heterophily have emerged as a powerful abstraction for modeling complex real-world systems, where nodes of different types and labels interact in diverse and often non-homophilous ways. Despite recent advances, robust representation learning for such graphs remains largely unexplored, particularly in the presence of noisy or misleading connectivity. In this work, we investigate this problem and identify structural noise as a critical challenge that significantly degrades model performance. To address this issue, we propose a unified framework, Heterogeneous Graph Unified Learning (HGUL), which jointly handles heterophily and noisy graph structures. The framework consists of three complementary modules: a kNN-based graph construction module that recovers reliable local neighborhoods, a graph structure learning module that adaptively refines the adjacency by filtering noisy edges, and a heterogeneous affinity learning module that captures class-level relationships via an extended affinity matrix derived from a polynomial graph kernel. Extensive experiments on multiple datasets demonstrate that HGUL consistently outperforms existing methods on clean graphs and maintains strong robustness under varying levels of structural noise. The results further underscore the importance of jointly modeling heterophily and noise in heterogeneous graph learning.

Current research on distributed multi-modal learning typically assumes that clients can access complete information across all modalities, which may not hold in practice. In this paper, we explore patchwork learning, in which the modalities available to different clients vary, and the objective is to impute the missing modalities for each client in an unsupervised manner. Existing methods are shown not to fully utilize the modality information as they tend to rely on only a subset of the observed modalities. To address this issue, we propose GraphPL, which combines graph neural networks with patchwork learning to flexibly integrate all observed modalities and remains robust with noisy inputs. Experimental results show that GraphPL achieves SOTA performance on benchmark datasets. Our results on real-world distributed electronic health record dataset show GraphPL learns strong downstream features and enables tasks like disease prediction via superior modality imputation.

Vision Graph Neural Networks (ViGs) represent an image as a graph of patch tokens, enabling adaptive, feature-driven neighborhoods. Unlike CNNs with fixed grid biases or Vision Transformers with global token interactions, ViGs rely on dynamic graph convolution: at each layer, a feature-dependent graph is built via k-nearest-neighbor (kNN) search on current patch features, followed by message passing. This per-layer graph construction is the main bottleneck, consuming 50--95% of graph convolution time on CPUs and GPUs, scaling as $O(N^2)$ with the number of patches $N$, and creating a sequential dependency between graph construction and feature updates. We introduce GraphLeap, a simple reformulation that removes this dependency by decoupling graph construction from feature update across layers. GraphLeap performs the feature update at layer $\ell$ using a graph built from the previous layer's features, while simultaneously using the current layer's features to construct the graph for layer $\ell+1$. This one-layer-lookahead graph construction enables concurrent graph construction and message passing. Although using prior-layer features can introduce minor accuracy degradation, lightweight fine-tuning for a few epochs is sufficient to recover the original accuracy. Building on GraphLeap, we present the first end-to-end FPGA accelerator for Vision GNNs. Our streaming, layer-pipelined design overlaps a kNN graph construction engine with a feature update engine, exploits node- and channel-level parallelism, and enables efficient on-chip dataflow without explicit edge-feature materialization. Evaluated on isotropic and pyramidal ViG models on an Alveo U280 FPGA, GraphLeap achieves up to $95.7\times$ speedup over CPU and $8.5\times$ speedup over GPU baselines, demonstrating the feasibility of real-time Vision GNN inference.

The consensus that GCN, GraphSAGE, GAT, and EvolveGCN outperform feature-only baselines on the Elliptic Bitcoin Dataset is widely cited but has not been rigorously stress-tested under a leakage-free evaluation protocol. We perform a seed-matched inductive-versus-transductive comparison and find that this consensus does not hold. Under a strictly inductive protocol, Random Forest on raw features achieves F1 = 0.821 and outperforms all evaluated GNNs, while GraphSAGE reaches F1 = 0.689 +/- 0.017. A paired controlled experiment reveals a 39.5-point F1 gap attributable to training-time exposure to test-period adjacency. Additionally, edge-shuffle ablations show that randomly wired graphs outperform the real transaction graph, indicating that the dataset's topology can be misleading under temporal distribution shift. Hybrid models combining GNN embeddings with raw features provide only marginal gains and remain substantially below feature-only baselines. We release code, checkpoints, and a strict-inductive protocol to enable reproducible, leakage-free evaluation.

Large Language Models (LLMs) have shown strong potential for recommendation (LLMRec) due to their powerful reasoning and generalization abilities. However, effectively aligning the textual semantics modeled by LLMs with the collaborative signals remains a key challenge. Existing methods either translate collaborative information into textual prompts or inject pre-trained embeddings into the LLM, both of which treat structural information as static input and fail to capture high-order relational dependencies. To bridge this gap, we propose GraphLoRA, a novel framework that generalizes low-rank adaptation from independent to structure-aware propagation. GraphLoRA embeds a trainable graph message-passing network within the low-rank adaptation pathway, enabling structural signals to propagate through the parameter space. This design allows collaborative topology to explicitly guide parameter updates, fostering deep integration between graph-structured and textual semantic information. Extensive experiments on multiple benchmarks demonstrate that GraphLoRA not only outperforms state-of-the-art LLM-based recommendation methods but also achieves superior generalization, effectively balancing structural reasoning capability with computational efficiency. Code is available at \href{https://github.com/wgj15965/GraphLoRA}{https://github.com/wgj15965/GraphLoRA}.

Ollivier-Ricci curvature (ORC), defined via the Wasserstein distance that captures rich geometric information, has received growing attention in both theory and applications. However, the high computational cost of Wasserstein distance evaluation has significantly limited the broader practical use of ORC. To alleviate this issue, previous work introduced a computationally efficient lower bound as a proxy for ORC based on 1-hop random walks, but this approach empirically exhibits large gaps from the exact ORC. In this paper, we establish a substantially tighter lower bound for ORC than the existing lower bound, while retaining much lower computational cost than exact ORC computation, with practical speedups of tens of times. Moreover, our bound is not restricted to 1-hop random walks, but also applies to k-hop random walks (k > 1). Experiments on several fundamental graph structures demonstrate the effectiveness of our bound in terms of both approximation accuracy and computational efficiency.

Learning algorithmic computation often requires explicit relational intermediate states, yet many graph processors maintain their primary states on individual entities. We introduce \fnet and \textbf{Pivotal Attention} (PA), which maintain ordered pair states and update a target relation $(i,k)$ by attending over candidates formed from $(i,j)$ and $(j,k)$ for every pivot $j$. Motivated by the pair-and-pivot structure of Floyd--Warshall, PA learns relation composition and pivot weighting in parallel rather than executing its ordered min-plus recurrence. The \kfnet{k} framework extends this operation to ordered $k$-tuples, with Self-Attention and PA as its $k=1$ and $k=2$ cases at the attention-operation level. Under atomic tuple initialization and invariant readout, we show that \kfnet{k} is no more graph-discriminative than k-FWL; on BREC, each evaluated variant matches the success set of its corresponding WL reference. \fnet further achieves 96.64% mean accuracy under the reported CLRS-30 protocol and a 99.8% optimality rate with 10 samples on held-out non-metric TSP instances.

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

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

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

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