Graph Representations

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.

One of the most challenging problems in graph machine learning is generalizing across graphs with diverse properties. Graph neural networks (GNNs) face a fundamental limitation: they require separate training for each new graph, preventing universal generalization across diverse graph datasets. A critical challenge facing GNNs lies in their reliance on labeled training data for each individual graph, a requirement that hinders the capacity for universal node classification due to the heterogeneity inherent in graphs -- differences in homophily levels, community structures, and feature distributions across datasets. Inspired by the success of large language models (LLMs) that achieve in-context learning through massive-scale pre-training on diverse datasets, we introduce NodePFN. This universal node classification method generalizes to arbitrary graphs without graph-specific training. NodePFN learns posterior predictive distributions (PPDs) by training only on thousands of synthetic graphs generated from carefully designed priors. Our synthetic graph generation covers real-world graphs through the use of random networks with controllable homophily levels and structural causal models for complex feature-label relationships. We develop a dual-branch architecture combining context-query attention mechanisms with local message passing to enable graph-aware in-context learning. Extensive evaluation on 23 benchmarks demonstrates that a single pre-trained NodePFN achieves 71.27 average accuracy. These results validate that universal graph learning patterns can be effectively learned from synthetic priors, establishing a new paradigm for generalization in node classification.

Current AI-assisted programming tools are predominantly linear and chat-based, which deviates from the iterative and branching nature of programming itself. Our preliminary study with developers using AI assistants suggested that they often struggle to explore alternatives, manage prompting sequences, and trace changes. Informed by these insights, we created EvoGraph, an IDE plugin that integrates AI interactions and code changes as a lightweight and interactive development graph. EvoGraph automatically records a branching AI-assisted coding history and allows developers to manipulate the graph to compare, merge, and revisit prior collaborative AI programming states. Our user study with 20 participants revealed that EvoGraph addressed developers' challenges identified in our preliminary study while imposing lower cognitive load. Participants also found the graph-based representation supported safe exploration, efficient iteration, and reflection on AI-generated changes. Our work highlights design opportunities for tools to help developers make sense of and act on their problem-solving progress in the emerging AI-mediated programming context.

Retrieval-augmented generation (RAG) remains unreliable in long-form settings, where retrieved evidence is noisy or contradictory, making it difficult for RAG pipelines to maintain factual consistency. Existing approaches focus on retrieval expansion or verification during generation, leaving conflict resolution entangled with generation. To address this limitation, we propose ArbGraph, a framework for pre-generation evidence arbitration in long-form RAG that explicitly resolves factual conflicts. ArbGraph decomposes retrieved documents into atomic claims and organizes them into a conflict-aware evidence graph with explicit support and contradiction relations. On top of this graph, we introduce an intensity-driven iterative arbitration mechanism that propagates credibility signals through evidence interactions, enabling the system to suppress unreliable and inconsistent claims before final generation. In this way, ArbGraph separates evidence validation from text generation and provides a coherent evidence foundation for downstream long-form generation. We evaluate ArbGraph on two widely used long-form RAG benchmarks, LongFact and RAGChecker, using multiple large language model backbones. Experimental results show that ArbGraph consistently improves factual recall and information density while reducing hallucinations and sensitivity to retrieval noise. Additional analyses show that these gains are evident under conflicting or ambiguous evidence, highlighting the effectiveness of evidence-level conflict resolution for improving the reliability of long-form RAG. The implementation is publicly available at https://github.com/1212Judy/ArbGraph.

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}.

The advent of Large Language Models (LLMs) has fundamentally reshaped the way we interact with graphs, giving rise to a new paradigm called GraphLLM. As revealed in recent studies, graph learning can benefit from LLMs. However, we observe limited benefits when we directly utilize LLMs to make predictions for graph-related tasks within GraphLLM paradigm, which even yields suboptimal results compared to conventional GNN-based approaches. Through in-depth analysis, we find this failure can be attributed to LLMs' limited capability for processing graph data and their tendency to overlook graph information. To address this issue, we propose LoReC (Look, Remember, and Contrast), a novel plug-and-play method for GraphLLM paradigm, which enhances LLM's understanding of graph data through three stages: (1) Look: redistributing attention to graph; (2) Remember: re-injecting graph information into the Feed-Forward Network (FFN); (3) Contrast: rectifying the vanilla logits produced in the decoding process. Extensive experiments demonstrate that LoReC brings notable improvements over current GraphLLM methods and outperforms GNN-based approaches across diverse datasets. The implementation is available at https://github.com/Git-King-Zhan/LoReC.

Equality saturation (EqSat) is a powerful optimization paradigm that compactly represents many equivalent programs in an e-graph and delays commitment until extraction selects a lowest-cost program. Making EqSat effective, therefore, requires not only domain-specific rewrite rules but also domain-specific strategies. Today, much of this strategy design is still manual, making it a major obstacle to automating e-graph-based compilers. Recent rule-synthesis frameworks can automatically infer large rewrite vocabularies from semantic specifications, but they also enlarge the rewrite space and further exacerbate e-graph explosion. Although large language models (LLMs) make automated strategy synthesis plausible, directly evolving backend code remains ineffective in practice. The search lacks reusable strategy abstractions and actionable feedback, and can easily trigger e-graph explosion or converge to poor designs. We present EggMind, an LLM-guided, end-to-end framework for synthesizing reusable EqSat strategies. At its core, EggMind introduces a domain-specific language, EqSatL, to represent EqSat strategies as explicit and inspectable artifacts. It then proposes an LLM-guided agentic workflow, equipped with novel techniques including proof-derived rewrite motif caching and tractability guidance, to search efficiently for high-quality strategies while keeping synthesis stable under e-graph growth. Evaluation shows that EggMind substantially improves the resource-quality trade-off on vectorization benchmarks, reducing final cost by 45.1% and peak RAM by 69.1% relative to full EqSat. We further show that the same methodology transfers effectively to an XLA-based tensor compiler, and demonstrate its practical potential in a logic-synthesis case study with augmented rewrite spaces.

Generating synthesizable Verilog for large, hierarchical hardware designs remains a significant challenge for large language models (LLMs), which struggle to replicate the structured reasoning that human experts employ when translating complex specifications into RTL. When tasked with producing hierarchical Verilog, LLMs frequently lose context across modules, hallucinate interfaces, fabricate inter-module wiring, and fail to maintain structural coherence - failures that intensify as design complexity grows and specifications involve informal prose, figures, and tables that resist direct operationalization. To address these challenges, we present VeriGraphi, a framework that introduces a spec-anchored Knowledge Graph as the architectural substrate driving the RTL generation pipeline. VeriGraphi constructs a HDA, a structured knowledge graph that explicitly encodes module hierarchy, port-level interfaces, wiring semantics, and inter-module dependencies as first-class graph entities and relations. Built through iterative multi-agent analysis of the specification, this Knowledge Graph provides a deterministic, machine-checkable structural scaffold before code generation. Guided by the KG, a progressive coding module incrementally generates pseudo-code and synthesizable RTL while enforcing interface consistency and dependency correctness at each submodule stage. We evaluate VeriGraphi on a benchmark of three representative specification documents from the National Institute of Standards and Technology and their corresponding implementations, and we present a RV32I processor as a detailed case study to illustrate the full pipeline. The results demonstrate that VeriGraphi enables reliable hierarchical RTL generation with minimal human intervention for RISC-V, marking a significant milestone for LLM-generated hardware design while maintaining strong functional correctness.

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.

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.

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

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

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

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

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

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

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

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

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

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.

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