Graph Representations

The HIPE-2026 shared task introduces person-place relation extraction from multilingual historical newspapers as a new evaluation track, classifying the at and isAt relations between pre-annotated person and location mentions in English, French, and German. Motivated by the cost of processing historical archives at scale, our team (DS@GT HIPE, team 2 in the official results) investigates how far a lightweight, interpretable system can go without any pretrained language model at the relation classification stage. Our approach builds a document-level graph from dependency parses, extracts proximity-based and part-of-speech features for each entity pair, and classifies them with small scikit-learn ensembles or compact Graph Attention Networks, keeping every submitted run under 847K parameters. On the official evaluation (Test A, the newspaper test set), our best run reached a macro recall of 0.5142, ranking 3rd on the Efficiency profile while placing mid-table on Accuracy among the 17 participating teams. Two findings stand out. First, minimum character distance alone captures most of the classification signal; adding further engineered features yields inconsistent gains and sometimes degrades performance, echoing prior evidence that argument distance dominates relation extraction. Second, document-grouped cross-validation is essential on this corpus: pair-level splits inflate scores by 25-37 percentage points because entity mentions recur across documents, a data-leakage effect that grouped cross-validation removes.

Vision-language models (VLMs) provide a unified representation space for textual and visual information, yet their potential as general-purpose backbones for graph-structured data remains largely unexplored. In practice, attributed graphs exhibit substantial modality heterogeneity: some graphs contain only textual node attributes, others only visual attributes, while still others provide both. Existing graph learning approaches are typically designed for fixed modality schemas, requiring separate models for different settings and limiting scalability and cross-graph generalization. To bridge this gap, we present OMG-VLM (One Model, Many Graphs with Vision-Language Models), a unified framework for learning over attributed graphs across heterogeneous modality schemas. OMG-VLM leverages a pretrained VLM as a shared backbone and introduces structure-aware graph adapters that integrate neighborhood information while remaining compatible with the VLM's native embedding space. This design enables effective learning over text-attributed, image-attributed, and multimodal-attributed graphs within a single model. Extensive experiments across diverse domains show that OMG-VLM consistently outperforms state-of-the-art GNN- and LLM-based baselines on attributed graph learning tasks such as node classification and link prediction, while exhibiting strong generalization to unseen graphs and varying modality schemas. The source code is available at https://github.com/Jo-eyang/OMG-VLM.

Node representation learning has advanced rapidly, yet most existing methods rely on per-dataset training and hyperparameter tuning. This dataset-specific optimization comes from the difficulty of designing reusable graph models that generalize across diverse graph datasets. In this work, we introduce Node4All, a node representation learner applicable to arbitrary graph datasets without any dataset-specific optimization. Node4All is built on two complementary ideas. At the architectural level, we introduce the Channel Graph Transformer (CGT), which enables a single fixed parameterization to process arbitrary graph datasets. At the learning level, we propose a self-supervised learning based on a series of synthetic graphs. Together, these components enable generalization beyond individual datasets, which is infeasible with existing architectures and learning frameworks. We extensively evaluate Node4All on node classification across 25 benchmarks against 21 baselines, covering both supervised and self-supervised methods. Despite all baselines being trained and optimized for each dataset, a single Node4All, applied uniformly across the datasets, achieves a competitive ranking of 5th among 21 baselines. Moreover, Node4All supports one-shot and in-context learning with an appropriate predictor and outperforms recent graph foundation models (GFMs) in these settings. These results demonstrate that Node4All not only achieves reusability across arbitrary graph datasets, but also remains an effective solution in practice. Code and model checkpoints are available in https://github.com/dooho00/node4all.

Large language models (LLMs) are increasingly used to automate data-processing workflows, yet coding agents typically produce scripts that are not automatically materialized as persistent, editable platform artifacts. We call this disconnect the \textit{NL2Pipeline gap}. To bridge it, we introduce \textsc{DataFlow-Harness}, a platform that guides an LLM agent to construct platform-native directed acyclic graphs (DAGs) through typed, incremental mutations rather than free-form scripts. The platform combines \textsc{DataFlow-Skills} for procedural guidance, a Model Context Protocol (MCP) layer that exposes the live operator registry and current pipeline state, and \textsc{DataFlow-WebUI}, which synchronizes conversational authoring with a visual DAG editor. On a 12-task data-engineering benchmark, \textsc{DataFlow-Harness} achieves a 93.3% observed end-to-end pass rate. Relative to Vanilla Claude Code, it reduces measured monetary cost by 72.5% and generation latency by 49.9%; its observed pass rate is within 0.9 percentage points of the Context-Aware Claude Code baseline while its cost is 42.8% lower. Per-task analysis indicates that Skills are most useful when construction depends on implicit procedural knowledge. These results show that live platform grounding can produce persistent, editable workflow artifacts with an observed reliability close to script-generation baselines and with lower measured construction cost and latency.

Exhaustive site-by-site interventions on a neural network's computational graph -- activation-patching sweeps, circuit-discovery searches, systematic ablation studies -- mutate the graph at every candidate site, and their cost is dominated by recomputation after each mutation. On a reactive graph engine whose invalidation provably touches exactly the downstream cone of a mutated node, we give a complete cost accounting for such workloads. First, the aggregate speedup of an exhaustive sweep over independent full recomputations is not a universal constant: if per-layer weight varies regularly with depth at Karamata index q, the ratio converges to (q+2)/(q+1) when weight concentrates near the output and to q+2 near the input, recovering 2 only in the depth-uniform case; a wall-clock corollary predicts a ceiling of about 1.79, below 2, until interpreter overhead is compiled away. Second, we prove the exact cost of a sequence of persistent mutations, never undone between insertions: the interleaved cost exceeds the isolated sum by an exact overcount summed over comparable site pairs, with closed-form extremes over insertion orders, while batched application is order-independent and sub-additive, costing exactly the union of the sites' cones plus the fresh nodes. Third, we prove the exact mirror of forward locality for the backward pass, showing it collapses the aggregate speedup to 1 under backpropagation on architectures without long skip connections. Every identity is validated on NeuroDSL, a reactive graph engine in Julia: measured sweep ratios converge to the predicted limits under four cost profiles; the training-mode ratio collapses to 1 at the predicted rate; and all 18 per-graft sequential costs and the batched total match the closed forms at zero tolerance across three insertion orders.

Function-preserving network growth techniques such as Net2Net and progressive stacking expand a model's capacity without destroying its learned function, but existing formulations either tolerate numerical perturbations or require a full rebuild of the training program. We formalize Exact Network Surgery: the in-place insertion of a residual block into a live computational graph such that (i) the network function is preserved -- bit-exactly under explicit floating-point hypotheses -- and (ii) inserted parameters remain trainable immediately after insertion. We prove an identity-morphism theorem for gated residual blocks, a structural-locality theorem showing that a reactive invalidation engine recomputes exactly the downstream cone of the insertion point, leaving every other node's value and optimizer state untouched, and an escape-from-initialization proposition showing that the Gradient Shadowing gate alpha, initialized at zero over a randomly initialized branch, receives a generically non-zero gradient at insertion time. We identify a degenerate configuration -- zero-initialized output projections combined with a zero gate -- that is an exact saddle point gradient descent cannot escape. Every claim is validated on the reference implementation in NeuroDSL, a reactive graph engine in Julia: grafting is bit-exact on every logit tested (0 mismatches out of 1600); the gate escapes zero at the first optimizer step and unlocks branch gradients at the second, exactly as predicted; the degenerate configuration exhibits gradients identically zero for the entire 600-step run; surgery cost tracks downstream cone size with r = 0.9992 while graft-plus-invalidation bookkeeping is constant (about 0.75 ms) across insertion depths; and training resumes bit-identically across a real process restart. A flagged preliminary appendix reports first single-seed observations on post-insertion gate dynamics.

Automated individual animal re-identification is essential for large-scale biodiversity monitoring; however, field imagery complicates separating identity cues from nuisance variation in pose, illumination, background, resolution, and species-specific morphology. The DS@GT ARC submission to AnimalCLEF 2026 introduces a multi-species image-clustering system for re-identifying Eurasian lynx, fire salamanders, loggerhead sea turtles, and Texas horned lizards. Instead of relying on a single descriptor or nearest-neighbor retrieval, this approach formulates re-identification as species-aware graph construction over candidate image pairs. The pipeline integrates tailored preprocessing, global candidate retrieval, LightGlue-based local verification with multiple keypoint families, LightGBM pair scoring, conservative edge admission, and Leiden community detection. This design directly addresses a primary failure mode of clustering-based re-identification: high-scoring false pairs that act as bridge edges and merge distinct individuals through transitive closure. Across species, ablation studies demonstrate that local feature support, foreground-aware preprocessing, and species-specific backbone selection enhance pair evidence, while graph operating points determine the trade-off between fragmentation and over-merging. The selected submission achieved a public ARI of 0.733 and a private ARI of 0.674, ranking fifth among 230 teams. These results indicate that robust wildlife re-identification requires not only strong visual representations but also calibrated integration of global similarity, local identity markings, neighborhood context, and graph-level constraints. The code can be found at https://github.com/dsgt-arc/animalclef-2026.

Egocentric Visual Question Answering (VQA) has attracted widespread attention as an important task for enabling Multimodal Large Language Models (MLLMs) to interact with the real world. However, existing MLLMs struggle to perform effective spatial reasoning in complex egocentric scenes due to their limited spatial perception capabilities. To this end, we introduce Ego Scene Augmentation (ESA), an egocentric spatial perception framework, which actively enhances the spatial perception capabilities from the egocentric perspective, powered by the proposed Ego-element Graph. Our core insight is leveraging the Ego-element Graph as an intermediary representation to augment the egocentric spatial perception of MLLMs via visual foundational models. Specifically, we 1) construct the Ego-element Graph, which encapsulates and integrates egocentric spatial features enabled by visual foundational models; 2) enhance the spatial perception capabilities of MLLMs via the Ego-element Graph for ego-perspective scenes. Our proposed ESA framework presents significant performance improvement on the EgoTextVQA benchmark. We achieve an 8.14% gain on the indoor setting and an 8.72% gain on the outdoor setting. Furthermore, our ESA shows the most impressive performance improvement in the shopping subset of the indoor setting. The project code is publicly available.

We present cayleyR, an R package for solving permutation puzzles by detecting cycle intersections in Cayley graphs. The core algorithm performs an iterative bidirectional search: from both the initial and target permutation states, random operation sequences generate cycles in the Cayley graph of the symmetric group Sn; their intersection yields a connecting path. When no direct intersection is found, a distance-guided bridge selection narrows the gap, and the process repeats. The package targets the TopSpin(n,k) puzzle, whose state space is a Cayley graph of Sn generated by a cyclic shift and a prefix reversal. We describe the mathematical framework, the algorithm, and its implementation, which combines a C++ hash-indexed state store with optional Vulkan GPU acceleration. The software is publicly available on CRAN.

Small language models (SLMs) have shown promise for zero-shot molecular property prediction from SMILES strings, yet they often suffer from structural blindness because sequence representations under-specify key graph-topological cues. We propose a modular Context-Augmented Prompting framework that enables agentic tool use at inference time: a trained GNN expert model provides a predictive hint with confidence, and a GNN extracts an instance-specific explanatory subgraph (e.g., a subgraph SMILES and an accompanying explanatory paragraph). We evaluate three commonly used SLMs on MUTAG and Tox21 under five prompting configurations ranging from SMILES-only to using all available tools at hand. Across two datasets, enriching prompts with graph-derived context yields substantial accuracy gains, often exceeding 25% relative improvement and up to 74% on Tox21. We further validate the functional relevance of the extracted motifs via a necessity-based edge-drop intervention. Despite the observed gains, a persistent gap remains to specialized GNN models, highlighting both the value and limits of text-conditioned reasoning for molecular structure.

Finite groups are rigid algebraic objects, whose Cayley graphs expose a rich network geometry through which group-theoretic structure can be measured, compared, and learned. In this paper, a dataset of $131{,}406$ Cayley graphs is constructed, covering all groups of order at most $767$ except order $512$, recording exact algebraic labels for group properties together with a broad collection of graph, cycle, distance, and spectral statistics. This census aims to provide novel benchmarks for studying how finite-group properties are reflected in Cayley graph observables. It also yields new enumerative contributions: alongside recovering known OEIS sequences for standard group classes, new sequences for monolithic groups and for groups generated by at most three, four, and five elements are contributed to the OEIS. The accompanying network analysis identifies several empirical regularities and formulates testable conjectures, including relationships involving square clustering, Cayley graph diameter, average graph disorder, and spectral eigengaps of nilpotent groups. Finally, a comparison between classical models, an MLP, and graph neural network architectures is performed for predicting algebraic group properties directly from Cayley graph data. The results show that engineered graph statistics are highly informative, while GNNs, especially GIN and in some fixed-order settings GCN, can recover substantial structural signal directly from the graph. Such that graph-aware architectures show phases of optimality on these group-theoretic graph representations.

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.

Determining whether one finite group is isomorphic to a subgroup of another is a fundamental problem in computational group theory. In this work, we propose a Siamese Graph Neural Network (Siamese GNN) for subgroup prediction using Cayley graph representations of finite groups. Each input group is represented by its undirected Cayley graph and encoded by one branch of a Siamese GNN to produce a graph embedding. The resulting graph embeddings are combined with algebraic features derived directly from the input groups to construct a joint feature vector, which is processed by a fully connected classifier to predict subgroup relations between finite groups. By integrating graph-based structural representations with algebraic features, the proposed framework provides a unified approach for learning subgroup relations from finite groups. Experimental results demonstrate the effectiveness of the proposed architecture, achieving a test accuracy of 95.9% (47/49) on an independent test set and illustrating the potential of geometric deep learning for subgroup prediction.

Graph neural networks (GNNs) are increasingly deployed in real-world applications where distribution shift is un-avoidable. However, how such shifts affect model calibration, defined as the agreement between predictive confidence and actual accuracy, remains poorly understood, and existing graph calibration methods typically rely on labeled validation data from the deployment distribution. In this work, I present the first closed-form theoretical characterization of GNN calibration under distribution shift. I show that calibration is governed by a single scalar quantity that explicitly depends on structural changes between the source and target graphs, as well as feature quality. This characterization precisely identifies when a model becomes over-confident, under-confident, or remains calibrated, and directly yields the optimal temperature scaling strategy. I further extend the analysis to graph convolutional networks with symmetric normalization, multi-class classification, and covariate shift, and derive a theoretical upper bound on the expected calibration error. My analysis also reveals that, under homogeneous distribution shift, a single global temperature is theoretically optimal, providing a principled explanation for why more complex node-wise recalibration methods offer no additional benefit. Building on these theoretical insights, I propose STAC, a source-free, label-free calibration method. Experiments on synthetic benchmarks demonstrate substantial calibration improvements, while evaluations on five real-world graph datasets show that reliable calibration without target labels remains challenging despite the strong predictive power of the theory.

Raag classification is a fundamental MIR task for Hindustani Music, with applications in recommendation, education, archiving, and intelligent search. However, raag clustering remains underexplored, as most existing approaches rely on annotated audio or labeled datasets. While annotated melodic phrases capture characteristic patterns, complete note sequences preserve temporal structure and contextual dependencies, making them more suitable for data-driven modeling. In this work, we introduce RaagBase, a notation-based text dataset consisting of note sequences from compositions by Pt. Bhatkhande. Furthermore we propose a novel graph-based representation of raag structures by modeling the dominance and absence of notes in compositions. Each composition is represented as a node, and the edges between two compositions corresponds the similarities between them based on the note frequency distribution. Further, we apply established graph clustering techniques to identify groups of similar raag compositions. Experimental results demonstrate highly coherent clusters with strong agreement to ground-truth raag labels, thereby validating both the dataset and the proposed representation. The dataset is publicly available at https://anonymous.4open.science/r/RaagBase-5427.

Here, we present a platform built on our inverted Graph Transformer Network, IMPRESSION-G2, which can accurately and rapidly reconstruct molecular bonding directly from experimental nuclear magnetic resonance (NMR) spectroscopic information. It comprises three interconnected stages: a one-shot model that predicts bond connectivity between atoms; a structure-correction stage that corrects the predicted structures by removing uncertain bonds and iteratively reassigning them; noise-augmented multi-shot prediction, generating an ensemble of candidate structures, which are ranked to identify the best-fit structure. By integrating a range of $^{1}$H and $^{13}$C NMR data, including two-dimensional (2D) experiments such as COSY, HSQC, and HMBC, the inverse-IMPRESSION platform correctly identifies the structures of 77.8% of molecules with up to 30 heavy atoms (H, C, N, O and F) using simulated NMR data, and 10 of 19 (53%) molecules using experimental NMR data. The experimental structures solved have molecular weights of up to 480 Da and are representative of the complex structures in synthetic and natural products that routinely challenge chemists. The inverse-IMPRESSION framework thus provides the first effective approach for automated molecular structure elucidation using graph-based machine learning on experimental data.

While UMAP is widely used for exploring high-dimensional data, typical workflows focus on its lower-dimensional embedding, largely overlooking the rich k-nearest-neighbor (kNN) graph that UMAP constructs internally. This graph encodes the data manifold in its original high-dimensional space, before the distortion that UMAP's 2D projection introduces. We demonstrate the untapped potential of this internal representation, showing how standard graph algorithms applied to this graph enhance data sensemaking: (1) PageRank identifies representative data points, (2) k-core decomposition reveals dense core regions versus sparse periphery, and (3) clustering coefficient detects tight-knit neighborhoods with highly-similar data points. Through quantitative and qualitative evaluation on MNIST and Fashion MNIST, we show that these graph-based analyses are not only practical but also competitive with or complementary to purpose-built methods (e.g., k-medoids for exemplar selection, HDBSCAN for density-based clustering).

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

Open-vocabulary 3D scene understanding aims to segment 3D scenes beyond predefined categories by transferring semantic knowledge from vision-language models. Existing methods have advanced this task by lifting language-aligned 2D features into 3D, yet they often rely on context-independent semantic representations, leaving object relationships underexplored for contextual refinement. We propose RelGraphOV, a relationship-aware framework that uses 3D scene graphs to enhance open-vocabulary 3D understanding. Our method constructs relational scene graphs from multi-view observations by leveraging vision-language reasoning to infer object relationships and prune geometrically implausible connections, without manual relationship annotations. To aggregate relational context while avoiding feature interference, we introduce an Adaptive Gated Dual-Stream Contextual GAT that separates dense geometric features and semantic CLIP embeddings, performs edge-guided message passing, and adaptively fuses complementary semantics. A hierarchical contrastive objective further promotes instance-level consistency and category-level discrimination. Experiments on ScanNetV2, ScanNet200, ScanNet$++$, and Replica demonstrate strong performance and generalization ability. Project Page: https://cxavireh.github.io/relgraphov-projectpage

Graph eXplainable AI (G-XAI) is increasingly important for making Graph Neural Networks interpretable and accountable. While a growing number of explainers are available, choosing the right method and assessing the trustworthiness of its outputs remains unclear. Consistent evaluation practices and actionable guidance are still missing, hindering practical adoption. In this paper, we introduce a unified, quantitative benchmarking framework for G-XAI that requires no ground-truth assumptions. We formalize tabular explainability metrics for graph data, evaluating topological structure and node features as independent components. Our large-scale benchmarking study identifies explainers that consistently lie on the Pareto front across metric pairs and tasks, establishing robustly non-dominated solutions - while confirming that no single explainer achieves universal superiority. We distill our findings into actionable G-XAI usability guidelines to support Machine Learning practitioners in evaluating and deploying trustworthy GNN-based pipelines.

Knowledge graphs (KGs) that underpin Graph-based Retrieval-Augmented Generation (Graph-RAG) are increasingly built automatically by LLM-driven extraction rather than curated by experts. Proper evaluation would require instrumenting all pertinent stages: extraction, graph construction, and inference, coherently enough to localize failures, so that a failure at one stage is not discovered as a wrong answer at the end. We introduce TRIAGE, a stage-aware instrumentation framework for automated, document-grounded graph-RAG that asks not only whether the underlying graph can be trusted but at what cost it can be queried. TRIAGE attaches stage-specific, independently interpretable metrics to three stages: the KG Implementation (triple confidence, source coverage, and schema and canonicalization checks), the KG Validation by expert (graph-level structural quality, with correctness and completeness computed only as offline calibration when a reference is available), and the KG Usage (retrieval coverage, faithfulness, and retrieval cost); the deployed metrics need no gold annotations, the gold-requiring ones serving only as offline calibration. At usage time these metrics form a diagnostic chain of necessary conditions whose first broken link localizes the failure, and the diagnosis maps to the stage levers that can remedy it: extraction, graph and schema, or retrieval. TRIAGE is a theoretical framework with a proof of concept and a reproducible evaluation protocol.

We study a broad class of graphical models whose independencies correspond to vertex separation in mixed graphs with directed, undirected, and bidirected edges, that are capable of encoding independence structures arising from feedback, latent and selection mechanisms. In particular, we introduce separable graphs, in which each missing edge implies the existence of a separating set for its endpoints, and essentially separable graphs, those graphs separation equivalent to a separable graph. We show that these models include many existing graph families used to define graphical models an provide several characterizations of separable graphs and essentially separable graphs. We also provide multiple characterizations of separation equivalence for separable graphs. One is a graphical characterization in terms of ordinary graph properties, extending earlier results for specific subfamilies Another is a separational characterization depending only on graph separation properties. Finally, we provide a canonical representation for the equivalence classes of essentially separable graphs and develop an algorithm that, under suitable assumptions, identifies the equivalence class of any essentially separable graph.

The stable coloring of the Weisfeiler-Leman (1-WL) test is a cornerstone of Graph Neural Networks because it provides an upper bound to the expressive power of message-passing architectures. Unfortunately, computing it presents two fundamental bottlenecks. First, classic algorithms are inherently sequential and cannot exploit modern massively parallel hardware. Second, these are \emph{global} algorithms, i.e., they require availability in memory of the full graph, severely limiting applicability to real-world instances. We leverage a linear-algebraic interpretation of 1-WL stable coloring and introduce two key contributions: (i)~a randomized refinement algorithm with tight probabilistic guarantees and (ii)~a correctness-preserving batching scheme that decomposes the graph into independently processable subgraphs while provably returning a stable coloring of the original graph. This approach maps directly to GPU-efficient primitives. In numerical experiments, our CUDA implementation delivers speedups up to two orders of magnitude over classical CPU-based partition refinement and, for the first time, successfully computes stable colorings on web-scale graphs with over 30 billion edges, where CPU baselines time out or fail.

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.

Skeleton-based action recognition has achieved remarkable success by exploiting joint coordinates and their topological connections, yet prevailing methods overwhelmingly assume complete and clean skeleton inputs. In real-world deployments, such as egocentric vision, crowded surveillance, wearable devices, or edge robotics, limited field-of-view (FoV) frequently causes substantial joint visibility dropout, leading to severe performance degradation that existing models are largely unprepared to handle. To bridge this critical yet underexplored gap, we introduce PartialVisGraph, a novel hypergraph framework tailored for robust skeleton action recognition under constrained FoV. We first construct highly expressive hypergraphs by introducing learnable virtual hyperedges that form a soft incidence matrix, capturing flexible high-order dependencies beyond conventional pairwise graphs. We then propose the Single-Head Sample-Adaptive Transformer, which adaptively aggregates joint features onto hyperedges while explicitly incorporating a visibility prior. This prior selectively gates information flow, preventing occluded or out-of-view joints from corrupting reliable feature propagation. We further establish rigorous evaluation protocols with realistic FoV simulation benchmarks on NTU RGB+D 60 and 120. Extensive experiments demonstrate that PartialVisGraph consistently achieves state-of-the-art accuracy under partial visibility, with gains of up to 68.8% on subsets with severe FoV restrictions compared to recent strong baselines, while remaining superior on full-visibility settings. Our approach offers a principled and practical pathway toward deployable skeleton-based action understanding in unconstrained environments.

Graphs are commonly visualized in 2D, where humans readily interpret spatial relationships, yet such layouts often distort higher-dimensional structure. We propose to embed graphs in high-dimensional space and search for informative 2D viewpoints that optimize aesthetic and readability metrics (e.g., edge crossings and angular resolution), enabled by a novel differentiable surrogate for edge crossings. Numerical experiments show that these viewpoints consistently outperform standard 2D layouts, and can even surpass methods explicitly designed to optimize these metrics. We further introduce DataFly, an interactive system for exploring multiple candidate viewpoints through seamless navigation. A usability study demonstrates that our approach reveals structural patterns that remain hidden in conventional 2D visualizations.

With the rise of data-intensive science, algorithms have become central to scientific research. In academic papers, algorithms are mentioned for different purposes, such as describing, using, comparing, or improving methods for specific research tasks. Identifying these purposes can reveal relationships among algorithms and help assess their roles and value. Taking natural language processing (NLP) as an example, this study proposes a sentence-level framework for identifying, analyzing, and tracing the evolution of motivations for mentioning algorithms. We first identify algorithm entities and algorithm-related sentences from full-text papers through manual annotation and machine learning. We then classify mention motivations using pretrained models and data augmentation, and analyze their distribution and temporal evolution. The results show that deep learning models trained with augmented data outperform traditional machine learning models in motivation classification. In NLP papers, more than half of algorithm-related sentences express direct use, whereas improvement is the least frequent motivation. The diversity of motivations has increased over time. For specific algorithm categories, grammar-based algorithms are more often mentioned for description, while machine learning algorithms are more often mentioned for use. Over time, use motivations have gradually replaced description motivations across different algorithms, and the number of motivation types associated with individual algorithms has declined significantly. This study reveals how authors mention algorithm entities in academic writing and provides a basis for future research on algorithm relationship identification and algorithm impact evaluation.

A Knowledge Graph (KG) represents facts as structured triples and is widely used to organize relational knowledge across diverse domains. Just as textual information ranges from words and sentences to complete documents, KG information can be interpreted at multiple levels, from entities, relations, and triples to subgraphs and entire KGs. However, existing KG embedding methods mainly focus on entities, relations, and triples, leaving graph-level semantics largely unaddressed. Conventional graph-level methods, which typically compare graphs based on structural patterns, are also insufficient because structural similarity alone cannot guarantee semantic similarity between KGs. To evaluate how well different methods capture such graph-level semantic information, we study graph-to-graph semantic similarity, which determines whether a pair of KGs represents semantically corresponding underlying information. To obtain reliable ground-truth correspondences, we construct a semantic matching dataset by modifying text documents, extracting KGs from both original and modified documents, and transferring their known correspondences to KG pairs. We compare text-based, structure-based, and KG embedding-based approaches on each dataset. For the KG embedding-based approach, we introduce two scoring functions: \textit{EmbPairSim}, which uses maximal pairwise entity similarity, and \textit{AvgEmbSim}, which uses a frequency-weighted centroid. Experiments on WikiText-2 and CC-News show that \textit{EmbPairSim} achieves up to 5.3 pp higher MRR than Sentence-BERT while using substantially fewer parameters. These results suggest that KGE representations can serve as compact and effective signals for graph-to-graph semantic similarity in KGs. Our code is available at https://github.com/SeungRyeolBaek/KG-to-KG-Semantic-Similarity.

Existing homomorphic encryption (HE)-based GNN systems adopt a graph-centric paradigm that couples per-query cost to global graph size, limiting evaluations to at most ~20k nodes and making them incompatible with dynamic, large-scale financial graphs. We propose TGHE (Template-based Graph Homomorphic Encryption), an ego-centric framework that resolves this by exploiting a template phenomenon: local computation trees in transaction graphs converge into a small set of structural shapes. TGHE canonicalizes ego-graphs at the edge and packs structurally identical trees into shared CKKS ciphertexts for SIMD-parallel encrypted inference, with two long-tail optimizers (Approximate Template Fitting and Topology Collapse) ensuring full SIMD coverage. On DGraphFin (3.7M nodes, 4.3M edges), TGHE-Collapse achieves a 66.9x speedup over the sequential encrypted baseline with less than 0.002 AUC loss.

A Graph Neural Network (GNN) framework for predicting the solvability of finite groups from their Cayley graph representations was introduced in [1]. In the present work, we generalize this approach and develop a property-independent framework for learning algebraic properties of finite groups directly from Cayley graphs. As representative case studies, we consider abelianity, nilpotency, and solvability. Using a common GNN architecture and training pipeline, we investigate the extent to which algebraic structure can be recovered from graph-based representations alone. Results on a collection of finite groups drawn from several families demonstrate that the framework successfully learns and distinguishes multiple algebraic properties from their associated Cayley graphs. These findings suggest that substantial algebraic information is encoded in graph representations and can be extracted through GNNs. More broadly, the proposed framework provides a proof of concept for applying graph representation learning to the study of algebraic properties of finite groups.

Mathematical knowledge is organized around statements and their dependencies, but this structure is exposed unevenly: informal papers cite mostly at the document level, while formal libraries record fine-grained dependencies over a much smaller body of mathematics. We introduce TheoremGraph, a unified statement-level dependency graph spanning both informal and formal mathematics. On the informal side, we parse 11.7M theorem-like environments from mathematics arXiv and recover 18.3M candidate directed dependencies, each labeled by the extractor that proposed it so downstream users can trade coverage for precision. On the formal side, we release LeanGraph, a Lean 4 elaborator-level extractor producing 388,105 declaration nodes and 11.3M typed edges across 25 Lean projects. We bridge the two graphs by embedding generated natural-language slogans into a shared semantic space, linking related statements across papers and across the informal/formal divide; an LLM judge affirms 47,952 such matches above a 0.8 cosine floor, with the judge-acceptance rate rising from 48% across the floor to 87% in the >=0.9 tier. On formal concept retrieval, our name-and-signature representation with graph expansion comes within 0.5pp of LeanSearch v2's reranked Recall@10 (0.775 vs. 0.780) without an LM reranker. We release the dataset, extractors, HTTP API, and MCP interface as infrastructure for mathematical search, attribution, and retrieval-augmented reasoning, available at theoremsearch.com and huggingface.co/datasets/uw-math-ai/theorem-matching.

Can one graph represent every kind of LLM agent's run? A trace records what each step did, never what it relied on, the state it read, and the results it reused. GRADE recovers that missing layer: it models any run as one graph over its step nodes with two edge layers, execution edges (what ran in what order) read from the trace for free, and dependency edges (what each step relied on) rarely logged, so each is graded by how it is known, observed, declared, or inferred. One representation, and each layer earns its place. Across six corpora of LLM agents spanning tool use, coding, and the web, the dependency layer can predict failure where run size is weak and, under leave-one-corpus-out transfer, stays above chance on every held-out class while run size fails. Meanwhile, the execution layer localizes the faulting step in a failed multi-agent run. This work also provides a more in-depth analysis of why generic graph neural networks may misread the dependency layer, unlike our feature-based alternative. The same graph representation opens further uses, carrying from failure diagnosis in a single run to efficiency and robustness optimization at scale.

Autonomous mobile robots are expected to exhibit socially compliant navigation for minimizing pedestrian disturbance. While capturing social interactions and incorporating pedestrian motion estimations into decision-making are beneficial for compliance, prior methods fail to address both spatial and temporal characteristics present in real-world data. Reinforcement Learning offers high capability, but it requires hand-crafted reward functions that reduce social behavior to static criteria, limiting its ability to reproduce patterns that exist in real pedestrian behavior. Imitation Learning offers direct training from real-world data but lacks modeling of social interactions and suffers from error accumulation. To this end, we propose an imitation learning framework that leverages spatiotemporal dynamics for socially compliant navigation. To represent social context based on interactions, we introduce a graph-based auxiliary network that encodes crowd states by attending to pedestrians. In addition, we present a navigation module that captures temporal dynamics and mitigates error accumulations by incorporating encoded state predictions and employing a trajectory-level learning objective. Our framework outperforms established data-driven baselines on simulation and a real-world dataset across diverse social metrics.

Graph neural networks (GNNs) tightly couple their input-output parameters to dataset-specific feature spaces and target sets, exhibiting limited transferability across different datasets. In contrast, language models (LMs) generalize flexibly via a unified input-output interface, motivating recent attempts to adapt LMs to graph tasks. However, existing methods struggle to encode whole-graph information, leading to potential information loss and suboptimal graph understanding. In this work, we propose a novel weight-level information injection paradigm for adapting LMs to graph tasks. This paradigm injects whole-graph information by generating task-specific weight updates that interact directly with hidden representations. Instantiating this paradigm following low-rank adaptation (LoRA), we introduce GaRA, a Graph-aware LoRA generation model. GaRA constructs low-rank weight updates conditioned on the original graph structures and constrains the norm of the generated updates, thus injecting whole-graph information and avoiding the optimization bias in the weight generation. Empirical studies demonstrate that GaRA consistently outperforms baselines on zero-shot graph learning tasks.

Training medical image classifiers on entire datasets is wasteful when annotation budgets are limited: not all samples contribute equally, yet acquiring expert labels is expensive. Active learning reduces annotation cost through iterative querying, but assumes repeated access to an oracle and requires multiple rounds of model training. One-shot geometry-based methods such as facility location avoid retraining but operate on pairwise distances that ignore the local structure of the data manifold. We propose a graph-based one-shot selection method that operates entirely on frozen foundation model embeddings. Given embeddings from a pretrained encoder, we construct a k-nearest neighbor graph over all training samples and derive a two-term coverage kernel from the heat diffusion kernel, capturing both direct and two-hop neighborhood relationships. Greedy facility location on this kernel selects class-balanced subsets that maximize coverage of the data manifold. The two-term kernel matches the full spectral heat kernel in selection behavior while reducing computation to sparse matrix operations with a single hyperparameter. We evaluate on five MedMNIST datasets spanning histopathology, radiology, and microscopy, comparing against both training-dynamics and geometry-based baselines. Our method achieves the highest balanced accuracy on nine of ten dataset-ratio conditions, with the largest gains on class-imbalanced datasets where global graph construction captures cross-class structure that per-class methods miss, all without any model training during selection. Code is available at https://github.com/zahiriddin-rustamov/graph-coverage-selection.

Medical image re-identification (MedReID) enables longitudinal patient linkage but remains vulnerable to shortcut learning and often produces decisions that clinicians cannot audit against named anatomy. We propose Graph-of-Differences (GoD), which grounds identity comparisons in explicit anatomical structure. Each image is represented as an anatomy graph whose nodes correspond to named anatomical regions; given an image pair, soft node correspondence is established, and differences are computed over matched anatomy. A graph-level difference alignment objective ties these anatomy-matched differences to the global backbone difference, ensuring the retrieval signal is anchored in homologous structures rather than arbitrary spatial tokens. Explanations are defined over named graph nodes and quantitatively audited via node insertion/deletion tests, replacing unstable pixel heatmaps with verifiable structure-level evidence. On internal benchmarks, GoD improves Rank-1 by +7.1 pp on fundus and +3.1 pp on CXR over a strong frozen-backbone baseline, with further gains on zero-shot external transfers confirming that anatomy grounding improves both accuracy and generalization. Code is available at https://github.com/GenMI-Lab/GoD.git.

Structurally constrained event sequence generation remains challenging because generated paths must preserve transition feasibility, temporal order, termination, and attribute consistency. In predictive process monitoring (PPM), this challenge appears as full event sequence generation, whereas existing work mainly addresses component tasks such as next activity, remaining time, outcome, and attribute prediction. This paper proposes the Graph Grounded Cross Attention Transformer Neural Network (GGATN) for this unified PPM task. GGATN uses a global process graph as structured activity memory, contextualizes sequence positions through Transformer self attention, and injects process topology through graph grounded cross attention. Unlike autoregressive decoding, GGATN generates activities, timestamps, length, and event level and sequence level attributes in a single pass, followed by Viterbi style graph constrained decoding for feasible paths and explicit termination. Experiments on six benchmark event logs show more reliable generation quality than local instruction prompted LLM baselines. GGATN achieves strong performance on sequence similarity, Damerau Levenshtein similarity, bigram based control flow similarity, and duration distribution, while maintaining zero hallucinated activities and zero sequence level attribute inconsistency. Ablation analyses confirm the global graph encoder as a stable structural prior. Interpretability analyses show how graph structure, sequence context, feedback refinement, and constrained decoding shape generation.

Computing geometric representations of data is a cornerstone of modern machine learning, typically achieved by training dual encoders which map queries and documents into a shared embedding space. Recent work of You et al. [NeurIPS '25] has extended this approach to hierarchical retrieval, where relevance is determined by the ancestor-descendant relationships in a Directed Acyclic Graph (DAG). While previous work has shown that valid embeddings exist when the number of descendants is small, these bounds degrade significantly for deep hierarchies, requiring dimensions as large as the total number of nodes. In this paper, we investigate compact reachability embeddings for more general graph classes and provide theoretical guarantees for representing hierarchies using embeddings whose dimension depends on structural graph parameters. We prove that for any directed tree, there exists a reachability embedding in constant dimension 3, independent of the tree's size or depth. We generalize this result to graphs characterized by treewidth $t$, constructing embeddings of dimension $O(t \log n)$, where $n$ is the number of nodes. Complementing these upper bounds, we provide matching or near-matching lower bounds, showing that dimension $Ω(n)$ is necessary for general DAGs and $Ω(t/\log(n/t))$ is required for graphs of treewidth $t$. We also obtain upper and lower bounds parameterized by the number of cross-edges in the DAG. We additionally show that our embeddings can be constructed on real world datasets, and that they give much smaller dimensions in high recall regimes compared to prior embeddings with theoretical guarantees.

We introduce Darshana Graph, a corpus of over 125,000 text records spanning classical Hindu, Buddhist, and Jain philosophical traditions, drawn from public-domain and openly licensed translations of sources including the Bhagavad Gita, Brahma Sutras, principal Upanishads, the Pali Canon, and core Jain texts. Its distinctive contribution lies in a structurally unique subset of roughly 8,500 Hindu and Jain records in which the same root verse or sutra is aligned across eighteen historical commentators representing five schools of Vedanta and other darshanas, enabling direct comparison of how independent interpretive traditions read identical source material. To our knowledge, no publicly available resource provides comparable cross-commentator alignment at this scale. We present two analyses built on this corpus. First, a transparent stylometric comparison requiring no machine learning measures argumentative style through scriptural citation density, explicit refutation rate, and sentence complexity. It finds a moderate negative correlation between citation density and refutation rate, a marked increase in refutation rate across three commentators in a related doctrinal lineage, and measurable genre-level differences within the Pali Canon itself. Second, we describe a constrained large language model pipeline that extracts typed philosophical relationships between concepts using a predefined relation vocabulary and deterministic post-hoc validation. The resulting graph surfaces cross-school disagreement patterns while also revealing important extraction limitations, including cases where an independent embedding-based analysis disagrees with the graph-derived findings. We release the full corpus, extracted relationship graph, and all source code.

A Markov Logic Network (MLN) is a probabilistic relational model used in Statistical Relational Artificial Intelligence for defining a probability distribution on the set of possible worlds with domain $D$ for an arbitrary finite domain $D$. An MLN consists of soft constraints with associated weights which are nonnegative real numbers. In this study we consider a language speaking about a property $P(x)$ and a relation $R(x, y)$. We consider an MLN for which every Boolean combination of $P(x)$ and $R(x, y)$ is a soft constraint (with associated weight). Let $n$ denote the size (cardinality) of the domain. We show that, for every choice of weights, if the weights are scaled by $1/n$ then, for every first-order sentence $\varphi$, the probability that $\varphi$ holds tends to either 0 or 1 as $n \to \infty$; that is, a 0-1 law for first-order logic holds. Morover, the limit probability does {\em not} depend on the weights. If we instead use the standard semantics of MLNs, in the case of which the weights are {\em not} scaled, then the limit behaviour is more complicated and {\em depends} on the weights. With unscaled weights we get 7 qualitatively different cases which depend on the weights. In some cases we have a 0-1 law for first-order logic, in some cases not, but we may still have a convergence law. The influence of the weights on the asymptotic probability of a first-order sentence may be in the form of a sudden ``phase transition'' from one of the 7 cases to another. The presence of a convergence law has positive implications for inference on large domains.

LLM-based agents have demonstrated strong capabilities in data-intensive analytical tasks, yet their outputs are rarely verifiable: a reliance on linear text trajectories makes their reasoning difficult to audit. In particular, deterministic computations over raw data and semantic deductions over natural-language claims are often entangled in an unstructured stream, leaving numerical conclusions hard to reproduce and qualitative judgments hard to inspect. To address this, we propose VeriGraph, a traceable neuro-symbolic reasoning framework that enables agents to construct an explicit heterogeneous evidence directed acyclic graph (DAG) during execution. VeriGraph introduces three evidence-expansion primitives, namely computational, grounding, and derivational expansion, to connect raw data, interpreter variables, computed results, and natural-language claims in a unified graph. Under this formulation, structural traceability is reduced to graph reachability from raw data sources to terminal claims, while semantic support is measured by claim-level evidence evaluation. To improve graph construction, we further design a graph-based policy optimization strategy with a composite reward that jointly supervises answer correctness, computational integrity, and derivational coherence. Experiments on four benchmarks show that VeriGraph-8B achieves the highest overall score among all baselines. More importantly, VeriGraph produces auditable evidence graphs with substantially stronger claim grounding, achieving a 87.61% Grounding Rate under our claim-level evidence support evaluation. These results suggest that explicit evidence-graph construction is a promising path toward verifiable data-analytic agents. Our code is available at https://github.com/ignorejjj/VeriGraph.

Traffic state prediction is a fundamental task in intelligent transportation systems. In practical applications, some regions suffer from limited traffic observations due to insufficient sensing infrastructure, making cross-domain knowledge transfer an important solution for data-scarce traffic prediction. However, existing cross-domain traffic prediction methods still face several limitations, including coarse-grained source-target adaptation, limited capability in handling unseen target-domain patterns, and insufficient modeling of continuous traffic dynamics under irregular or heterogeneous temporal conditions. To address these issues, this paper proposes a continuous cross-domain traffic prediction framework, termed Memory-Augmented Graph Liquid Time-Constant Network (MA-GLTC). Specifically, we first construct spatio-temporal units (STUs) to decompose traffic networks into transferable local units, enabling fine-grained knowledge alignment across domains. Then, a graph liquid time-constant network (GLTC) is developed to model graph-coupled traffic evolution in continuous time. Different from generic graph neural ODE-based models, GLTC introduces graph-coupled recurrent conductance into liquid time-constant dynamics, allowing node states to evolve with leakage, adaptive time constants, and neighborhood-aware feedback. Furthermore, a Memory-based Transfer Storage (MTS) mechanism is designed to preserve source-domain knowledge, retrieve matched traffic patterns, and update reliable target-domain patterns when unseen states emerge. Experiments on five public traffic datasets demonstrate that MA-GLTC consistently outperforms representative innerdomain and cross-domain baselines in both short-term and longterm prediction tasks. Compared with the second-best method, MA-GLTC reduces the average prediction errors by 3.02%, 0.33%, 8.92%, 10.09%, and 2.11%, respectively.

Graph-based recommender systems are highly effective at extracting collaborative signals from user--item interactions, and federated learning (FL) allows these models to be trained while preserving user privacy. However, aggregating graph representations across distributed, non-IID clients remains a challenge; structural embeddings learned locally often misalign, and naive averaging fails to capture meaningful cross-client relationships. Most existing federated graph methods rely exclusively on structural aggregation, neglecting the rich, global semantic context available in large language models (LLMs). In this paper, we propose a novel framework that uses LLM-encoded knowledge to guide federated graph recommendation. Specifically, clients learn structural representations from local graphs while simultaneously summarizing their typical interaction patterns into compact semantic vectors via a frozen LLM. The central server then uses these LLM-encoded semantic signals to discover related preference patterns across clients, guiding the selective aggregation of their structural representations. This enables semantically informed cross-client collaboration without exposing raw data. Extensive experiments on standard benchmarks show that guiding structural alignment with LLM-encoded knowledge consistently improves recommendation accuracy over existing federated graph baselines.

Large language model (LLM) agents are increasingly deployed in multi-agent systems where they must coordinate and agree on shared decisions. We ask whether classical resilient consensus theory, developed for deterministic agents, transfers to LLM agents that may behave adversarially. Framing LLM agreement as a Byzantine consensus game, we run controlled experiments on complete and general communication graphs. We find that prompted LLM agents fail to reach agreement that is achievable in principle: consensus can fail even in settings where classical theory guarantees that a convergent algorithm exists, and this failure persists across temperatures and horizons. At the same time, wrapping the agents with classical resilient consensus filters improves agreement. The benefit of filtering depends on how much robustness the underlying topology already provides. Our results suggest that classical resilient consensus theory is a useful lens for the safety of agentic AI.

Autonomous driving systems rely on precise trajectory prediction to plan safe and efficient movement. Graph Neural Networks (GNNs) have become a promising approach for modelling spatiotemporal interactions among road agents. However, designing GNN architectures for trajectory prediction remains non-standardized, with little guidance on which graph layers effectively capture spatial interactions and temporal dynamics. This paper offers a detailed comparative study of 19 graph layer types, focusing on their spatial and temporal processing capabilities to discover the most effective architectures for trajectory prediction. Within the explored hyperparameter setting, we highlight five standout layer combinations, with ARMA, Chebyshev, and topology-aware layers consistently performing better than others. Beyond performance metrics, our findings yield practical design principles: sum-based aggregation is more effective than mean-based methods, multi-head attention mechanisms enable richer interactions, and assigning different weights to different hop distances significantly improves prediction accuracy. These findings offer useful guidance for designing more interpretable and effective trajectory prediction models.

Property Graphs are rapidly being adopted as database frameworks for representing heterogeneous data sources. To enable precise access to the information contained in them we need conversational interfaces based on Text-To-Cypher (Text2Cypher) parsers. This paper presents an automatic synthetic data generation method that can be leveraged to fine-tune small LLMs for this task. We conduct experiments on all the major Text-To-Cypher benchmarks, demonstrating that with our synthetic data generation approach we can significantly increase the performance of small LLMs, allowing them to compete with much larger proprietary models. This means that in settings in which models must be locally deployed we can ensure data-sovereignty without sacrificing accuracy and without costly annotation campaigns.

The performance of modern language models depends critically on pretraining data composition. Yet existing data selection methods rely on auxiliary classifiers for document scoring or mixture optimization, adding computational overhead and dependence on labeled data. We propose WebGraphMix, a lightweight data selection framework that computes structural centrality scores over the Common Crawl host-level web graph and uses them to vary the proportion of central versus peripheral documents in the pretraining mixture. We hypothesize that central hosts expose models to reusable abstractions, while peripheral hosts encode specialized, long-tail knowledge. WebGraphMix computes centrality scores efficiently at web scale, requiring no model training, labeled data, or downstream supervision. We integrate WebGraphMix into the DataComp-LM pipeline and train models at 400M and 1B parameter scales with 8B and 28B tokens respectively, evaluating on 23 tasks ranging from factual knowledge to symbolic reasoning. Our experiments show that central and peripheral web regions encode complementary capabilities. Mixture combining both at a ratio of 1:1 achieves 41.4% on average, compared to 39.8% for uniform sampling. Combining structural scores with document-level quality classifier scores further improves performance to 43.8%. These findings demonstrate that web graph topology is a meaningful axis for pretraining data curation, capturing information that is largely orthogonal to existing content-based approaches.

Autonomous improvement loops are hard to trust because the improvement process is usually external scaffolding bolted onto the agent: failures go unlogged, diagnoses cannot be replayed, and promote-or-discard decisions land in a side database rather than the agent's own history. We show that an event-sourced agent runtime removes that friction and turns controlled improvement into a first-class workflow. When the agent's state is a deterministic projection of an append-only event log, failures are recorded, a run replays exactly from its log, candidate patches scope to typed pipeline seams, gates are auditable, and every promotion or discard is itself an event. We demonstrate this with Regimes, a loop on the ActiveGraph runtime that diagnoses failed evaluations, proposes a repair at a pipeline point, and promotes it only after static checks, sandbox execution, in-sample evaluation, and held-out validation. The loop is target-agnostic: the same control flow runs against different tasks through a common interface. On LongMemEval-S the dominant failure is not retrieval but reconciliation: the evidence is already in the assembled context, yet the reader answers incorrectly. Across five seeded held-out splits, Regimes discovers reader-prompt repairs that improve final held-out accuracy by +0.05 to +0.10 in four splits and +0.01 in one over-promotion split; two splits are individually significant (seed 5 unadjusted for its sequential promotion structure), and the pooled count is descriptive only, since the splits share one 500-question pool. The durable contributions are ActiveGraph as an auditable substrate that makes controlled improvement loops tractable, the held-out-gated loop it supports, the failure-regime taxonomy routing each failure to a pipeline location (whose marginal value over an unrouted baseline is the primary open question), and the prompt-as-discovery-probe hypothesis.

Modeling interacting dynamical systems requires capturing spatial interactions alongside long-range temporal dependencies. Graph neural networks (GNNs) provide a natural representation but typically rely on autoregressive rollouts and treat spatial and temporal dynamics separately, leading to error accumulation over long horizons. Existing approaches also focus on local interactions and short temporal contexts, limiting their ability to capture multi-hop dependencies and global structure. We introduce the Graph Mamba Operator (GraMO), a latent-space simulator that integrates state-space models with graph-based interaction learning. In contrast to prior work that sequences nodes or applies spatial and temporal updates in separate stages, GraMO couples graph-based interactions and temporal state updates within a single recurrence. The update is linear in the latent state, with input-dependent coefficients that adapt across regimes. We evaluate GraMO on N-body systems, motion capture, and robotics datasets, achieving the lowest error across benchmarks and the largest gains in long-horizon prediction.

We study causal discovery from observational data when some variables are hidden and the data-generating process follows a location-scale noise model (LSNM). Existing methods that handle hidden confounders typically assume additive noise, but in practice, causes often modulate not just the mean but also the variance of their effects. We prove that acyclic directed mixed graphs (ADMGs) satisfying a bow-free condition are identifiable under LSNM with hidden variables, establishing the first identifiability result for causally insufficient models beyond noise additivity. We further provide sufficient conditions for identifying causal direction even when the bow-free assumption is violated. Our two-stage algorithm, LSNM-UV, is sound and complete, and experiments demonstrate improved performance over additive baselines on heteroscedastic data.

The paradigm of global weather forecasting is rapidly shifting with the emergence of Machine Learning Weather Prediction models (MLWP). While these data-driven architectures demonstrate remarkable global skill, regional benchmarks in the Global South remain scarce, leaving their efficacy in complex, highly convective environments largely unverified. This study evaluates the performance of GraphCast operational against the deterministic ECMWF IFS HRES as baseline across four distinct Brazilian climatic sub-regions. Utilizing a scalable, cloud-native pipeline and the WeatherBench-X framework for benchmarking weather models, we assess selected tropospheric variables ($T_{850}$, $Q_{850}$, $Z_{500}$) over four selected seasonal windows, employing the operational IFS analysis as the ground truth to calculate the statistical metrics for both models. Results reveal a regime-dependent skill profile. During the austral winter, GraphCast underperforms in the medium range (lead days 2-7) for $Z_{500}$ when resolving fast-propagating baroclinic systems over southern Brazil, but regains an advantage in the extended range, where its inherent smoothing of chaotic small-scale variability becomes beneficial under deterministic skill metrics. Conversely, during the austral summer wet season, GraphCast accurately captures large-scale moisture transport while intrinsically dampening the high-frequency convective variability that degrades deterministic NWP temperature forecasts. These findings establish a baseline for Brazil and define the specific physical boundaries that will guide future ``tropicalization'' efforts, aiming to optimize these foundational AI models for regional resilience.

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.

Agent Skills today consist largely of free-form prose requiring the agent to read, interpret, and re-derive how to act in every session. This imposes two compounding costs: reduced reliability on implementation-heavy tasks, and difficulty in skill creation and improvement, since editing prose is a fragile process that both humans and agents struggle with, particularly for domain-specific procedural knowledge underrepresented in model training. The Agent Instruction Protocol (AIP) addresses both by modeling a skill as a directed execution graph: discrete steps as nodes backed by deterministic scripts or natural-language descriptions, connected by explicit typed input/output edges, and governed by a schema-validated YAML specification. A compiler meta-skill translates existing human-written skills into this form. The benefits are twofold. First, compiling human-written skills to AIP raised Claude Sonnet's mean task reward from 0.60 to 0.71 and pass rate from 53% to 67% across 27 real agent tasks from SkillsBench - a statistically significant gain (Wilcoxon signed-rank p = 0.011), winning 12 tasks to 2 with 13 ties - often in less wall-clock time. The graph delivers vetted, runnable units to the agent rather than asking it to re-derive code, commands, and tool calls from natural language. Second, on creation and improvement, because each skill is schema-validated, functionally testable, and addressable node-by-node, failures can be diagnosed and repaired precisely. Two authored-skill failures were traced to the script level. After adjusting the AIP spec and recompiling, both recovered with zero regressions (one task going from 0/5 to 5/5), turning skill improvement into a measurable tuning loop rather than a prose rewrite. That same graph structure supports corpus-level governance and skill introspection, and provides a natural action space for reinforcement learning over skills.

Active learning (AL) for node classification typically focuses on selecting the most informative nodes for annotation within one or a few large graphs (e.g., in social network analysis). However, in other domains, such as molecular chemistry or electronic design automation, datasets consist of thousands of independent graphs. In many of these inductive settings, annotating an individual node requires a full-graph analysis, which effectively yields the remaining node labels on-the-fly. Therefore, these scenarios require AL strategies that select entire graphs instead of single nodes, a problem which has not been tackled in the literature so far. Thus, we introduce ALINC, an AL framework for inductive node classification via graph sampling. It bridges the existing methodological gap by elevating node-level utility measures to graph-level selection criteria through various aggregation mechanisms. In an extensive benchmark including ten strategies, three aggregation methods, and four datasets, we identify CoreSet, TypiClust, and BADGE as the top-performing graph sampling strategies. Our detailed analysis further reveals that the choice of the aggregation method is pivotal, as it substantially affects model performance and annotation costs. Finally, we demonstrate the effectiveness of ALINC in two use case studies: site-of-metabolism prediction in molecules and design automation of printed circuit board schematics.

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.

We present a Graph Neural Network (GNN) framework for the classification of finite groups according to their solvability. Using graph representations associated with finite groups, including Cayley graphs (CG), the proposed model is trained to distinguish solvable and non-solvable groups using structural graph information alone. The framework is evaluated on groups outside the training dataset in order to investigate the extent to which GNNs can learn algebraic properties arising in group theory. More broadly, the present work explores the relationship between algebraic structure and graph-based geometric representations of finite groups. The present study is intended as a proof-of-concept investigation of whether GNNs can learn algebraic properties of finite groups from graph-based representations

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.

Large language model (LLM) agents have shown strong capabilities in reasoning, tool use, and multi-step interaction, but they often solve tasks from scratch and fail to reuse successful strategies or failure lessons from prior experience. Fine-tuning on collected experience can improve reuse, but it is inflexible when stronger or more suitable executors emerge. We propose ExpGraph, a model-agnostic experience learning framework that enables frozen and replaceable LLM executors to improve through external experience reuse without parameter updates. ExpGraph summarizes historical trajectories into reusable skills and failure lessons, organizes them as nodes in a self-evolving experience graph, and retrieves useful experiences through graph diffusion and utility-aware ranking. A lightweight retrieval copilot is trained with reinforcement learning using feedback that compares executor performance with and without retrieved experiences, while the graph is updated online from downstream task outcomes. We evaluate ExpGraph on ExpSuite, covering question answering, mathematical reasoning, code generation, and multi-step agentic environments including ALFWorld and AppWorld. ExpGraph improves over the strongest baseline by 12.2% and 4.7% on static tasks with smaller and larger executors, and by 21.4% and 12.7% in agentic environments, while reducing average interaction steps by 12.7% and 21.6%. Ablations show that graph-structured experience, utility-aware ranking, and adaptive retrieval jointly enable effective experience reuse across diverse tasks and executor 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.