Kalman Filtering of Stationary Graph Signals

In this paper, we propose a novel definition of stationary graph signals, formulated with respect to a symmetric graph shift, such as the graph Laplacian. We show that stationary graph signals can be generated by transmitting white noise through polynomial graph channels, and that their stationarity is preserved under polynomial channel transmission. In this paper, we also investigate Kalman filtering to dynamical systems characterized by polynomial state and observation matrices. We demonstrate that Kalman filtering maintains the stationarity of graph signals, while effectively incorporating both system dynamics and noise structure. In comparison to the static inverse filtering method and naive zero-signal strategy, the Kalman filtering procedure yields more accurate and adaptive signal estimates, highlighting its robustness and versatility in graph signal processing.

Zero-shot Graph Reasoning via Retrieval Augmented Framework with LLMs

We propose a new, training-free method, Graph Reasoning via Retrieval Augmented Framework (GRRAF), that harnesses retrieval-augmented generation (RAG) alongside the code-generation capabilities of large language models (LLMs) to address a wide range of graph reasoning tasks. In GRRAF, the target graph is stored in a graph database, and the LLM is prompted to generate executable code queries that retrieve the necessary information. This approach circumvents the limitations of existing methods that require extensive finetuning or depend on predefined algorithms, and it incorporates an error feedback loop with a time-out mechanism to ensure both correctness and efficiency. Experimental evaluations on the GraphInstruct dataset reveal that GRRAF achieves 100% accuracy on most graph reasoning tasks, including cycle detection, bipartite graph checks, shortest path computation, and maximum flow, while maintaining consistent token costs regardless of graph sizes. Imperfect but still very high performance is observed on subgraph matching. Notably, GRRAF scales effectively to large graphs with up to 10,000 nodes.

JANUS: A Dual-Constraint Generative Framework for Stealthy Node Injection Attacks

Graph Neural Networks (GNNs) have demonstrated remarkable performance across various applications, yet they are vulnerable to sophisticated adversarial attacks, particularly node injection attacks. The success of such attacks heavily relies on their stealthiness, the ability to blend in with the original graph and evade detection. However, existing methods often achieve stealthiness by relying on indirect proxy metrics, lacking consideration for the fundamental characteristics of the injected content, or focusing only on imitating local structures, which leads to the problem of local myopia. To overcome these limitations, we propose a dual-constraint stealthy node injection framework, called Joint Alignment of Nodal and Universal Structures (JANUS). At the local level, we introduce a local feature manifold alignment strategy to achieve geometric consistency in the feature space. At the global level, we incorporate structured latent variables and maximize the mutual information with the generated structures, ensuring the injected structures are consistent with the semantic patterns of the original graph. We model the injection attack as a sequential decision process, which is optimized by a reinforcement learning agent. Experiments on multiple standard datasets demonstrate that the JANUS framework significantly outperforms existing methods in terms of both attack effectiveness and stealthiness.

A Graph Machine Learning Approach for Detecting Topological Patterns in Transactional Graphs

The rise of digital ecosystems has exposed the financial sector to evolving abuse and criminal tactics that share operational knowledge and techniques both within and across different environments (fiat-based, crypto-assets, etc.). Traditional rule-based systems lack the adaptability needed to detect sophisticated or coordinated criminal behaviors (patterns), highlighting the need for strategies that analyze actors' interactions to uncover suspicious activities and extract their modus operandi. For this reason, in this work, we propose an approach that integrates graph machine learning and network analysis to improve the detection of well-known topological patterns within transactional graphs. However, a key challenge lies in the limitations of traditional financial datasets, which often provide sparse, unlabeled information that is difficult to use for graph-based pattern analysis. Therefore, we firstly propose a four-step preprocessing framework that involves (i) extracting graph structures, (ii) considering data temporality to manage large node sets, (iii) detecting communities within, and (iv) applying automatic labeling strategies to generate weak ground-truth labels. Then, once the data is processed, Graph Autoencoders are implemented to distinguish among the well-known topological patterns. Specifically, three different GAE variants are implemented and compared in this analysis. Preliminary results show that this pattern-focused, topology-driven method is effective for detecting complex financial crime schemes, offering a promising alternative to conventional rule-based detection systems.

Soft Graph Transformer for MIMO Detection

We propose the Soft Graph Transformer (SGT), a Soft-Input-Soft-Output neural architecture tailored for MIMO detection. While Maximum Likelihood (ML) detection achieves optimal accuracy, its prohibitive exponential complexity renders it impractical for real-world systems. Conventional message passing algorithms offer tractable alternatives but rely on large-system asymptotics and random matrix assumptions, both of which break down under practical implementations. Prior Transformer-based detectors, on the other hand, fail to incorporate the MIMO factor graph structure and cannot utilize decoder-side soft information, limiting their standalone performance and their applicability in iterative detection-decoding (IDD). To overcome these limitations, SGT integrates message passing directly into a graph-aware attention mechanism and supports decoder-informed updates through soft-input embeddings. This design enables effective soft-output generation while preserving computational efficiency. As a standalone detector, SGT closely approaches ML performance and surpasses prior Transformer-based approaches.

Structured Information Loss in Network Embeddings

We analyze a simple algorithm for network embedding, explicitly characterizing conditions under which the learned representation encodes the graph's generative model fully, partially, or not at all. In cases where the embedding loses some information (i.e., is not invertible), we describe the equivalence classes of graphons that map to the same embedding, finding that these classes preserve community structure but lose substantial density information. Finally, we show implications for community detection and link prediction. Our results suggest strong limitations on the effectiveness of link prediction based on embeddings alone, and we show common conditions under which naive link prediction adds edges in a disproportionate manner that can either mitigate or exacerbate structural biases.

Knowledge Graph Tokenization for Behavior-Aware Generative Next POI Recommendation

Generative paradigm, especially powered by Large Language Models (LLMs), has emerged as a new solution to the next point-of-interest (POI) recommendation. Pioneering studies usually adopt a two-stage pipeline, starting with a tokenizer converting POIs into discrete identifiers that can be processed by LLMs, followed by POI behavior prediction tasks to instruction-tune LLM for next POI recommendation. Despite of remarkable progress, they still face two limitations: (1) existing tokenizers struggle to encode heterogeneous signals in the recommendation data, suffering from information loss issue, and (2) previous instruction-tuning tasks only focus on users' POI visit behavior while ignore other behavior types, resulting in insufficient understanding of mobility. To address these limitations, we propose KGTB (Knowledge Graph Tokenization for Behavior-aware generative next POI recommendation). Specifically, KGTB organizes the recommendation data in a knowledge graph (KG) format, of which the structure can seamlessly preserve the heterogeneous information. Then, a KG-based tokenizer is developed to quantize each node into an individual structural ID. This process is supervised by the KG's structure, thus reducing the loss of heterogeneous information. Using generated IDs, KGTB proposes multi-behavior learning that introduces multiple behavior-specific prediction tasks for LLM fine-tuning, e.g., POI, category, and region visit behaviors. Learning on these behavior tasks provides LLMs with comprehensive insights on the target POI visit behavior. Experiments on four real-world city datasets demonstrate the superior performance of KGTB.

Unsupervised Atomic Data Mining via Multi-Kernel Graph Autoencoders for Machine Learning Force Fields

Constructing a chemically diverse dataset while avoiding sampling bias is critical to training efficient and generalizable force fields. However, in computational chemistry and materials science, many common dataset generation techniques are prone to oversampling regions of the potential energy surface. Furthermore, these regions can be difficult to identify and isolate from each other or may not align well with human intuition, making it challenging to systematically remove bias in the dataset. While traditional clustering and pruning (down-sampling) approaches can be useful for this, they can often lead to information loss or a failure to properly identify distinct regions of the potential energy surface due to difficulties associated with the high dimensionality of atomic descriptors. In this work, we introduce the Multi-kernel Edge Attention-based Graph Autoencoder (MEAGraph) model, an unsupervised approach for analyzing atomic datasets. MEAGraph combines multiple linear kernel transformations with attention-based message passing to capture geometric sensitivity and enable effective dataset pruning without relying on labels or extensive training. Demonstrated applications on niobium, tantalum, and iron datasets show that MEAGraph efficiently groups similar atomic environments, allowing for the use of basic pruning techniques for removing sampling bias. This approach provides an effective method for representation learning and clustering that can be used for data analysis, outlier detection, and dataset optimization.

Composable Score-based Graph Diffusion Model for Multi-Conditional Molecular Generation

Controllable molecular graph generation is essential for material and drug discovery, where generated molecules must satisfy diverse property constraints. While recent advances in graph diffusion models have improved generation quality, their effectiveness in multi-conditional settings remains limited due to reliance on joint conditioning or continuous relaxations that compromise fidelity. To address these limitations, we propose Composable Score-based Graph Diffusion model (CSGD), the first model that extends score matching to discrete graphs via concrete scores, enabling flexible and principled manipulation of conditional guidance. Building on this foundation, we introduce two score-based techniques: Composable Guidance (CoG), which allows fine-grained control over arbitrary subsets of conditions during sampling, and Probability Calibration (PC), which adjusts estimated transition probabilities to mitigate train-test mismatches. Empirical results on four molecular datasets show that CSGD achieves state-of-the-art performance, with a 15.3% average improvement in controllability over prior methods, while maintaining high validity and distributional fidelity. Our findings highlight the practical advantages of score-based modeling for discrete graph generation and its capacity for flexible, multi-property molecular design.

Measuring Epistemic Humility in Multimodal Large Language Models

Hallucinations in multimodal large language models (MLLMs) -- where the model generates content inconsistent with the input image -- pose significant risks in real-world applications, from misinformation in visual question answering to unsafe errors in decision-making. Existing benchmarks primarily test recognition accuracy, i.e., evaluating whether models can select the correct answer among distractors. This overlooks an equally critical capability for trustworthy AI: recognizing when none of the provided options are correct, a behavior reflecting epistemic humility. We present HumbleBench, a new hallucination benchmark designed to evaluate MLLMs' ability to reject plausible but incorrect answers across three hallucination types: object, relation, and attribute. Built from a panoptic scene graph dataset, we leverage fine-grained scene graph annotations to extract ground-truth entities and relations, and prompt GPT-4-Turbo to generate multiple-choice questions, followed by a rigorous manual filtering process. Each question includes a "None of the above" option, requiring models not only to recognize correct visual information but also to identify when no provided answer is valid. We evaluate a variety of state-of-the-art MLLMs -- including both general-purpose and specialized reasoning models -- on HumbleBench and share valuable findings and insights with the community. By incorporating explicit false-option rejection, HumbleBench fills a key gap in current evaluation suites, providing a more realistic measure of MLLM reliability in safety-critical settings. Our code and dataset are released publicly and can be accessed at https://github.com/maifoundations/HumbleBench.