RiemannGL: Riemannian Geometry Changes Graph Deep Learning

Graphs are ubiquitous, and learning on graphs has become a cornerstone in artificial intelligence and data mining communities. Unlike pixel grids in images or sequential structures in language, graphs exhibit a typical non-Euclidean structure with complex interactions among the objects. This paper argues that Riemannian geometry provides a principled and necessary foundation for graph representation learning, and that Riemannian graph learning should be viewed as a unifying paradigm rather than a collection of isolated techniques. While recent studies have explored the integration of graph learning and Riemannian geometry, most existing approaches are limited to a narrow class of manifolds, particularly hyperbolic spaces, and often adopt extrinsic manifold formulations. We contend that the central mission of Riemannian graph learning is to endow graph neural networks with intrinsic manifold structures, which remains underexplored. To advance this perspective, we identify key conceptual and methodological gaps in existing approaches and outline a structured research agenda along three dimensions: manifold type, neural architecture, and learning paradigm. We further discuss open challenges, theoretical foundations, and promising directions that are critical for unlocking the full potential of Riemannian graph learning. This paper aims to provide a coherent viewpoint and to stimulate broader exploration of Riemannian geometry as a foundational framework for future graph learning research.

RiemannGFM: Learning a Graph Foundation Model from Riemannian Geometry

The foundation model has heralded a new era in artificial intelligence, pretraining a single model to offer cross-domain transferability on different datasets. Graph neural networks excel at learning graph data, the omnipresent non-Euclidean structure, but often lack the generalization capacity. Hence, graph foundation model is drawing increasing attention, and recent efforts have been made to leverage Large Language Models. On the one hand, existing studies primarily focus on text-attributed graphs, while a wider range of real graphs do not contain fruitful textual attributes. On the other hand, the sequential graph description tailored for the Large Language Model neglects the structural complexity, which is a predominant characteristic of the graph. Such limitations motivate an important question: Can we go beyond Large Language Models, and pretrain a universal model to learn the structural knowledge for any graph? The answer in the language or vision domain is a shared vocabulary. We observe the fact that there also exist shared substructures underlying graph domain, and thereby open a new opportunity of graph foundation model with structural vocabulary. The key innovation is the discovery of a simple yet effective structural vocabulary of trees and cycles, and we explore its inherent connection to Riemannian geometry. Herein, we present a universal pretraining model, RiemannGFM. Concretely, we first construct a novel product bundle to incorporate the diverse geometries of the vocabulary. Then, on this constructed space, we stack Riemannian layers where the structural vocabulary, regardless of specific graph, is learned in Riemannian manifold offering cross-domain transferability. Extensive experiments show the effectiveness of RiemannGFM on a diversity of real graphs.

KAnoCLIP: Zero-Shot Anomaly Detection through Knowledge-Driven Prompt Learning and Enhanced Cross-Modal Integration

Zero-shot anomaly detection (ZSAD) identifies anomalies without needing training samples from the target dataset, essential for scenarios with privacy concerns or limited data. Vision-language models like CLIP show potential in ZSAD but have limitations: relying on manually crafted fixed textual descriptions or anomaly prompts is time-consuming and prone to semantic ambiguity, and CLIP struggles with pixel-level anomaly segmentation, focusing more on global semantics than local details. To address these limitations, We introduce KAnoCLIP, a novel ZSAD framework that leverages vision-language models. KAnoCLIP combines general knowledge from a Large Language Model (GPT-3.5) and fine-grained, image-specific knowledge from a Visual Question Answering system (Llama3) via Knowledge-Driven Prompt Learning (KnPL). KnPL uses a knowledge-driven (KD) loss function to create learnable anomaly prompts, removing the need for fixed text prompts and enhancing generalization. KAnoCLIP includes the CLIP visual encoder with V-V attention (CLIP-VV), Bi-Directional Cross-Attention for Multi-Level Cross-Modal Interaction (Bi-CMCI), and Conv-Adapter. These components preserve local visual semantics, improve local cross-modal fusion, and align global visual features with textual information, enhancing pixel-level anomaly detection. KAnoCLIP achieves state-of-the-art performance in ZSAD across 12 industrial and medical datasets, demonstrating superior generalization compared to existing methods.