Instance-Prototype Affinity Learning for Non-Exemplar Continual Graph Learning

Graph Neural Networks (GNN) endure catastrophic forgetting, undermining their capacity to preserve previously acquired knowledge amid the assimilation of novel information. Rehearsal-based techniques revisit historical examples, adopted as a principal strategy to alleviate this phenomenon. However, memory explosion and privacy infringements impose significant constraints on their utility. Non-Exemplar methods circumvent the prior issues through Prototype Replay (PR), yet feature drift presents new challenges. In this paper, our empirical findings reveal that Prototype Contrastive Learning (PCL) exhibits less pronounced drift than conventional PR. Drawing upon PCL, we propose Instance-Prototype Affinity Learning (IPAL), a novel paradigm for Non-Exemplar Continual Graph Learning (NECGL). Exploiting graph structural information, we formulate Topology-Integrated Gaussian Prototypes (TIGP), guiding feature distributions towards high-impact nodes to augment the model's capacity for assimilating new knowledge. Instance-Prototype Affinity Distillation (IPAD) safeguards task memory by regularizing discontinuities in class relationships. Moreover, we embed a Decision Boundary Perception (DBP) mechanism within PCL, fostering greater inter-class discriminability. Evaluations on four node classification benchmark datasets demonstrate that our method outperforms existing state-of-the-art methods, achieving a better trade-off between plasticity and stability.

Learning Graph Representation of Agent Diffusers

Diffusion-based generative models have significantly advanced text-to-image synthesis, demonstrating impressive text comprehension and zero-shot generalization. These models refine images from random noise based on textual prompts, with initial reliance on text input shifting towards enhanced visual fidelity over time. This transition suggests that static model parameters might not optimally address the distinct phases of generation. We introduce LGR-AD (Learning Graph Representation of Agent Diffusers), a novel multi-agent system designed to improve adaptability in dynamic computer vision tasks. LGR-AD models the generation process as a distributed system of interacting agents, each representing an expert sub-model. These agents dynamically adapt to varying conditions and collaborate through a graph neural network that encodes their relationships and performance metrics. Our approach employs a coordination mechanism based on top-$k$ maximum spanning trees, optimizing the generation process. Each agent's decision-making is guided by a meta-model that minimizes a novel loss function, balancing accuracy and diversity. Theoretical analysis and extensive empirical evaluations show that LGR-AD outperforms traditional diffusion models across various benchmarks, highlighting its potential for scalable and flexible solutions in complex image generation tasks. Code is available at: https://github.com/YousIA/LGR_AD

Negative Metric Learning for Graphs

Graph contrastive learning (GCL) often suffers from false negatives, which degrades the performance on downstream tasks. The existing methods addressing the false negative issue usually rely on human prior knowledge, still leading GCL to suboptimal results. In this paper, we propose a novel Negative Metric Learning (NML) enhanced GCL (NML-GCL). NML-GCL employs a learnable Negative Metric Network (NMN) to build a negative metric space, in which false negatives can be distinguished better from true negatives based on their distance to anchor node. To overcome the lack of explicit supervision signals for NML, we propose a joint training scheme with bi-level optimization objective, which implicitly utilizes the self-supervision signals to iteratively optimize the encoder and the negative metric network. The solid theoretical analysis and the extensive experiments conducted on widely used benchmarks verify the superiority of the proposed method.

Schreier-Coset Graph Propagation

Graph Neural Networks (GNNs) offer a principled framework for learning over graph-structured data, yet their expressive capacity is often hindered by over-squashing, wherein information from distant nodes is compressed into fixed-size vectors. Existing solutions, including graph rewiring and bottleneck-resistant architectures such as Cayley and expander graphs, avoid this problem but introduce scalability bottlenecks. In particular, the Cayley graphs constructed over $SL(2,\mathbb{Z}_n)$ exhibit strong theoretical properties, yet suffer from cubic node growth $O(n^3)$, leading to high memory usage. To address this, this work introduces Schrier-Coset Graph Propagation (SCGP), a group-theoretic augmentation method that enriches node features through Schreier-coset embeddings without altering the input graph topology. SCGP embeds bottleneck-free connectivity patterns into a compact feature space, improving long-range message passing while maintaining computational efficiency. Empirical evaluations across standard node and graph classification benchmarks demonstrate that SCGP achieves performance comparable to, or exceeding, expander graph and rewired GNN baselines. Furthermore, SCGP exhibits particular advantages in processing hierarchical and modular graph structures, offering reduced inference latency, improved scalability, and a low memory footprint, making it suitable for real-time and resource-constrained applications.

Leveraging Graph Retrieval-Augmented Generation to Support Learners' Understanding of Knowledge Concepts in MOOCs

Massive Open Online Courses (MOOCs) lack direct interaction between learners and instructors, making it challenging for learners to understand new knowledge concepts. Recently, learners have increasingly used Large Language Models (LLMs) to support them in acquiring new knowledge. However, LLMs are prone to hallucinations which limits their reliability. Retrieval-Augmented Generation (RAG) addresses this issue by retrieving relevant documents before generating a response. However, the application of RAG across different MOOCs is limited by unstructured learning material. Furthermore, current RAG systems do not actively guide learners toward their learning needs. To address these challenges, we propose a Graph RAG pipeline that leverages Educational Knowledge Graphs (EduKGs) and Personal Knowledge Graphs (PKGs) to guide learners to understand knowledge concepts in the MOOC platform CourseMapper. Specifically, we implement (1) a PKG-based Question Generation method to recommend personalized questions for learners in context, and (2) an EduKG-based Question Answering method that leverages the relationships between knowledge concepts in the EduKG to answer learner selected questions. To evaluate both methods, we conducted a study with 3 expert instructors on 3 different MOOCs in the MOOC platform CourseMapper. The results of the evaluation show the potential of Graph RAG to empower learners to understand new knowledge concepts in a personalized learning experience.

Learning Kronecker-Structured Graphs from Smooth Signals

Graph learning, or network inference, is a prominent problem in graph signal processing (GSP). GSP generalizes the Fourier transform to non-Euclidean domains, and graph learning is pivotal to applying GSP when these domains are unknown. With the recent prevalence of multi-way data, there has been growing interest in product graphs that naturally factorize dependencies across different ways. However, the types of graph products that can be learned are still limited for modeling diverse dependency structures. In this paper, we study the problem of learning a Kronecker-structured product graph from smooth signals. Unlike the more commonly used Cartesian product, the Kronecker product models dependencies in a more intricate, non-separable way, but posits harder constraints on the graph learning problem. To tackle this non-convex problem, we propose an alternating scheme to optimize each factor graph and provide theoretical guarantees for its asymptotic convergence. The proposed algorithm is also modified to learn factor graphs of the strong product. We conduct experiments on synthetic and real-world graphs and demonstrate our approach's efficacy and superior performance compared to existing methods.

Rhomboid Tiling for Geometric Graph Deep Learning

Graph Neural Networks (GNNs) have proven effective for learning from graph-structured data through their neighborhood-based message passing framework. Many hierarchical graph clustering pooling methods modify this framework by introducing clustering-based strategies, enabling the construction of more expressive and powerful models. However, all of these message passing framework heavily rely on the connectivity structure of graphs, limiting their ability to capture the rich geometric features inherent in geometric graphs. To address this, we propose Rhomboid Tiling (RT) clustering, a novel clustering method based on the rhomboid tiling structure, which performs clustering by leveraging the complex geometric information of the data and effectively extracts its higher-order geometric structures. Moreover, we design RTPool, a hierarchical graph clustering pooling model based on RT clustering for graph classification tasks. The proposed model demonstrates superior performance, outperforming 21 state-of-the-art competitors on all the 7 benchmark datasets.

Radiogenomic Bipartite Graph Representation Learning for Alzheimer's Disease Detection

Imaging and genomic data offer distinct and rich features, and their integration can unveil new insights into the complex landscape of diseases. In this study, we present a novel approach utilizing radiogenomic data including structural MRI images and gene expression data, for Alzheimer's disease detection. Our framework introduces a novel heterogeneous bipartite graph representation learning featuring two distinct node types: genes and images. The network can effectively classify Alzheimer's disease (AD) into three distinct stages:AD, Mild Cognitive Impairment (MCI), and Cognitive Normal (CN) classes, utilizing a small dataset. Additionally, it identified which genes play a significant role in each of these classification groups. We evaluate the performance of our approach using metrics including classification accuracy, recall, precision, and F1 score. The proposed technique holds potential for extending to radiogenomic-based classification to other diseases.

All You Need Is Synthetic Task Augmentation

Injecting rule-based models like Random Forests into differentiable neural network frameworks remains an open challenge in machine learning. Recent advancements have demonstrated that pretrained models can generate efficient molecular embeddings. However, these approaches often require extensive pretraining and additional techniques, such as incorporating posterior probabilities, to boost performance. In our study, we propose a novel strategy that jointly trains a single Graph Transformer neural network on both sparse multitask molecular property experimental targets and synthetic targets derived from XGBoost models trained on Osmordred molecular descriptors. These synthetic tasks serve as independent auxiliary tasks. Our results show consistent and significant performance improvement across all 19 molecular property prediction tasks. For 16 out of 19 targets, the multitask Graph Transformer outperforms the XGBoost single-task learner. This demonstrates that synthetic task augmentation is an effective method for enhancing neural model performance in multitask molecular property prediction without the need for feature injection or pretraining.

Learning Multi-Attribute Differential Graphs with Non-Convex Penalties

We consider the problem of estimating differences in two multi-attribute Gaussian graphical models (GGMs) which are known to have similar structure, using a penalized D-trace loss function with non-convex penalties. The GGM structure is encoded in its precision (inverse covariance) matrix. Existing methods for multi-attribute differential graph estimation are based on a group lasso penalized loss function. In this paper, we consider a penalized D-trace loss function with non-convex (log-sum and smoothly clipped absolute deviation (SCAD)) penalties. Two proximal gradient descent methods are presented to optimize the objective function. Theoretical analysis establishing sufficient conditions for consistency in support recovery, convexity and estimation in high-dimensional settings is provided. We illustrate our approaches with numerical examples based on synthetic and real data.