Aspect-Aware MOOC Recommendation in a Heterogeneous Network

MOOC recommendation systems have received increasing attention to help learners navigate and select preferred learning content. Traditional methods such as collaborative filtering and content-based filtering suffer from data sparsity and over-specialization. To alleviate these limitations, graph-based approaches have been proposed; however, they still rely heavily on manually predefined metapaths, which often capture only superficial structural relationships and impose substantial burdens on domain experts as well as significant engineering costs. To overcome these limitations, we propose AMR (Aspect-aware MOOC Recommendation), a novel framework that models path-specific multiple aspects by embedding the semantic content of nodes within each metapath. AMR automatically discovers metapaths through bi-directional walks, derives aspect-aware path representations using a bi-LSTM-based encoder, and incorporates these representations as edge features in the learner-learner and KC-KC subgraphs to achieve fine-grained semantically informed KC recommendations. Extensive experiments on the large-scale MOOCCube and PEEK datasets show that AMR consistently outperforms state-of-the-art graph neural network baselines across key metrics such as HR@K and nDCG@K. Further analysis confirms that AMR effectively captures rich path-specific aspect information, allowing more accurate recommendations than those methods that rely solely on predefined metapaths. The code will be available upon accepted.

Breaking Symmetry Bottlenecks in GNN Readouts

Graph neural networks (GNNs) are widely used for learning on structured data, yet their ability to distinguish non-isomorphic graphs is fundamentally limited. These limitations are usually attributed to message passing; in this work we show that an independent bottleneck arises at the readout stage. Using finite-dimensional representation theory, we prove that all linear permutation-invariant readouts, including sum and mean pooling, factor through the Reynolds (group-averaging) operator and therefore project node embeddings onto the fixed subspace of the permutation action, erasing all non-trivial symmetry-aware components regardless of encoder expressivity. This yields both a new expressivity barrier and an interpretable characterization of what global pooling preserves or destroys. To overcome this collapse, we introduce projector-based invariant readouts that decompose node representations into symmetry-aware channels and summarize them with nonlinear invariant statistics, preserving permutation invariance while retaining information provably invisible to averaging. Empirically, swapping only the readout enables fixed encoders to separate WL-hard graph pairs and improves performance across multiple benchmarks, demonstrating that readout design is a decisive and under-appreciated factor in GNN expressivity.

Training A Foundation Model to Represent Graphs as Vectors

This paper aims to train a graph foundation model that is able to represent any graph as a vector preserving structural and semantic information useful for downstream graph-level tasks such as graph classification and graph clustering. To learn the features of graphs from diverse domains while maintaining strong generalization ability to new domains, we propose a multi-graph-based feature alignment method, which constructs weighted graphs using the attributes of all nodes in each dataset and then generates consistent node embeddings. To enhance the consistency of the features from different datasets, we propose a density maximization mean alignment algorithm with guaranteed convergence. The original graphs and generated node embeddings are fed into a graph neural network to achieve discriminative graph representations in contrastive learning. More importantly, to enhance the information preservation from node-level representations to the graph-level representation, we construct a multi-layer reference distribution module without using any pooling operation. We also provide a theoretical generalization bound to support the effectiveness of the proposed model. The experimental results of few-shot graph classification and graph clustering show that our model outperforms strong baselines.

Plain Transformers are Surprisingly Powerful Link Predictors

Link prediction is a core challenge in graph machine learning, demanding models that capture rich and complex topological dependencies. While Graph Neural Networks (GNNs) are the standard solution, state-of-the-art pipelines often rely on explicit structural heuristics or memory-intensive node embeddings -- approaches that struggle to generalize or scale to massive graphs. Emerging Graph Transformers (GTs) offer a potential alternative but often incur significant overhead due to complex structural encodings, hindering their applications to large-scale link prediction. We challenge these sophisticated paradigms with PENCIL, an encoder-only plain Transformer that replaces hand-crafted priors with attention over sampled local subgraphs, retaining the scalability and hardware efficiency of standard Transformers. Through experimental and theoretical analysis, we show that PENCIL extracts richer structural signals than GNNs, implicitly generalizing a broad class of heuristics and subgraph-based expressivity. Empirically, PENCIL outperforms heuristic-informed GNNs and is far more parameter-efficient than ID-embedding--based alternatives, while remaining competitive across diverse benchmarks -- even without node features. Our results challenge the prevailing reliance on complex engineering techniques, demonstrating that simple design choices are potentially sufficient to achieve the same capabilities.

Enhancing Imbalanced Node Classification via Curriculum-Guided Feature Learning and Three-Stage Attention Network

Imbalanced node classification in graph neural networks (GNNs) happens when some labels are much more common than others, which causes the model to learn unfairly and perform badly on the less common classes. To solve this problem, we propose a Curriculum-Guided Feature Learning and Three-Stage Attention Network (CL3AN-GNN), a learning network that uses a three-step attention system (Engage, Enact, Embed) similar to how humans learn. The model begins by engaging with structurally simpler features, defined as (1) local neighbourhood patterns (1-hop), (2) low-degree node attributes, and (3) class-separable node pairs identified via initial graph convolutional networks and graph attention networks (GCN and GAT) embeddings. This foundation enables stable early learning despite label skew. The Enact stage then addresses complicated aspects: (1) connections that require multiple steps, (2) edges that connect different types of nodes, and (3) nodes at the edges of minority classes by using adjustable attention weights. Finally, Embed consolidates these features via iterative message passing and curriculum-aligned loss weighting. We evaluate CL3AN-GNN on eight Open Graph Benchmark datasets spanning social, biological, and citation networks. Experiments show consistent improvements across all datasets in accuracy, F1-score, and AUC over recent state-of-the-art methods. The model's step-by-step method works well with different types of graph datasets, showing quicker results than training everything at once, better performance on new, imbalanced graphs, and clear explanations of each step using gradient stability and attention correlation learning curves. This work provides both a theoretically grounded framework for curriculum learning in GNNs and practical evidence of its effectiveness against imbalances, validated through metrics, convergence speeds, and generalisation tests.

Topology Matters: A Cautionary Case Study of Graph SSL on Neuro-Inspired Benchmarks

Understanding how local interactions give rise to global brain organization requires models that can represent information across multiple scales. We introduce a hierarchical self-supervised learning (SSL) framework that jointly learns node-, edge-, and graph-level embeddings, inspired by multimodal neuroimaging. We construct a controllable synthetic benchmark mimicking the topological properties of connectomes. Our four-stage evaluation protocol reveals a critical failure: the invariance-based SSL model is fundamentally misaligned with the benchmark's topological properties and is catastrophically outperformed by classical, topology-aware heuristics. Ablations confirm an objective mismatch: SSL objectives designed to be invariant to topological perturbations learn to ignore the very community structure that classical methods exploit. Our results expose a fundamental pitfall in applying generic graph SSL to connectome-like data. We present this framework as a cautionary case study, highlighting the need for new, topology-aware SSL objectives for neuro-AI research that explicitly reward the preservation of structure (e.g., modularity or motifs).

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits

We study the statistical behaviour of reasoning probes in a stylized model of looped reasoning, given by Boolean circuits whose computational graph is a perfect $ν$-ary tree ($ν\ge 2$) and whose output is appended to the input and fed back iteratively for subsequent computation rounds. A reasoning probe has access to a sampled subset of internal computation nodes, possibly without covering the entire graph, and seeks to infer which $ν$-ary Boolean gate is executed at each queried node, representing uncertainty via a probability distribution over a fixed collection of $\mathtt{m}$ admissible $ν$-ary gates. This partial observability induces a generalization problem, which we analyze in a realizable, transductive setting. We show that, when the reasoning probe is parameterized by a graph convolutional network (GCN)-based hypothesis class and queries $N$ nodes, the worst-case generalization error attains the optimal rate $\mathcal{O}(\sqrt{\log(2/δ)}/\sqrt{N})$ with probability at least $1-δ$, for $δ\in (0,1)$. Our analysis combines snowflake metric embedding techniques with tools from statistical optimal transport. A key insight is that this optimal rate is achievable independently of graph size, owing to the existence of a low-distortion one-dimensional snowflake embedding of the induced graph metric. As a consequence, our results provide a sharp characterization of how structural properties of the computational graph govern the statistical efficiency of reasoning under partial access.

PIMPC-GNN: Physics-Informed Multi-Phase Consensus Learning for Enhancing Imbalanced Node Classification in Graph Neural Networks

Graph neural networks (GNNs) often struggle in class-imbalanced settings, where minority classes are under-represented and predictions are biased toward majorities. We propose \textbf{PIMPC-GNN}, a physics-informed multi-phase consensus framework for imbalanced node classification. Our method integrates three complementary dynamics: (i) thermodynamic diffusion, which spreads minority labels to capture long-range dependencies, (ii) Kuramoto synchronisation, which aligns minority nodes through oscillatory consensus, and (iii) spectral embedding, which separates classes via structural regularisation. These perspectives are combined through class-adaptive ensemble weighting and trained with an imbalance-aware loss that couples balanced cross-entropy with physics-based constraints. Across five benchmark datasets and imbalance ratios from 5-100, PIMPC-GNN outperforms 16 state-of-the-art baselines, achieving notable gains in minority-class recall (up to +12.7\%) and balanced accuracy (up to +8.3\%). Beyond empirical improvements, the framework also provides interpretable insights into consensus dynamics in graph learning. The code is available at \texttt{https://github.com/afofanah/PIMPC-GNN}.

Hyperbolic Graph Neural Networks Under the Microscope: The Role of Geometry-Task Alignment

Many complex networks exhibit hyperbolic structural properties, making hyperbolic space a natural candidate for representing hierarchical and tree-like graphs with low distortion. Based on this observation, Hyperbolic Graph Neural Networks (HGNNs) have been widely adopted as a principled choice for representation learning on tree-like graphs. In this work, we question this paradigm by proposing an additional condition of geometry-task alignment, i.e., whether the metric structure of the target follows that of the input graph. We theoretically and empirically demonstrate the capability of HGNNs to recover low-distortion representations on two synthetic regression problems, and show that their geometric inductive bias becomes helpful when the problem requires preserving metric structure. Additionally, we evaluate HGNNs on the tasks of link prediction and node classification by jointly analyzing predictive performance and embedding distortion, revealing that only link prediction is geometry-aligned. Overall, our findings shift the focus from only asking "Is the graph hyperbolic?" to also questioning "Is the task aligned with hyperbolic geometry?", showing that HGNNs consistently outperform Euclidean models under such alignment, while their advantage vanishes otherwise.

Learning Consistent Causal Abstraction Networks

Causal artificial intelligence aims to enhance explainability, trustworthiness, and robustness in AI by leveraging structural causal models (SCMs). In this pursuit, recent advances formalize network sheaves and cosheaves of causal knowledge. Pushing in the same direction, we tackle the learning of consistent causal abstraction network (CAN), a sheaf-theoretic framework where (i) SCMs are Gaussian, (ii) restriction maps are transposes of constructive linear causal abstractions (CAs) adhering to the semantic embedding principle, and (iii) edge stalks correspond--up to permutation--to the node stalks of more detailed SCMs. Our problem formulation separates into edge-specific local Riemannian problems and avoids nonconvex objectives. We propose an efficient search procedure, solving the local problems with SPECTRAL, our iterative method with closed-form updates and suitable for positive definite and semidefinite covariance matrices. Experiments on synthetic data show competitive performance in the CA learning task, and successful recovery of diverse CAN structures.