Graph anomaly detection (GAD) is widely prevalent in scenarios such as financial fraud detection, anti-money laundering and social bot detecion. However, structural distribution shifts are commonly observed in real-world GAD data due to selection bias, resulting in reduced homophily. Existing GAD methods tend to rely on homophilic shortcuts when trained on high-homophily structures, limiting their ability to generalize well to data with low homophily under structural distribution shifts. In this study, we propose to handle structural distribution shifts by generating novel environments characterized by diverse homophilic structures and utilizing invariant patterns, i.e., features and structures with the capability of stable prediction across structural distribution shifts, which face two challenges: (1) How to discover invariant patterns from entangled features and structures, as structures are sensitive to varying homophilic distributions.

Effective generalization in robotic manipulation requires representations that capture invariant patterns of interaction across environments and tasks. We present a self-supervised framework for learning hierarchical manipulation concepts that encode these invariant patterns through cross-modal sensory correlations and multi-level temporal abstractions without requiring human annotation. Our approach combines a cross-modal correlation network that identifies persistent patterns across sensory modalities with a multi-horizon predictor that organizes representations hierarchically across temporal scales. Manipulation concepts learned through this dual structure enable policies to focus on transferable relational patterns while maintaining awareness of both immediate actions and longer-term goals. Empirical evaluation across simulated benchmarks and real-world deployments demonstrates significant performance improvements with our concept-enhanced policies. Analysis reveals that the learned concepts resemble human-interpretable manipulation primitives despite receiving no semantic supervision. This work advances both the understanding of representation learning for manipulation and provides a practical approach to enhancing robotic performance in complex scenarios.

Dynamic graph neural networks (DyGNNs) currently struggle with handling distribution shifts that are inherent in dynamic graphs. Existing work on DyGNNs with out-of-distribution settings only focuses on the time domain, failing to handle cases involving distribution shifts in the spectral domain. In this paper, we discover that there exist cases with distribution shifts unobservable in the time domain while observable in the spectral domain, and propose to study distribution shifts on dynamic graphs in the spectral domain for the first time. However, this investigation poses two key challenges: i) it is non-trivial to capture different graph patterns that are driven by various frequency components entangled in the spectral domain; and ii) it remains unclear how to handle distribution shifts with the discovered spectral patterns. To address these challenges, we propose Spectral Invariant Learning for Dynamic Graphs under Distribution Shifts (SILD), which can handle distribution shifts on dynamic graphs by capturing and utilizing invariant and variant spectral patterns. Specifically, we first design a DyGNN with Fourier transform to obtain the ego-graph trajectory spectrums, allowing the mixed dynamic graph patterns to be transformed into separate frequency components. We then develop a disentangled spectrum mask to filter graph dynamics from various frequency components and discover the invariant and variant spectral patterns. Finally, we propose invariant spectral filtering, which encourages the model to rely on invariant patterns for generalization under distribution shifts. Experimental results on synthetic and real-world dynamic graph datasets demonstrate the superiority of our method for both node classification and link prediction tasks under distribution shifts.

Dynamic graph neural networks (DyGNNs) currently struggle with handling distribution shifts that are inherent in dynamic graphs.

Lastly, we propose an invariance regularization term to minimize the variance of predictions in intervened distributions so that our model can make predictions based on invariant patterns with stable predictive abilities and thereforehandle distribution shifts. Experiments onthree real-worlddatasets andone synthetic dataset demonstrate the superiority ofour method overstate-of-the-art baselines under distribution shifts.