In panoptic segmentation, individual instances must be separated within semantic classes. As state-of-the-art methods rely on a pre-defined set of classes, they struggle with novel categories and out-of-distribution (OOD) data. This is particularly problematic in safety-critical applications, such as autonomous driving, where reliability in unseen scenarios is essential. We address the gap between outstanding benchmark performance and reliability by proposing Prior2Former (P2F), the first approach for segmentation vision transformers rooted in evidential learning. P2F extends the mask vision transformer architecture by incorporating a Beta prior for computing model uncertainty in pixel-wise binary mask assignments. This design enables high-quality uncertainty estimation that effectively detects novel and OOD objects enabling state-of-the-art anomaly instance segmentation and open-world panoptic segmentation. Unlike most segmentation models addressing unknown classes, P2F operates without access to OOD data samples or contrastive training on void (i.e., unlabeled) classes, making it highly applicable in real-world scenarios where such prior information is unavailable. Additionally, P2F can be flexibly applied to anomaly instance and panoptic segmentation. Through comprehensive experiments on the Cityscapes, COCO, SegmentMeIfYouCan, and OoDIS datasets, P2F demonstrates state-of-the-art performance across the board.

Many applications in traffic, civil engineering, or electrical engineering revolve around edge-level signals. Such signals can be categorized as inherently directed, for example, the water flow in a pipe network, and undirected, like the diameter of a pipe. Topological methods model edge signals with inherent direction by representing them relative to a so-called *orientation* assigned to each edge. They can neither model undirected edge signals nor distinguish if an edge itself is directed or undirected. We address these shortcomings by (i) revising the notion of *orientation equivariance* to enable edge direction-aware topological models, (ii) proposing *orientation invariance* as an additional requirement to describe signals without inherent direction, and (iii) developing EIGN, an architecture composed of novel direction-aware edge-level graph shift operators, that provably fulfils the aforementioned desiderata. It is the first work that discusses modeling directed and undirected signals while distinguishing between directed and undirected edges. A comprehensive evaluation shows that EIGN outperforms prior work in edge-level tasks, improving in RMSE on flow simulation tasks by up to 23.5%.

While uncertainty estimation for graphs recently gained traction, most methods rely on homophily and deteriorate in heterophilic settings. We address this by analyzing message passing neural networks from an information-theoretic perspective and developing a suitable analog to data processing inequality to quantify information throughout the model’s layers. In contrast to non-graph domains, information about the node-level prediction target can increase with model depth if a node’s features are semantically different from its neighbors. Therefore, on heterophilic graphs, the latent embeddings of an MPNN each provide different information about the data distribution - different from homophilic settings. This reveals that considering all node representations simultaneously is a key design principle for epistemic uncertainty estimation on graphs beyond homophily. We empirically confirm this with a simple post-hoc density estimator on the joint node embedding space that provides state-of-the-art uncertainty on heterophilic graphs. At the same time, it matches prior work on homophilic graphs without explicitly exploiting homophily through post-processing.

Uncertainty Sampling is an Active Learning strategy that aims to improve the data efficiency of machine learning models by iteratively acquiring labels of data points with the highest uncertainty. While it has proven effective for independent data its applicability to graphs remains under-explored. We propose the first extensive study of Uncertainty Sampling for node classification: (1) We benchmark Uncertainty Sampling beyond predictive uncertainty and highlight a significant performance gap to other Active Learning strategies. (2) We develop ground-truth Bayesian uncertainty estimates in terms of the data generating process and prove their effectiveness in guiding Uncertainty Sampling toward optimal queries. We confirm our results on synthetic data and design an approximate approach that consistently outperforms other uncertainty estimators on real datasets. (3) Based on this analysis, we relate pitfalls in modeling uncertainty to existing methods. Our analysis enables and informs the development of principled uncertainty estimation on graphs.

In domains with interdependent data, such as graphs, quantifying the epistemic uncertainty of a Graph Neural Network (GNN) is challenging as uncertainty can arise at different structural scales. Existing techniques neglect this issue or only distinguish between structure-aware and structure-agnostic uncertainty without combining them into a single measure. We propose GEBM, an energy-based model (EBM) that provides high-quality uncertainty estimates by aggregating energy at different structural levels that naturally arise from graph diffusion. In contrast to logit-based EBMs, we provably induce an integrable density in the data space by regularizing the energy function. We introduce an evidential interpretation of our EBM that significantly improves the predictive robustness of the GNN. Our framework is a simple and effective post hoc method applicable to any pre-trained GNN that is sensitive to various distribution shifts. It consistently achieves the best separation of in-distribution and out-of-distribution data on 6 out of 7 anomaly types while having the best average rank over shifts on *all* datasets.