A key challenge in graph out-of-distribution (OOD) detection lies in the absence of ground-truth OOD samples during training. Existing methods are typically optimized to capture features within the in-distribution (ID) data and calculate OOD scores, which often limits pre-trained models from representing distributional boundaries, leading to unreliable OOD detection. Moreover, the latent structure of graph data is often governed by multiple underlying factors, which remains less explored. To address these challenges, we propose a novel test-time graph OOD detection method, termed BaCa, that calibrates OOD scores using dual dynamically updated dictionaries without requiring fine-tuning the pre-trained model. Specifically, BaCa estimates graphons and applies a mix-up strategy solely with test samples to generate diverse boundary-aware discriminative topologies, eliminating the need for exposing auxiliary datasets as outliers. We construct dual dynamic dictionaries via priority queues and attention mechanisms to adaptively capture latent ID and OOD representations, which are then utilized for boundary-aware OOD score calibration. To the best of our knowledge, extensive experiments on real-world datasets show that BaCa significantly outperforms existing state-of-the-art methods in OOD detection.

With the emerging of huge amount of unlabeled data, unsupervised out-of-distribution (OOD) detection is vital for ensuring the reliability of graph neural networks (GNNs) by identifying OOD samples from in-distribution (ID) ones during testing, where encountering novel or unknown data is inevitable. Existing methods often suffer from compromised performance due to redundant information in graph structures, which impairs their ability to effectively differentiate between ID and OOD data. To address this challenge, we propose SEGO, an unsupervised framework that integrates structural entropy into OOD detection regarding graph classification. Specifically, within the architecture of contrastive learning, SEGO introduces an anchor view in the form of coding tree by minimizing structural entropy. The obtained coding tree effectively removes redundant information from graphs while preserving essential structural information, enabling the capture of distinct graph patterns between ID and OOD samples. Furthermore, we present a multi-grained contrastive learning scheme at local, global, and tree levels using triplet views, where coding trees with essential information serve as the anchor view. Extensive experiments on real-world datasets validate the effectiveness of SEGO, demonstrating superior performance over state-of-the-art baselines in OOD detection. Specifically, our method achieves the best performance on 9 out of 10 dataset pairs, with an average improvement of 3.7% on OOD detection datasets, significantly surpassing the best competitor by 10.8% on the FreeSolv/ToxCast dataset pair.

Out-of-distribution (OOD) detection for graph-structured data remains a challenging problem, particularly when test-time OOD samples deviate significantly from the training outliers. Existing methods are typically optimized to capture the features within the in-distribution (ID) training data, but often fail to model the transitional region near the boundary between ID and OOD samples. Moreover, since data distributions are usually governed by multiple latent factors, pre-trained models constrained by the scope and diversity of training data struggle to represent the full spectrum of sample characteristics and distributional boundaries. To address this dilemma, we propose a novel test-time graph OOD detection method, termed D2GO, that constructs and dynamically updates ID and OOD graphon dictionaries for OOD score calibration, without requiring fine-tuning. Specifically, D2GO estimates graphons from test graphs and employs a mix-up strategy to generate boundary samples, eliminating the need for exposing auxiliary datasets or training graphs. Priority queues are utilized to expand the ID and OOD dictionaries by incorporating diverse graphons based on pseudo-labels at test-time, and the OOD scores are calibrated by computing the similarity between test samples and both graphon dictionaries. Extensive experiments on real-world datasets show that D2GO significantly outperforms existing state-of-the-art methods in OOD detection.

Distributional discrepancy between training and test data can lead models to make inaccurate predictions when encountering out-of-distribution (OOD) samples in real-world applications. Although existing graph OOD detection methods leverage data-centric techniques to extract effective representations, their performance remains compromised by structural redundancy that induces semantic shifts. To address this dilemma, we propose RedOUT, an unsupervised framework that integrates structural entropy into test-time OOD detection for graph classification. Concretely, we introduce the Redundancy-aware Graph Information Bottleneck (ReGIB) and decompose the objective into essential information and irrelevant redundancy. By minimizing structural entropy, the decoupled redundancy is reduced, and theoretically grounded upper and lower bounds are proposed for optimization. Extensive experiments on real-world datasets demonstrate the superior performance of RedOUT on OOD detection. Specifically, our method achieves an average improvement of 6.7\%, significantly surpassing the best competitor by 17.3\% on the ClinTox/LIPO dataset pair.