HOPE: Heterophily-Aware Open-Set Node Classification with Pseudo-Extrapolation

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Standard open-set node classification methods rely on the homophily assumption, where connected nodes share labels. However, real-world graphs are often heterophilic, exposing the limitations of current methods and posing new challenges to open-set node classification. On the one hand, cross-class connectivity causes representations from different known or unknown classes to become intertwined after aggregation, undermining their discriminative capacity. On the other hand, structural mixture invalidates threshold-based open-set methods and cross-class feature interpolation, leading to unreliable unknown-class rejection. To address these challenges, we propose HOPE, a Heterophily-aware Open-set node classification method with Pseudo-Extrapolation. To adapt open-set graph neural networks (GNNs) to heterophilic scenarios, HOPE uses a structure-augmented feature initialization layer to capture multi-hop structural patterns. Meanwhile, we design a trustworthy neighborhood aggregation mechanism for standard GNNs to dynamically filter noisy cross-class neighbors. To enhance unknown-class rejection, we introduce a heterophily-guided pseudo-extrapolation strategy. It dynamically maintains known-class centers and extrapolates along cross-class neighborhood displacement directions, synthesizing pseudo-unknown proxies near structurally ambiguous regions. Finally, we optimize the network with joint classification and logit margin regularization, routing synthetic proxies into a dedicated rejection slot without imposing geometric margin constraints in the representation space. Extensive experiments on multiple datasets show that HOPE consistently outperforms state-of-the-art models, validating its effectiveness, robustness, and efficiency.