  In many real-world applications, test data may commonly exhibit categorical
shifts, characterized by the emergence of novel classes, as well as
distribution shifts arising from feature distributions different from the ones
the model was trained on. However, existing methods either discover novel
classes in the open-world setting or assume domain shifts without the ability
to discover novel classes. In this work, we consider a cross-domain open-world
discovery setting, where the goal is to assign samples to seen classes and
discover unseen classes under a domain shift. To address this challenging
problem, we present CROW, a prototype-based approach that introduces a
cluster-then-match strategy enabled by a well-structured representation space
of foundation models. In this way, CROW discovers novel classes by robustly
matching clusters with previously seen classes, followed by fine-tuning the
representation space using an objective designed for cross-domain open-world
discovery. Extensive experimental results on image classification benchmark
datasets demonstrate that CROW outperforms alternative baselines, achieving an
8% average performance improvement across 75 experimental settings.
