CIGR: Causal Invariant Representation Learning Framework With Global Redundancy Information for Open-Set Multi-Target Domain Adaptation

Prior studies on domain adaptation typically assume a single target domain and a closed-set label space, whereas real-world open-world settings often involve multiple target domains and an open-set label space. Motivated by this gap, we propose a novel Open-Set Multi-Target Domain Adaptation (OSMTDA) setting, enabling adaptation from a labeled source domain to multiple unlabeled targets under open-set conditions. To this end, we derive a theoretical upper bound on the joint optimization risk for OSMTDA, covering known-class classification, unknown-class recognition, and cross-domain alignment. Based on this analysis, we propose a Causal-Invariant representation learning framework with Global Redundancy information (CIGR) for OSMTDA. Specifically, by characterizing the relationship between features and labels, we propose a global redundant-information separation strategy and develop a causal correction and augmentation module (CCAM) to effectively leverage the separated redundant information, thereby improving the recognition of both known and unknown classes. Further, we propose a novel structural causal model for the open-set setting and formulate a causal-invariance objective that jointly covers known and unknown classes. Finally, we propose a graph-based multi-domain causal invariance learning (MCIL) module that generates virtual unknown features from redundant factors, enabling causally invariant representations for known and unknown classes. Extensive experiments on four datasets with two backbones have been conducted to validate the consistently superior performance of CIGR.