We introduce Low-Shot Open-Set Domain Generalization (LSOSDG), a novel paradigm unifying low-shot learning with open-set domain generalization (ODG). While prompt-based methods using models like CLIP have advanced DG, they falter in low-data regimes (e.g., 1-shot) and lack precision in detecting open-set samples with finegrained semantics related to training classes. To address these challenges, we propose OSLoPrompt, an advanced prompt-learning framework for CLIP with two core innovations. First, to manage limited supervision across source domains and improve DG, we introduce a domainagnostic prompt-learning mechanism that integrates adaptable domain-specific cues and visually guided semantic attributes through a novel cross-attention module, besides being supported by learnable domain- and class-generic visual prompts to enhance cross-modal adaptability. Second, to improve outlier rejection during inference, we classify unfamiliar samples as “unknown” and train specialized prompts with systematically synthesized pseudo-open samples that maintain fine-grained relationships to known classes, generated through a targeted query strategy with off-the-shelf foundation models. This strategy enhances feature learning, enabling our model to detect open samples with varied granularity more effectively. Extensive evaluations across five benchmarks demonstrate that OSLO- Prompt establishes a new state-of-the-art in LSOSDG, significantly outperforming existing methods.1

Generalized Category Discovery (GCD) aims to classify test-time samples into either seen categories—available during training—or novel ones, without relying on label supervision. Most existing GCD methods assume simultaneous access to labeled and unlabeled data during training and arising from the same domain, limiting applicability in open-world scenarios involving distribution shifts. Domain Generalization with GCD (DG-GCD) lifts this constraint by requiring models to generalize to unseen domains containing novel categories, without accessing target-domain data during training. The only prior DG-GCD method, DG$^2$CD-Net~\cite{dg2net}, relies on episodic training with multiple synthetic domains and task vector aggregation, incurring high computational cost and error accumulation. We propose \textsc{HiDISC}, a hyperbolic representation learning framework that achieves domain and category-level generalization without episodic simulation. To expose the model to minimal but diverse domain variations, we augment the source domain using GPT-guided diffusion, avoiding overfitting while maintaining efficiency. To structure the representation space, we introduce \emph{Tangent CutMix}, a curvature-aware interpolation that synthesizes pseudo-novel samples in tangent space, preserving manifold consistency. A unified loss—combining penalized Busemann alignment, hybrid hyperbolic contrastive regularization, and adaptive outlier repulsion—facilitates compact, semantically structured embeddings. A learnable curvature parameter further adapts the geometry to dataset complexity. \textsc{HiDISC} achieves state-of-the-art results on PACS~\cite{pacs}, Office-Home~\cite{officehome}, and DomainNet~\cite{domainnet}, consistently outperforming the existing Euclidean and hyperbolic (DG)-GCD baselines.