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.

Domain generalization aims to train models that perform robustly on unseen target domains without access to target data. The realm of vision-language foundation model has opened a new venue owing to its inherent out-of-distribution generalization capability. However, the static alignment to class-level textual anchors remains insufficient to handle the dramatic distribution discrepancy from diverse domain-specific visual features. In this work, we propose a novel cross-domain Schrödinger Bridge (SB) method, namely SBGen, to handle this challenge, which explicitly formulates the stochastic semantic evolution, to gain better generalization to unseen domains. Technically, the proposed SBGen consists of three key components: (1) text-guided domain-aware feature selection to isolate semantically aligned image tokens; (2) stochastic cross-domain evolution to simulate the SB dynamics via a learnable time-conditioned drift; and (3) stochastic domain-agnostic interpolation to construct semantically grounded feature trajectories. Empirically, SBGen achieves state-of-the-art performance on domain generalization in both classification and segmentation. This work highlights the importance of modeling domain shifts as structured stochastic processes grounded in semantic alignment.

We study a fundamental question of domain generalization: given a family of domains (i.e., data distributions), how many randomly sampled domains do we need to collect data from in order to learn a model that performs reasonably well on every seen and unseen domain in the family? We model this problem in the PAC framework and introduce a new combinatorial measure, which we call the domain shattering dimension. We show that this dimension characterizes the domain sample complexity. Furthermore, we establish a tight quantitative relationship between the domain shattering dimension and the classic VC dimension, demonstrating that every hypothesis class that is learnable in the standard PAC setting is also learnable in our setting.

Distribution shifts between training and test data undermine the reliability of deep neural networks, challenging real-world applications across domains and subpopulations. While distributionally robust optimization (DRO) methods like GroupDRO aim to improve robustness by optimizing worst-case performance over predefined groups, their use of a single global classifier can be restrictive when facing substantial inter-environment variability. We propose Multi-Expert Distributionally Robust Optimization (MEDRO), a novel extension of GroupDRO designed to address such complex shifts. MEDRO employs a shared feature extractor with m environment-specific expert classifier heads, and introduces a min-max objective over all m2 expert-environment pairings, explicitly modeling cross-environment risks. This expanded uncertainty set captures fine-grained distributional variations that a single classifier might overlook. Empirical evaluations on a range of standard distribution shift benchmarks demonstrate that MEDRO often achieves robust predictive performance compared to existing methods. Furthermore, MEDRO offers practical inference strategies, such as ensembling or gating mechanisms, for typical scenarios where environment labels are unavailable at test time. Our findings suggest MEDRO as a promising step toward resilient and generalizable machine learning under real-world distribution shifts.

Many confounding-resistant domain generalization methods for image classification have been developed based on causal interventions. However, their reliance on strong assumptions limits their effectiveness in handling unobserved confounders. Although recent work introduces instrumental variables (IVs) to overcome this limitation, the reliance on manually predefined instruments, particularly in the context of visual data, may result in severe bias or invalidity when IV conditions are violated. To address these issues, we propose a novel approach to automatically learning Visual Instrumental Variables for confounding-resistant Domain Generalization (VIV-DG). We observe that certain non-causal visual attributes in image data naturally satisfy the basic conditions required for valid IVs. Motivated by this insight, we propose the visual instrumental variable, a novel concept that extends classical IV theory to the visual domain. Furthermore, we develop an automatic visual instrumental variable learner that enforces IV conditions on learned representations, enabling the automatic learning of valid visual instrumental variables from image data. Ultimately, VIV-DG inherits the strengths of classical IVs to mitigate unobserved confounding and avoids the significant bias caused by violations of IV conditions in predefined IVs. Extensive experiments on multiple benchmarks verify that VIV-DG achieves superior generalization ability.

Real-world data distributions often shift continuously across multiple latent factors such as time, geography, and socioeconomic contexts. However, existing domain generalization approaches typically treat domains as discrete or as evolving along a single axis (e.g., time). This oversimplification fails to capture the complex, multidimensional nature of real-world variation. This paper introduces the task of Continuous Domain Generalization (CDG), which aims to generalize predictive models to unseen domains defined by arbitrary combinations of continuous variations. We present a principled framework grounded in geometric and algebraic theories, showing that optimal model parameters across domains lie on a low-dimensional manifold. To model this structure, we propose a Neural Lie Transport Operator (NeuralLio), which enables structure-preserving parameter transitions by enforcing geometric continuity and algebraic consistency. To handle noisy or incomplete domain variation descriptors, we introduce a gating mechanism to suppress irrelevant dimensions and a local chart-based strategy for robust generalization. Extensive experiments on synthetic and real-world datasets, including remote sensing, scientific documents, and traffic forecasting, demonstrate that our method significantly outperforms existing baselines in both generalization accuracy and robustness.

Domain Generalization (DG) aims to train models that generalize to unseen target domains but often overfit to domain-specific features, known as undesired correlations. Gradient-based DG methods typically guide gradients in a dominant direction but often inadvertently reinforce spurious correlations. Recent work has employed dropout to regularize overconfident parameters, but has not explicitly adjusted gradient alignment or ensured balanced parameter updates. We propose GENIE (Generalization-ENhancing Iterative Equalizer), a novel optimizer that leverages the One-Step Generalization Ratio (OSGR) to quantify each parameter's contribution to loss reduction and assess gradient alignment. By dynamically equalizing OSGR via a preconditioning factor, GENIE prevents a small subset of parameters from dominating optimization, thereby promoting domain-invariant feature learning. Theoretically, GENIE balances convergence contribution and gradient alignment among parameters, achieving higher OSGR while retaining SGD's convergence rate. Empirically, it outperforms existing optimizers and enhances performance when integrated with various DG and single-DG methods.

The generalization ability of deep learning has been extensively studied in supervised settings, yet it remains less explored in unsupervised scenarios. Recently, the Unsupervised Domain Generalization (UDG) task has been proposed to enhance the generalization of models trained with prevalent unsupervised learning techniques, such as Self-Supervised Learning (SSL). UDG confronts the challenge of distinguishing semantics from variations without category labels. Although some recent methods have employed domain labels to tackle this issue, such domain labels are often unavailable in real-world contexts. In this paper, we address these limitations by formalizing UDG as the task of learning a Minimal Sufficient Semantic Representation: a representation that (i) preserves all semantic information shared across augmented views (sufficiency), and (ii) maximally removes information irrelevant to semantics (minimality). We theoretically ground these objectives from the perspective of information theory, demonstrating that optimizing representations to achieve sufficiency and minimality directly reduces out-of-distribution risk. Practically, we implement this optimization through Minimal-Sufficient UDG (MSUDG), a learnable model by integrating (a) an InfoNCE-based objective to achieve sufficiency; (b) two complementary components to promote minimality: a novel semantic-variation disentanglement loss and a reconstruction-based mechanism for capturing adequate variation. Empirically, MS-UDG sets a new state-of-the-art on popular unsupervised domain-generalization benchmarks, consistently outperforming existing SSL and UDG methods, without category or domain labels during representation learning.

Open-Vocabulary semantic segmentation (OVSS) and domain generalization in semantic segmentation (DGSS) highlight a subtle complementarity that motivates Open-Vocabulary Domain-Generalized Semantic Segmentation (OV-DGSS). OV-DGSS aims to generate pixel-level masks for unseen categories while maintaining robustness across unseen domains, a critical capability for real-world scenarios such as autonomous driving in adverse conditions. We introduce Vireo, a novel single-stage framework for OV-DGSS that unifies the strengths of OVSS and DGSS for the first time. Vireo builds upon the frozen Visual Foundation Models (VFMs) and incorporates scene geometry via Depth VFMs to extract domain-invariant structural features. To bridge the gap between visual and textual modalities under domain shift, we propose three key components: (1) GeoText Query, which align geometric features with language cues and progressively refine VFM encoder representations; (2) Coarse Mask Prior Embedding (CMPE) for enhancing gradient flow for faster convergence and stronger textual influence; and (3) the Domain-Open-Vocabulary Vector Embedding Head (DOV-VEH), which fuses refined structural and semantic features for robust prediction. Comprehensive evaluation on these components demonstrates the effectiveness of our designs. Our proposed Vireo achieves the state-of-the-art performance and surpasses existing methods by a large margin in both domain generalization and open-vocabulary recognition, offering a unified and scalable solution for robust visual understanding in diverse and dynamic environments. Code is available at https://github.com/SY-Ch/Vireo.