Continuous Domain Generalization

2025-05-17

AI Summary

Real-world data distributions dynamically drift under multidimensional continuous factors—e.g., time, geography, and socioeconomic indicators—yet existing domain generalization (DG) methods typically assume discrete or unidimensional domain shifts, failing to capture their intrinsic continuity. This work formally introduces *Continuous Domain Generalization (CDG)*: the task of generalizing to unseen domains defined by arbitrary combinations of continuous domain descriptors. We theoretically show that optimal model parameters lie on a low-dimensional manifold in parameter space. Leveraging this insight, we propose the *Neural Lie Transport Operator (NeuralLTO)*, which integrates differential geometry and Lie algebra to enable geometrically continuous and algebraically consistent parameter transport across domains. We further design a domain-descriptor gating mechanism and a local coordinate chart strategy for robust generalization. Extensive experiments on remote sensing, scientific literature analysis, and traffic forecasting demonstrate significant improvements over SOTA methods, with strong robustness to descriptor noise and missing descriptors.

Technology Category

• Machine Learning: Transfer, Domain Adaptation, Multi-Task Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Real-world data distributions often shift continuously across multiple latent factors such as time, geography, and socioeconomic context. However, existing domain generalization approaches typically treat domains as discrete or evolving along a single axis (e.g., time), which fails to capture the complex, multi-dimensional 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 variation descriptors. We present a principled framework grounded in geometric and algebraic theory, showing that optimal model parameters across domains lie on a low-dimensional manifold. To model this structure, we propose a Neural Lie Transport Operator (NeuralLTO), which enables structured parameter transitions by enforcing geometric continuity and algebraic consistency. To handle noisy or incomplete domain 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 generalization accuracy and robustness under descriptor imperfections.

Problem

• Generalizing models to unseen domains with continuous multi-dimensional shifts
• Addressing limitations of discrete or single-axis domain generalization approaches
• Handling noisy or incomplete domain descriptors for robust generalization

Innovation

• Neural Lie Transport Operator enables structured parameter transitions
• Gating mechanism suppresses irrelevant domain descriptor dimensions
• Local chart-based strategy ensures robust generalization