Continuous Domain Generalization

TL;DR

This paper introduces Continuous Domain Generalization (CDG), a new task addressing complex, multidimensional domain shifts, and proposes a geometric-algebraic framework with NeuralLio for robust, structure-preserving model adaptation across continuous variations.

Contribution

It formulates CDG as a low-dimensional manifold problem and develops NeuralLio, a novel operator enforcing geometric and algebraic consistency for continuous domain adaptation.

Findings

Outperforms existing methods in accuracy on synthetic and real datasets.

Demonstrates robustness to noisy and incomplete domain descriptors.

Validates the low-dimensional manifold assumption for domain parameters.

Abstract

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.