# Continuous Domain Generalization

arXiv: https://arxiv.org/abs/2505.13519 · HTML: https://mlsanity.com/paper/2505.13519/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 61 references that are in the map.
- First posted on arXiv 17 May 2025.

## Builds on (most cited first, 30 of 47)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Domain Randomization for Transferring Deep Neural Networks from Simulation to the Real World](https://mlsanity.com/paper/1703.06907/) (2017)
- [Adversarial Discriminative Domain Adaptation](https://mlsanity.com/paper/1702.05464/) (2017)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [Generalizing to Unseen Domains: A Survey on Domain Generalization](https://mlsanity.com/paper/2103.03097/) (2021)
- [Learning to Generalize: Meta-Learning for Domain Generalization](https://mlsanity.com/paper/1710.03463/) (2017)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [Self-Challenging Improves Cross-Domain Generalization](https://mlsanity.com/paper/2007.02454/) (2020)
- [Domain Generalization via Model-Agnostic Learning of Semantic Features](https://mlsanity.com/paper/1910.13580/) (2019)
- [Functional Map of the World](https://mlsanity.com/paper/1711.07846/) (2017)
- [Unified Deep Supervised Domain Adaptation and Generalization](https://mlsanity.com/paper/1709.10190/) (2017)
- [Unsupervised Pixel-Level Domain Adaptation with Generative Adversarial Networks](https://mlsanity.com/paper/1612.05424/) (2016)
- [Learning to Learn Single Domain Generalization](https://mlsanity.com/paper/2003.13216/) (2020)
- [Training Deep Networks with Synthetic Data: Bridging the Reality Gap by Domain Randomization](https://mlsanity.com/paper/1804.06516/) (2018)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [Improve Unsupervised Domain Adaptation with Mixup Training](https://mlsanity.com/paper/2001.00677/) (2020)
- [DLOW: Domain Flow for Adaptation and Generalization](https://mlsanity.com/paper/1812.05418/) (2018)
- [OpenAlex: A fully-open index of scholarly works, authors, venues, institutions, and concepts](https://mlsanity.com/paper/2205.01833/) (2022)
- [Asymmetric Tri-training for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1702.08400/) (2017)
- [AdaRNN: Adaptive Learning and Forecasting of Time Series](https://mlsanity.com/paper/2108.04443/) (2021)
- [On the Use of ArXiv as a Dataset](https://mlsanity.com/paper/1905.00075/) (2019)
- [Learning to Learn with Variational Information Bottleneck for Domain Generalization](https://mlsanity.com/paper/2007.07645/) (2020)
- [Wild-Time: A Benchmark of in-the-Wild Distribution Shift over Time](https://mlsanity.com/paper/2211.14238/) (2022)

## Built on by (most cited first, 2 of 2)

- [Parameter-Efficient Temporal Domain Generalization](https://mlsanity.com/paper/2602.11965/) (2026)
- [FreKoo++: Learning Continuous Spectral Dynamics for Temporal Domain Generalization](https://mlsanity.com/paper/2608.22224/) (2026)

## Abstract (arXiv)

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.