# Learning Fine-grained Domain Generalization via Hyperbolic State Space Hallucination

arXiv: https://arxiv.org/abs/2504.08020 · HTML: https://mlsanity.com/paper/2504.08020/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 52 references that are in the map.
- First posted on arXiv 10 Apr 2025.

## Builds on (most cited first, 30 of 31)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Arbitrary Style Transfer in Real-time with Adaptive Instance Normalization](https://mlsanity.com/paper/1703.06868/) (2017)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [Remote Sensing Image Scene Classification: Benchmark and State of the Art](https://mlsanity.com/paper/1703.00121/) (2017)
- [Learning to Generalize: Meta-Learning for Domain Generalization](https://mlsanity.com/paper/1710.03463/) (2017)
- [Combining Recurrent, Convolutional, and Continuous-time Models with Linear State-Space Layers](https://mlsanity.com/paper/2110.13985/) (2021)
- [Domain Generalization with MixStyle](https://mlsanity.com/paper/2104.02008/) (2021)
- [HINet: Half Instance Normalization Network for Image Restoration](https://mlsanity.com/paper/2105.06086/) (2021)
- [Improve Unsupervised Domain Adaptation with Mixup Training](https://mlsanity.com/paper/2001.00677/) (2020)
- [Exact Feature Distribution Matching for Arbitrary Style Transfer and Domain Generalization](https://mlsanity.com/paper/2203.07740/) (2022)
- [Structured State Space Models for In-Context Reinforcement Learning](https://mlsanity.com/paper/2303.03982/) (2023)
- [Sharpness-Aware Gradient Matching for Domain Generalization](https://mlsanity.com/paper/2303.10353/) (2023)
- [Style-Hallucinated Dual Consistency Learning for Domain Generalized Semantic Segmentation](https://mlsanity.com/paper/2204.02548/) (2022)
- [Sparse Mixture-of-Experts are Domain Generalizable Learners](https://mlsanity.com/paper/2206.04046/) (2022)
- [WildNet: Learning Domain Generalized Semantic Segmentation from the Wild](https://mlsanity.com/paper/2204.01446/) (2022)
- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
- [Adversarial Style Augmentation for Domain Generalized Urban-Scene Segmentation](https://mlsanity.com/paper/2207.04892/) (2022)
- [Self-Distilled Vision Transformer for Domain Generalization](https://mlsanity.com/paper/2207.12392/) (2022)
- [RAMS-Trans: Recurrent Attention Multi-scale Transformer forFine-grained Image Recognition](https://mlsanity.com/paper/2107.08192/) (2021)
- [Learning Content-enhanced Mask Transformer for Domain Generalized Urban-Scene Segmentation](https://mlsanity.com/paper/2307.00371/) (2023)
- [Fine-Grained Object Classification via Self-Supervised Pose Alignment](https://mlsanity.com/paper/2203.15987/) (2022)
- [Style-Hallucinated Dual Consistency Learning: A Unified Framework for Visual Domain Generalization](https://mlsanity.com/paper/2212.09068/) (2022)
- [Learning Spectral-Decomposed Tokens for Domain Generalized Semantic Segmentation](https://mlsanity.com/paper/2407.18568/) (2024)
- [Robust Large-Margin Learning in Hyperbolic Space](https://mlsanity.com/paper/2004.05465/) (2020)
- [Hyperbolic Representation Learning: Revisiting and Advancing](https://mlsanity.com/paper/2306.09118/) (2023)
- [On the Eigenvalues of Global Covariance Pooling for Fine-grained Visual Recognition](https://mlsanity.com/paper/2205.13282/) (2022)
- [Hyperbolic Space with Hierarchical Margin Boosts Fine-Grained Learning from Coarse Labels](https://mlsanity.com/paper/2311.11019/) (2023)

## Built on by (most cited first, 7 of 7)

- [Fast and Geometrically Grounded Lorentz Neural Networks](https://mlsanity.com/paper/2601.21529/) (2026)
- [Single Domain Generalization for Multimodal Cross-Cancer Prognosis via Dirac Rebalancer and Distribution Entanglement](https://mlsanity.com/paper/2507.08340/) (2025)
- [Fine-Grained Generalization via Structuralizing Concept and Feature Space into Commonality, Specificity and Confounding](https://mlsanity.com/paper/2601.03056/) (2026)
- [HypCBC: Domain-Invariant Hyperbolic Cross-Branch Consistency for Generalizable Medical Image Analysis](https://mlsanity.com/paper/2602.03264/) (2026)
- [The Finer the Better: Towards Granular-aware Open-set Domain Generalization](https://mlsanity.com/paper/2511.16979/) (2025)
- [HyTBE: Hyperbolic Target-Background Expert Model for Cross-Domain Infrared Small Target Detection](https://mlsanity.com/paper/2608.05771/) (2026)
- [A Controlled Evaluation of Curvature Inspired Scalar Feature Scaling for Domain Generalization](https://mlsanity.com/paper/2610.18227/) (2026)

## Abstract (arXiv)

Fine-grained domain generalization (FGDG) aims to learn a fine-grained representation that can be well generalized to unseen target domains when only trained on the source domain data. Compared with generic domain generalization, FGDG is particularly challenging in that the fine-grained category can be only discerned by some subtle and tiny patterns. Such patterns are particularly fragile under the cross-domain style shifts caused by illumination, color and etc. To push this frontier, this paper presents a novel Hyperbolic State Space Hallucination (HSSH) method. It consists of two key components, namely, state space hallucination (SSH) and hyperbolic manifold consistency (HMC). SSH enriches the style diversity for the state embeddings by firstly extrapolating and then hallucinating the source images. Then, the pre- and post- style hallucinate state embeddings are projected into the hyperbolic manifold. The hyperbolic state space models the high-order statistics, and allows a better discernment of the fine-grained patterns. Finally, the hyperbolic distance is minimized, so that the impact of style variation on fine-grained patterns can be eliminated. Experiments on three FGDG benchmarks demonstrate its state-of-the-art performance.