Robust generalization beyond training distributions remains a critical challenge for deep neural networks. This is especially pronounced in medical image analysis, where data is often scarce and covariate shifts arise from different hardware devices, imaging protocols, and heterogeneous patient populations. These factors collectively hinder reliable performance and slow down clinical adoption. Despite recent progress, existing learning paradigms primarily rely on the Euclidean manifold, whose flat geometry fails to capture the complex, hierarchical structures present in clinical data. In this work, we exploit the advantages of hyperbolic manifolds to model complex data characteristics. We present the first comprehensive validation of hyperbolic representation learning for medical image analysis and demonstrate statistically significant gains across eleven in-distribution datasets and three ViT models. We further propose an unsupervised, domain-invariant hyperbolic cross-branch consistency constraint. Extensive experiments confirm that our proposed method promotes domain-invariant features and outperforms state-of-the-art Euclidean methods by an average of $+2.1\%$ AUC on three domain generalization benchmarks: Fitzpatrick17k, Camelyon17-WILDS, and a cross-dataset setup for retinal imaging. These datasets span different imaging modalities, data sizes, and label granularities, confirming generalization capabilities across substantially different conditions. The code is available at https://github.com/francescodisalvo05/hyperbolic-cross-branch-consistency .

翻译：深度神经网络在训练分布之外的鲁棒泛化能力仍然是一个关键挑战。这一问题在医学图像分析中尤为突出，因为医学数据通常稀缺，且协变量偏移源于不同的硬件设备、成像协议以及异质性患者群体。这些因素共同阻碍了可靠的性能表现，并延缓了临床应用的进程。尽管近期取得了一些进展，现有的学习范式主要依赖于欧几里得流形，其平坦的几何结构无法捕捉临床数据中存在的复杂层次化结构。在本工作中，我们利用双曲流形的优势来建模复杂的数据特性。我们首次对医学图像分析中的双曲表示学习进行了全面验证，并在十一个域内数据集和三种ViT模型上展示了统计学上显著的性能提升。我们进一步提出了一种无监督的、域不变的双曲交叉分支一致性约束。大量实验证实，我们提出的方法能够促进域不变特征的学习，并在三个域泛化基准测试（Fitzpatrick17k、Camelyon17-WILDS以及一个视网膜成像的跨数据集设置）上，平均AUC优于最先进的欧几里得方法$+2.1\%$。这些数据集涵盖了不同的成像模态、数据规模和标签粒度，证实了该方法在显著不同条件下的泛化能力。代码可在 https://github.com/francescodisalvo05/hyperbolic-cross-branch-consistency 获取。