Accurate analysis of histopathological images is critical for disease diagnosis and treatment planning. Whole-slide images (WSIs), which digitize tissue specimens at gigapixel resolution, are fundamental to this process but require aggregating thousands of patches for slide-level predictions. Multiple Instance Learning (MIL) tackles this challenge with a two-stage paradigm, decoupling tile-level embedding and slide-level prediction. However, most existing methods implicitly embed patch representations in homogeneous Euclidean spaces, overlooking the hierarchical organization and regional heterogeneity of pathological tissues. This limits current models' ability to capture global tissue architecture and fine-grained cellular morphology. To address this limitation, we introduce a hybrid hyperbolic-Euclidean representation that embeds WSI features in dual geometric spaces, enabling complementary modeling of hierarchical tissue structures and local morphological details. Building on this formulation, we develop BatMIL, a WSI classification framework that leverages both geometric spaces. To model long-range dependencies among thousands of patches, we employ a structured state space sequence model (S4) backbone that encodes patch sequences with linear computational complexity. Furthermore, to account for regional heterogeneity, we introduce a chunk-level mixture-of-experts (MoE) module that groups patches into regions and dynamically routes them to specialized subnetworks, improving representational capacity while reducing redundant computation. Extensive experiments on seven WSI datasets spanning six cancer types demonstrate that BatMIL consistently outperforms state-of-the-art MIL approaches in slide-level classification tasks. These results indicate that geometry-aware representation learning offers a promising direction for next-generation computational pathology.

翻译：组织病理图像的精确分析对于疾病诊断和治疗规划至关重要。全切片图像（WSI）以千兆像素分辨率数字化组织标本，是该过程的基础，但需要聚合数千个图像块以进行切片级预测。多实例学习（MIL）通过两阶段范式应对这一挑战，解耦了图块级嵌入和切片级预测。然而，现有方法大多在均匀欧几里得空间中隐式嵌入图像块表示，忽视了病理组织的层级组织和区域异质性，限制了当前模型捕捉全局组织结构与精细细胞形态的能力。为解决这一局限，我们引入一种混合双曲-欧几里得表示，将WSI特征嵌入双几何空间，实现对层级组织结构和局部形态细节的互补建模。基于此公式，我们开发了BatMIL——一个利用双几何空间的WSI分类框架。为建模数千图像块间的长程依赖关系，我们采用结构状态空间序列模型（S4）作为主干，以线性计算复杂度编码图像块序列。此外，为应对区域异质性，我们引入分块级混合专家（MoE）模块，将图像块分组为区域并动态路由至专门子网络，在提升表示能力的同时降低冗余计算。在涵盖六种癌症类型的七个WSI数据集上进行的大量实验表明，BatMIL在切片级分类任务中始终优于最先进的MIL方法。这些结果表明，几何感知表示学习为下一代计算病理学提供了有前景的方向。