Biological Spatial Priors Regularize Foundation Model Representations for Cross-Site MSI Generalization in Colorectal Cancer

Whole-slide MIL models are often called context-aware once graphs, Transform ers, or state-space modules are placed above patch embeddings. We show that this label can be deceptive. On pathology tasks where tissue architecture is part of the diagnostic signal, several strong MIL baselines retain nearly unchanged slide level AUC after patch coordinates are permuted. Their predictions are accurate, but largely compositional. We refer to this failure mode as spatial blindness. Our explanation is optimization-based: dense appearance statistics are learned early under slide-level supervision, leaving weak gradients for sparse spatial relations. ResTopoMIL addresses the issue by first fitting a permutation-invariant prototype histogram and then freezing it while a lightweight graph branch learns the residual under a coordinate-shuffling constraint. The architecture is simple by design; the intervention is in how the spatial branch is trained. Across 9 public WSI bench marks, ResTopoMIL improves classification and survival prediction with 1.15M parameters, restores sensitivity to coordinate perturbation, and gives stronger lo calization evidence on CAMELYON-16.

Multiple instance learning (MIL) is the dominant framework for whole-slide image analysis in computational pathology, typically combining a frozen patch encoder, a projection layer, and a slide-level aggregator. While encoders and aggregators have been extensively studied, the projection layer remains a largely morphology-only bottleneck. This limits endpoints such as biomarker status and survival, which are governed by a molecular state that is not fully captured by H&E morphology. We introduce Molecularly Informed Staining Transform (MIST), a plug-in replacement for the MIL projection layer that uses paired spatial transcriptomics only during training to construct virtual molecular stains. MIST clusters gene expression profiles into cross-modal prototypes, anchors them in the frozen foundation model feature space, and uses them to reorganize H&E patch features along molecularly guided axes. It requires no transcriptomics at inference and can be inserted before standard MIL aggregators. We evaluate MIST across 23 downstream tasks and 8 MIL aggregators. MIST improves 240 of 256 configurations over the standard projection layer, with an average gain of +3.5%, observed consistently across endpoint types: +5.2% on survival prediction, +3.3% on tissue subtyping, and +2.6% on biomarker prediction. Ablations confirm that gene-derived prototypes are the primary source of the gains, while spatial, biological, and pathological analyses show that cross-modal prototype affinities capture spatially coherent molecular programs from H&E alone.

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.