C$^2$MIL: Synchronizing Semantic and Topological Causalities in Multiple Instance Learning for Robust and Interpretable Survival Analysis

Graph-based Multiple Instance Learning (MIL) is widely used in survival analysis with Hematoxylin and Eosin (H\&E)-stained whole slide images (WSIs) due to its ability to capture topological information. However, variations in staining and scanning can introduce semantic bias, while topological subgraphs that are not relevant to the causal relationships can create noise, resulting in biased slide-level representations. These issues can hinder both the interpretability and generalization of the analysis. To tackle this, we introduce a dual structural causal model as the theoretical foundation and propose a novel and interpretable dual causal graph-based MIL model, C$^2$MIL. C$^2$MIL incorporates a novel cross-scale adaptive feature disentangling module for semantic causal intervention and a new Bernoulli differentiable causal subgraph sampling method for topological causal discovery. A joint optimization strategy combining disentangling supervision and contrastive learning enables simultaneous refinement of both semantic and topological causalities. Experiments demonstrate that C$^2$MIL consistently improves generalization and interpretability over existing methods and can serve as a causal enhancement for diverse MIL baselines. The code is available at https://github.com/mimic0127/C2MIL.