Geometric Residual Learning for 3D Medical Image Segmentation via DDL-Mamba

Project Abstract & Overview

Dense 3D State Space Models (SSMs) used in volumetric medical imaging suffer from inherent representation drift across deep encoder layers. We are developing a novel Delta-Mamba framework that integrates Deep Delta Learning (DDL) blocks into a 3D U-Mamba backbone to stabilize the geometric manifold. By engineering a DDL block with L_2-normalized, Softplus-constrained weights, our framework enforces strictly non-negative global slot amplitudes, resolving layer-wise representation degradation. The architecture targets complex concentric cardiac structures and organs-at-risk, with validation experiments actively in progress on the ACDC cardiac and Synapse multi-organ benchmarks.

Key Methodologies & Contributions

• Representation Drift Resolution: Formulated a mathematically constrained DDL block that stabilizes the spatial manifolds inherent in deep 3D State Space Models.
• Layer-Wise beta-Gate Explainability: Implemented a visual interpretation mechanism using beta-gate activations, providing geometrically interpretable explainability for complex boundary segmentation choices—a feature structurally impossible in vanilla Transformers or prior Mamba implementations.
• Dual Benchmark Validation: Testing and optimizing the framework across the ACDC and Synapse datasets to evaluate segmentation robustness under highly variable structural constraints.