X-VMamba: Explainable Vision Mamba

State Space Models (SSMs), particularly the Mamba architecture, have recently emerged as powerful alternatives to Transformers for sequence modeling, offering linear computational complexity while achieving competitive performance. Yet, despite their effectiveness, understanding how these Vision SSMs process spatial information remains challenging due to the lack of transparent, attention-like mechanisms. To address this gap, we introduce a controllability-based interpretability framework that quantifies how different parts of the input sequence (tokens or patches) influence the internal state dynamics of SSMs. We propose two complementary formulations: a Jacobian-based method applicable to any SSM architecture that measures influence through the full chain of state propagation, and a Gramian-based approach for diagonal SSMs that achieves superior speed through closed-form analytical solutions. Both methods operate in a single forward pass with linear complexity, requiring no architectural modifications or hyperparameter tuning. We validate our framework through experiments on three diverse medical imaging modalities, demonstrating that SSMs naturally implement hierarchical feature refinement from diffuse low-level textures in early layers to focused, clinically meaningful patterns in deeper layers. Our analysis reveals domain-specific controllability signatures aligned with diagnostic criteria, progressive spatial selectivity across the network hierarchy, and the substantial influence of scanning strategies on attention patterns. Beyond medical imaging, we articulate applications spanning computer vision, natural language processing, and cross-domain tasks. Our framework establishes controllability analysis as a unified, foundational interpretability paradigm for SSMs across all domains. Code and analysis tools will be made available upon publication

A Hybrid CNN-VSSM model for Multi-View, Multi-Task Mammography Analysis: Robust Diagnosis with Attention-Based Fusion

Early and accurate interpretation of screening mammograms is essential for effective breast cancer detection, yet it remains a complex challenge due to subtle imaging findings and diagnostic ambiguity. Many existing AI approaches fall short by focusing on single view inputs or single-task outputs, limiting their clinical utility. To address these limitations, we propose a novel multi-view, multitask hybrid deep learning framework that processes all four standard mammography views and jointly predicts diagnostic labels and BI-RADS scores for each breast. Our architecture integrates a hybrid CNN VSSM backbone, combining convolutional encoders for rich local feature extraction with Visual State Space Models (VSSMs) to capture global contextual dependencies. To improve robustness and interpretability, we incorporate a gated attention-based fusion module that dynamically weights information across views, effectively handling cases with missing data. We conduct extensive experiments across diagnostic tasks of varying complexity, benchmarking our proposed hybrid models against baseline CNN architectures and VSSM models in both single task and multi task learning settings. Across all tasks, the hybrid models consistently outperform the baselines. In the binary BI-RADS 1 vs. 5 classification task, the shared hybrid model achieves an AUC of 0.9967 and an F1 score of 0.9830. For the more challenging ternary classification, it attains an F1 score of 0.7790, while in the five-class BI-RADS task, the best F1 score reaches 0.4904. These results highlight the effectiveness of the proposed hybrid framework and underscore both the potential and limitations of multitask learning for improving diagnostic performance and enabling clinically meaningful mammography analysis.