Geometric Fragility in Alzheimer’s Disease: Probing the Loss of Hippocampal Hierarchical Abstraction via Contrastive Point Cloud Modeling

While human spatial cognition relies on hierarchical abstraction to integrate local features, Alzheimer's disease (AD) pathology is often reduced to local volumetric atrophy. We propose geometric fragility as a distinct failure of global topological integrity within the hippocampus rather than a mere accumulation of local errors. Using a texture-invariant point cloud framework, we contrasted local feature aggregation with global hierarchical attention as computational probes for structural perception. The global paradigm demonstrated enhanced diagnostic sensitivity and exhibited cognitive resilience under simulated neuronal sparsity by maintaining structural recognition where local models suffered pattern collapse. Global modeling effectively unfolded the pathological manifold, revealing a linear trajectory of geometric degradation consistently correlated with clinical cognitive decline. These findings indicate that AD progression may be characterized as a systemic topological dissolution and suggest that effective biomarkers should prioritize hierarchical shape abstraction to accurately map the continuous transition from healthy cognition to dementia.