Diagnosing Neural Convergence with Topological Alignment Spectra

ArXi:2411.08687v2 Announce Type: replace Representational similarity in neural networks is inherently scale-dependent, yet widely used metrics such as Centered Kernel Alignment (CKA) and Procrustes analysis provide only global scalar estimates. These scalars often fail to distinguish micro-scale geometric jitter (local noise) from macro-scale semantic reorganization, compressing multi-scale structural relationships into a single uninformative value. We