This research introduces a unified topological toolkit (SRTD and NTS) to address the limitations of existing divergence metrics in comparing neural network representations. The framework provides scale-invariant, asymmetry-resolved metrics essential for robust cross-scenario benchmarks
Topological Data Analysis (TDA) is leveraged to offer a principled way to compare neural representations. The authors propose a unified framework consisting of Symmetric Representation Topology Divergence (SRTD) and Normalized Topological Similarity (NTS). SRTD resolves the theoretical asymmetry found in prior divergence metrics by consolidating diagnostic information into a single cross-barcode signature. Furthermore, NTS measures the rank correlation of hierarchical merge orders, providing a scale-invariant metric bounded between -1 and 1. Experiments demonstrate that this topological toolkit robustly maps LLM genealogy and captures functional shifts in CNNs that traditional geometric measures miss, offering a rigorous, topology-aware perspective on model comparison.