Symmetric Divergence and Normalized Similarity: A Unified Topological Framework for Representation Analysis
arXiv:2606.06342v1 Announce Type: cross Abstract: Topological Data Analysis (TDA) offers a principled, intrinsic lens for comparing neural representations. However, existing paired topological divergences (e.g., RTD) are limited by heuristic asymmetry and, more critically, unbounded scores that depend on sample size, hindering reliable cross-scenario benchmarking. To address these challenges, we develop a unified topological toolkit serving two complementary needs: fine-grained structural diagnosis and robust, standardized evaluation. First, we complete the RTD framework by introducing Symmetr
The proliferation of complex AI models necessitates more robust and standardized methods for comparing and understanding their internal representations, a gap that Topological Data Analysis is increasingly positioned to fill.
Improved methods for analyzing AI representations will accelerate research, facilitate more reliable model comparison, and potentially unlock new insights into AI safety and explainability, impacting all sectors deploying advanced AI.
The development of a unified topological framework offers a standardized and less heuristic approach to evaluating neural representations, moving beyond current limitations of existing divergence measures.
- · AI researchers
- · Machine learning developers
- · AI safety institutions
- · Developers reliant on heuristic model comparison
- · Organizations with opaque AI evaluation processes
This research provides a more mathematically rigorous foundation for comparing and understanding the internal workings of neural networks.
Standardized representation analysis could lead to more efficient model development pipelines and stronger benchmarks for AI performance and intrinsic safety properties.
A deeper topological understanding of AI could reveal fundamental principles of intelligence or facilitate the development of more intrinsically interpretable and robust AI systems.
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Read at arXiv cs.LG