Reproduce “Representation Topology Divergence: A Method for Comparing Neural Network Representations” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Serguei Barannikov, Ilya Trofimov, Nikita Balabin, Evgeny Burnaev
This paper presents Representation Topology Divergence (RTD), a method for quantitatively comparing neural network representations by analyzing their multi-scale topological structures. RTD accurately identifies changes in data manifold topology, outperforming statistical methods like CKA in capturing structural complexity on synthetic data and demonstrating high correlation with prediction disagreement in various deep learning tasks.
Key insights
- Representation Topology Divergence (RTD) offers a topologically-inspired metric sensitive to multi-scale features like clusters, holes, and connectivity, providing deeper insights than purely statistical measures.
- RTD addresses key limitations of prior methods by accommodating representations in different ambient spaces and effectively utilizing the one-to-one correspondence between data points.
- The strong empirical correlation between RTD scores and prediction disagreement suggests a fundamental connection between the topological structure of internal representations and a model's performance or uncertainty.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.