Understanding Differentiable Embeddings Through Differential and Integral Geometry
How can an analyst decide whether a nonlinear dimensionality reduction embedding can be trusted? Existing diagnostics provide only partial answers: projection glyphs characterize local sensitivity, map-continuity scores measure local conditioning, and transport-based analyses reveal path-dependent inconsistencies. However, these methods appear unrelated and provide no common framework for understanding when they agree or not. We show that they are all derived from a single geometric object induced by every differentiable embedding, whether defined implicitly through optimization or explicitly by a learned mapping. This framework provides two complementary geometric views of an embedding. ...
| Authors | Xinyu Zhang, Klaus Mueller |
|---|---|
| Primary category | cs.LG |
| Published | 7 August 2026 |
| Last updated at source | 7 August 2026 |
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