DiRe-RAPIDS: Topology-faithful dimensionality reduction at scale

Alexander Kolpakov; Igor Rivin

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arXiv · 2604.25209

DiRe-RAPIDS: Topology-faithful dimensionality reduction at scale

Alexander Kolpakov·Igor Rivin

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Abstract

Dimensionality reduction methods such as UMAP and t-SNE are central tools for visualising high-dimensional data, but their local-neighborhood objectives can preserve sampling noise while distorting global topology. We show that standard local metrics reward this noise memorisation: top-performing embeddings invent cycles and disconnected islands absent from the data. We introduce a topology-faithfulness benchmark based on noisy manifolds with known homology, tune DiRe against it, and find Pareto-optimal configurations that match or beat GPU-accelerated UMAP on classification while recovering exact first Betti numbers on stress tests. On 723K arXiv paper embeddings, DiRe preserves 3-4 times more topological structure than UMAP at comparable wall-clock.

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BibTeX RIS

Alexander Kolpakov, Igor Rivin. 2026-04-28. DiRe-RAPIDS: Topology-faithful dimensionality reduction at scale. https://arxiv.org/abs/2604.25209

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