DiRe-RAPIDS: Topology-faithful dimensionality reduction at scale

• URL: http://arxiv.org/abs/2604.25209v2
• Date: Wed, 29 Apr 2026 14:47:00 GMT
• Title: DiRe-RAPIDS: Topology-faithful dimensionality reduction at scale
• Abstract summary: We show that top-performing embeddings invent cycles and disconnected islands absent from the data.<n>On 723K arXiv paper embeddings, DiRe preserves 3-4 times more topological structure than UMAP at comparable wall-clock.
• Score: 47.983130047068165
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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