DiRe-RAPIDS: Topology-faithful dimensionality reduction at scale

About

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.

Alexander Kolpakov, Igor Rivin · 2026

Related benchmarks

Task	Dataset	Result
Dimensionality Reduction	MFeat factors	kNN Accuracy91.5	3
Dimensionality Reduction	Isolet	kNN Accuracy84.2	3
Dimensionality Reduction	HAR	kNN Accuracy93.6	3
Dimensionality Reduction	Letter	kNN Accuracy89.5	3
Dimensionality Reduction	Fashion MNIST	kNN Accuracy79.8	3
Dimensionality Reduction	connect-4	kNN Accuracy66.3	3
Dimensionality Reduction	Covertype	kNN Accuracy72.7	3
Dimensionality Reduction	SATIMAGE	kNN Accuracy87.6	3
Dimensionality Reduction	pendigits	kNN Accuracy98.5	3
Dimensionality Reduction	magic	kNN Accuracy76.2	3