DiRe-RAPIDS: Topology-faithful dimensionality reduction at scale
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909000560279552 |
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| author | Kolpakov, Alexander Rivin, Igor |
| author_facet | Kolpakov, Alexander Rivin, Igor |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25209 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | DiRe-RAPIDS: Topology-faithful dimensionality reduction at scale Kolpakov, Alexander Rivin, Igor Machine Learning Artificial Intelligence Software Engineering Social and Information Networks 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. |
| title | DiRe-RAPIDS: Topology-faithful dimensionality reduction at scale |
| topic | Machine Learning Artificial Intelligence Software Engineering Social and Information Networks |
| url | https://arxiv.org/abs/2604.25209 |