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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.25228 |
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| _version_ | 1866914169709658112 |
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| author | Amin, Ahmad Ayaz Kazi, Baha Uddin |
| author_facet | Amin, Ahmad Ayaz Kazi, Baha Uddin |
| contents | We introduce Random Projection Flows (RPFs), a principled framework for injective normalizing flows that leverages tools from random matrix theory and the geometry of random projections. RPFs employ random semi-orthogonal matrices, drawn from Haar-distributed orthogonal ensembles via QR decomposition of Gaussian matrices, to project data into lower-dimensional latent spaces for the base distribution. Unlike PCA-based flows or learned injective maps, RPFs are plug-and-play, efficient, and yield closed-form expressions for the Riemannian volume correction term. We demonstrate that RPFs are both theoretically grounded and practically effective, providing a strong baseline for generative modeling and a bridge between random projection theory and normalizing flows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25228 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simple, Fast and Efficient Injective Manifold Density Estimation with Random Projections Amin, Ahmad Ayaz Kazi, Baha Uddin Machine Learning We introduce Random Projection Flows (RPFs), a principled framework for injective normalizing flows that leverages tools from random matrix theory and the geometry of random projections. RPFs employ random semi-orthogonal matrices, drawn from Haar-distributed orthogonal ensembles via QR decomposition of Gaussian matrices, to project data into lower-dimensional latent spaces for the base distribution. Unlike PCA-based flows or learned injective maps, RPFs are plug-and-play, efficient, and yield closed-form expressions for the Riemannian volume correction term. We demonstrate that RPFs are both theoretically grounded and practically effective, providing a strong baseline for generative modeling and a bridge between random projection theory and normalizing flows. |
| title | Simple, Fast and Efficient Injective Manifold Density Estimation with Random Projections |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2509.25228 |