Summary of Score-based Pullback Riemannian Geometry, by Willem Diepeveen et al.
Score-based pullback Riemannian geometry
by Willem Diepeveen, Georgios Batzolis, Zakhar Shumaylov, Carola-Bibiane Schönlieb
First submitted to arxiv on: 2 Oct 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Differential Geometry (math.DG); Machine Learning (stat.ML)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary Data-driven Riemannian geometry has shown promise for interpretable representation learning, improving efficiency in downstream tasks. This paper proposes a framework for scalable Riemannian geometry called score-based pullback Riemannian geometry, integrating concepts from pullback Riemannian geometry and generative models. The framework focuses on unimodal distributions, using closed-form geodesics to pass through the data probability density. A Riemannian autoencoder (RAE) is constructed with error bounds for discovering the correct data manifold dimension. This framework can be used with anisotropic normalizing flows by adopting isometry regularization during training. Experimental results on various datasets demonstrate that the proposed framework produces high-quality geodesics, estimates intrinsic dimension reliably, and provides a global chart of the manifold even in high-dimensional ambient spaces. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper explores a new way to analyze data called Riemannian geometry. It helps us understand how data is connected and organized. The goal is to make this process faster and more efficient. To achieve this, the paper proposes a new framework that combines two important concepts: generative models and pullback Riemannian geometry. This framework can be used with different types of datasets and has been tested on several examples. The results show that it’s effective in producing accurate maps of data connections and estimating the intrinsic dimension of the data. |
Keywords
» Artificial intelligence » Autoencoder » Probability » Regularization » Representation learning
