A VAE decoder's pullback metric, measured by the numerical rank of its Jacobian, estimates dataset intrinsic dimension and guides mixture-VAE atlas construction and pruning monitoring on a CT dataset.
Manifold learning: What, how, and why
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Estimating Dataset Dimension via Singular Metrics under the Manifold Hypothesis: Application to Inverse Problems
A VAE decoder's pullback metric, measured by the numerical rank of its Jacobian, estimates dataset intrinsic dimension and guides mixture-VAE atlas construction and pruning monitoring on a CT dataset.