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Riemannian Geometry is a subfield of Differential Geometry, which specifically studies "Riemannian Manifolds", manifolds with "Riemannian Metrics", which means that they are equipped with continuous inner products.
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Invertibility of neural network as operator on Wasserstein space
Here is a sufficient condition for non-injectivity under the assumption that $w=(\omega,\beta)$ and $\sigma(x;w)=\sigma(\omega\cdot x + \beta)$ i.e. an artificial neuron with activation $\sigma$, weig …
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Can a knotted sphere isometrically embed into $\mathbb R^3$?
All smooth simple closed curves in $\mathbb R^3$ (knotted or not) can be isometrically embedded into $\mathbb R^2$ as a circle of equal arclength.
The situation for knotted spheres seems more complica …