Any finite number of compact sets in R^n can be relocated to arbitrary targets by diffeomorphisms of R^n and embedded into R^{n+1} to become linearly separable, allowing width-n DNNs with Leaky-ReLU, ELU or SELU activations to separate them under mild conditions.
D., Sompolinsky, H.: Separability and geometry of object manifolds in deep neural networks
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Relocation of compact sets in $\mathbb{R}^n$ by diffeomorphisms and linear separability of datasets in $\mathbb{R}^n$
Any finite number of compact sets in R^n can be relocated to arbitrary targets by diffeomorphisms of R^n and embedded into R^{n+1} to become linearly separable, allowing width-n DNNs with Leaky-ReLU, ELU or SELU activations to separate them under mild conditions.