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arXiv Machine Learning By Xiao-Song Yang, Xuan Zhou, Qi Zhou

Relocation of compact sets in $\mathbb{R}^n$ by diffeomorphisms and linear separability of datasets in $\mathbb{R}^n$

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The paper develops a theory for relocating a finite number of compact sets in ℝ^n to arbitrary target domains using diffeomorphisms of ℝ^n. It proves that any such collection can be embedded differentiably into ℝ^{n+1} so that the images become linearly separable. The authors apply this result to show that compact datasets in ℝ^n can be made linearly separable by width‑n deep neural networks with Leaky‑ReLU, ELU, or SELU activations, and that mutually disjoint compact datasets can be separated in ℝ^{n+1} by a width‑(n+1) DNN.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

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