Researchers have developed a theory for relocating compact sets in $\mathbb{R}^n$ to arbitrary target domains using diffeomorphisms. This work demonstrates that such collections can be embedded into $\mathbb{R}^{n+1}$ to achieve linear separability. The findings are applied to show that finite datasets in $\mathbb{R}^n$ can be made linearly separable by deep neural networks with specific activation functions, under certain conditions. AI
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IMPACT Provides theoretical underpinnings for making datasets linearly separable using deep neural networks, potentially improving classification accuracy.
RANK_REASON This is a research paper published on arXiv detailing theoretical advancements in data classification and deep neural networks.
