New theory shows compact datasets can be made linearly separable by DNNs

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

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.

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• arXiv
• DNN
• ELU
• Leaky-ReLU
• $\\mathbb{R}^n$

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