New simplex-based symmetry measure improves analysis of convex sets

Researchers have introduced a novel simplex-based measure of symmetry for compact convex sets, which can be defined as an affine-invariant version of the classical Minkowski measure of symmetry. This new measure improves the stability analysis for the Minkowski measure, showing that sets with high symmetry are close to a simplex. Additionally, the study provides a new characterization of simplices and explores their depth complexity in relation to neural network expressivity, establishing a bound for polytopes of a given depth complexity. AI

IMPACT Provides theoretical underpinnings for understanding the expressivity of ReLU neural networks and the complexity of polytopes.

RANK_REASON The cluster contains an academic paper detailing a new mathematical measure and its theoretical properties. [lever_c_demoted from research: ic=1 ai=0.4]

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• $\\Delta$
• $\\lambda_K(L)$
• Minkowski measure of symmetry
• ReLU neural networks
• $\\rho_\Delta(L)$

• paper
• other

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