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New simplex-based symmetry measure improves analysis of convex sets

By PulseAugur Editorial · [1 sources] ·

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]

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

New simplex-based symmetry measure improves analysis of convex sets

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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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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Egor Bakaev, Amir Yehudayoff ·

    A simplex-based measure of symmetry

    arXiv:2607.03815v1 Announce Type: cross Abstract: For compact convex sets $L,K \subset \mathbb{R}^n$, denote by $\lambda_K(L)$ the smallest size of a homothet of $K$ that contains $L$. We define a measure of symmetry based on the $n$-simplex $\Delta = \Delta^n \subset \mathbb{R}^…

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