New research explores boundary geometry's impact on shallow ReLU neural network approximation

This paper investigates how the geometric properties of boundaries influence the approximation capabilities of shallow ReLU neural networks. The research establishes upper and lower bounds for approximation on convex bodies within weighted variation spaces, extending classical results to higher dimensions and various norms. It identifies specific geometric exponents that dictate the optimal approximation rates and determines sharp weight thresholds for maintaining classical approximation rates. The findings indicate that boundary geometry can significantly alter optimal approximation exponents even when other factors like dimension and error norm remain constant. AI

IMPACT Provides theoretical insights into the approximation capabilities of ReLU networks, potentially informing future model architectures.

RANK_REASON The cluster contains an academic paper detailing theoretical research on neural network approximation. [lever_c_demoted from research: ic=1 ai=1.0]

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