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Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks
April 30, 2024, 4:43 a.m. | Fanghui Liu, Leello Dadi, Volkan Cevher
cs.LG updates on arXiv.org arxiv.org
Abstract: Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks as the curse of dimensionality (CoD) cannot be evaded when trying to approximate even a single ReLU neuron (Bach, 2017). In this paper, we study a suitable function space for over-parameterized two-layer neural networks with bounded norms (e.g., the path norm, the Barron norm) in the perspective of sample complexity and generalization properties. First, …
abstract arxiv cs.lg dimensionality functions kernel layer networks neural networks neuron norm paper relu show space stat.ml studies study the curse of dimensionality type
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