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Depth Separation in Neural Networks: Depth-3 ReLU Superiority Proven

By PulseAugur Editorial · [1 sources] ·

Researchers have demonstrated that depth-3 ReLU neural networks can approximate certain radial functions with polynomial size in dimensions, while depth-2 networks require exponential size or subexponentially bounded weights. This finding, building on work by Eldan and Shamir, and Daniely, highlights the importance of network depth for efficient approximation under the Gaussian measure. The proofs for these theorems have been formally verified using the Lean 4 Programming Language. AI

IMPACT This research contributes to the theoretical understanding of neural network expressivity and efficiency, potentially guiding future architectural designs.

RANK_REASON Academic paper on neural network theory. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

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

Depth Separation in Neural Networks: Depth-3 ReLU Superiority Proven

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Academic paper on neural network theory. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Cynthia Bortolotto, Francisco Ganacim, Roberto I. Oliveira ·

    Depth Separation for Neural Networks under Gaussian Measure

    arXiv:2610.28800v1 Announce Type: cross Abstract: We revisit the problem of depth separation for neural networks, as studied by Eldan and Shamir, Daniely, and others. Specifically, we consider the natural setting of $L^2$ approximation of radial functions under the standard Gauss…

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