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Computer Science > Machine Learning

arXiv:2205.11786 (cs)
[Submitted on 24 May 2022 (v1), last revised 7 Jun 2023 (this version, v2)]

Title:Transition to Linearity of General Neural Networks with Directed Acyclic Graph Architecture

Authors:Libin Zhu, Chaoyue Liu, Mikhail Belkin
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Abstract:In this paper we show that feedforward neural networks corresponding to arbitrary directed acyclic graphs undergo transition to linearity as their "width" approaches infinity. The width of these general networks is characterized by the minimum in-degree of their neurons, except for the input and first layers. Our results identify the mathematical structure underlying transition to linearity and generalize a number of recent works aimed at characterizing transition to linearity or constancy of the Neural Tangent Kernel for standard architectures.
Comments: NeurIPS 2022
Subjects: Machine Learning (cs.LG); Optimization and Control (math.OC); Machine Learning (stat.ML)
Cite as: arXiv:2205.11786 [cs.LG]
  (or arXiv:2205.11786v2 [cs.LG] for this version)
  https://doi.org/10.48550/arXiv.2205.11786

Submission history

From: Libin Zhu [view email]
[v1] Tue, 24 May 2022 04:57:35 UTC (136 KB)
[v2] Wed, 7 Jun 2023 22:20:05 UTC (316 KB)
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