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Nonlinear Sciences > Adaptation and Self-Organizing Systems

arXiv:2008.10498 (nlin)
[Submitted on 24 Aug 2020 (v1), last revised 4 Dec 2021 (this version, v5)]

Title:Noise-induced degeneration in online learning

Authors:Yuzuru Sato, Daiji Tsutsui, Akio Fujiwara
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Abstract:In order to elucidate the plateau phenomena caused by vanishing gradient, we herein analyse stability of stochastic gradient descent near degenerated subspaces in a multi-layer perceptron. In stochastic gradient descent for Fukumizu-Amari model, which is the minimal multi-layer perceptron showing non-trivial plateau phenomena, we show that (1) attracting regions exist in multiply degenerated subspaces, (2) a strong plateau phenomenon emerges as a noise-induced synchronisation, which is not observed in deterministic gradient descent, (3) an optimal fluctuation exists to minimise the escape time from the degenerated subspace. The noise-induced degeneration observed herein is expected to be found in a broad class of machine learning via neural networks.
Comments: 16 pages, 5 figures, submitted to Physica D
Subjects: Adaptation and Self-Organizing Systems (nlin.AO); Machine Learning (cs.LG); Dynamical Systems (math.DS); Chaotic Dynamics (nlin.CD); Machine Learning (stat.ML)
Cite as: arXiv:2008.10498 [nlin.AO]
  (or arXiv:2008.10498v5 [nlin.AO] for this version)
  https://doi.org/10.48550/arXiv.2008.10498

Submission history

From: Yuzuru Sato [view email]
[v1] Mon, 24 Aug 2020 15:03:58 UTC (2,243 KB)
[v2] Thu, 27 Aug 2020 16:33:57 UTC (2,258 KB)
[v3] Wed, 18 Nov 2020 04:06:18 UTC (2,400 KB)
[v4] Sat, 21 Nov 2020 03:20:47 UTC (2,400 KB)
[v5] Sat, 4 Dec 2021 23:52:53 UTC (2,404 KB)
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