Noise-induced degeneration in online learning

Yuzuru Sato; Daiji Tsutsui; Akio Fujiwara

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arXiv · 2008.10498

Noise-induced degeneration in online learning

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.

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Yuzuru Sato, Daiji Tsutsui, Akio Fujiwara. 2020-08-24. Noise-induced degeneration in online learning. https://arxiv.org/abs/2008.10498

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