💤Quietscore 54.0Jun 15, 2026·2606.17013math.OCcs.LG

Exploding and vanishing gradients in deep neural networks: the effect of residual connections

Vivek S Borkar

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Abstract

The well known phenomenon of exploding and vanishing gradients in deep neural networks is analyzed using multiplicative ergodic theory. The effect of adding a residual connection is explained in this context. Specifically, a characterization of Liapunov exponents due to Furstenberg and Kifer is exploited in order to make a precise statement about the Liapunov spectrum and the effect of residual connections on it.

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GitHub repos (5)

ehijano/rss_fetch⭐ 11
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sairaman436/vybe-intelligence-vault⭐ 5
“source_name: arXiv Machine Learning source_url: https://arxiv.org/abs/2606.17013 authors: []”
Miruuuu-sue/ijas-readability⭐ 0
“2606.17022v1,Learning the Geometry of Data: A Mathematical Review of Shape Space Analysis,Gary P. T. Choi; Khanh Dao Duc; Shira Faigenbaum-Golovin; Karen Habermann; Emmanuel Hartman; Christoph von Tycowicz; Chi Zhang; Wenjun Zhao; Felix Zhou,math.ST; cs.LG; stat.ML,2026-06-15T17:”
sirichen2/sirichen2.github.io⭐ 0
“ "authors": [ "Vivek S Borkar" ], "abs_url": "https://arxiv.org/abs/2606.17013v1", "pdf_url": "https://arxiv.org/pdf/2606.17013v1", "published": "2026-06-15T17:46:16+00:00", "updated": "2026-06-15T17:46:16+00:00",”
yizhenliu99/coding-blog⭐ 0
“ "published": "2026-06-15", "summary": "The well known phenomenon of exploding and vanishing gradients in deep neural networks is analyzed using multiplicative ergodic theory. The effect of adding a residual connection is explained in this context. Specifically, a char”