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

Vivek S Borkar

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arXiv · 2606.17013

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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Vivek S Borkar. 2026-06-15. Exploding and vanishing gradients in deep neural networks: the effect of residual connections. https://arxiv.org/abs/2606.17013

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