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

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.

Optimization and Control (math.OC); Machine Learning (cs.LG)

arXiv:2606.17013 [math.OC]

(or arXiv:2606.17013v1 [math.OC] for this version)

https://doi.org/10.48550/arXiv.2606.17013 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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