Exploding and vanishing gradients in deep neural networks: the effect of residual connections
arXiv:2606.17013v1 Announce Type: cross 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.
The paper contributes to ongoing research in deep learning optimization, specifically addressing a core challenge in training very deep neural networks.
Improving the understanding and mitigation of exploding/vanishing gradients is crucial for developing more stable, efficient, and capable AI models.
A more precise theoretical framework for understanding residual connections could lead to more effective architectural designs and training methodologies for deep learning.
- · AI researchers
- · Deep learning practitioners
- · Companies developing AI models
- · AI compute infrastructure providers
- · Inefficient deep learning architectures
The findings could lead to more robust training algorithms for deep neural networks.
This improved stability could enable the development of deeper and more complex AI models.
More capable AI models could accelerate advancements across various AI applications, potentially impacting broader technological and economic landscapes.
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Read at arXiv cs.LG