arXiv:2506.08764v3 Announce Type: replace Abstract: Deep neural networks are known to suffer from exploding or vanishing gradients as depth increases, a phenomenon closely tied to the spectral behavior of the input-output Jacobian. Prior work has identified critical initialization schemes that ensure Jacobian stability, but these analyses are typically restricted to fully connected networks with i.i.d. weights. In this work, we go significantly beyond these limitations: we establish a general stability theorem for deep neural networks that accommodates sparsity (such as that introduced by prun
The continuous push for deeper and more complex neural networks necessitates foundational research into their stability and training dynamics, especially as AI systems are deployed in critical applications.
Improved understanding and control of neural network stability can lead to more robust, efficient, and scalable AI models, reducing training failures and improving performance in real-world scenarios.
The theoretical advancements enable the design of more reliable deep neural networks by offering a general stability theorem that accounts for network sparsity, moving beyond prior limitations.
- · AI researchers
- · Deep learning practitioners
- · Developers of large-scale AI models
- · High-performance computing sector
- · Developers reliant on ad-hoc stability solutions
- · Underperforming AI architectures
- · Those with limited theoretical understanding of neural networks
More stable and predictable training of very deep and sparse neural networks becomes achievable.
This foundational work can accelerate the development of more complex and specialized AI models, particularly in resource-constrained or edge computing environments.
The enhanced reliability of deep learning models could lead to broader AI adoption in sensitive areas where stability is paramount, potentially reducing computational waste.
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Read at arXiv cs.LG