arXiv:2606.30930v1 Announce Type: cross Abstract: Modern deep learning has been shown to operate at the edge of stability, routinely using learning rates far larger than those justified by classical optimization theory. Most prior analyses of the edge of stability phenomenon focus on deterministic gradient descent, leaving the stochastic setting largely unexplored. In this work, we provide sharp convergence guarantees for Stochastic Gradient Descent (SGD) applied to the multiclass cross-entropy loss, for both linear classifiers and two-layer neural networks. We show that the stochasticity of S
The paper provides new theoretical understanding of SGD's behavior, particularly its 'edge of stability' phenomenon, which is critical as AI models become more complex and learning rates increase.
Understanding the theoretical underpinnings of deep learning optimization allows for more efficient model training, potentially leading to faster development cycles and more performant AI systems.
This research provides sharper convergence guarantees for SGD, allowing for more predictable and efficient use of large learning rates in multi-class classification, impacting both linear and two-layer neural networks.
- · AI researchers and developers
- · Deep learning framework providers
- · SaaS companies leveraging deep learning
- · High-performance computing providers
- · AI models that rely on suboptimal optimization
- · Resource-constrained AI development teams
Improved stability and efficiency in training large deep learning models, particularly those using stochastic gradient descent with large learning rates.
Faster iteration cycles for AI model research and development, potentially accelerating breakthroughs across various AI applications.
Enhanced commercial viability of complex AI systems due to more robust and less resource-intensive training, potentially leading to broader AI adoption.
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Read at arXiv cs.LG