arXiv:2603.05002v2 Announce Type: replace Abstract: The Edge of Stability (EoS) is a phenomenon where the sharpness (largest eigenvalue) of the Hessian approaches and then hovers near the stability threshold $2/\eta$ during gradient descent (GD) with step size $\eta$. Despite (apparently) violating classical smoothness assumptions, EoS has been widely observed in deep learning, but its theoretical foundations remain incomplete. We provide an interpretation of EoS through the lens of Directional Smoothness [Mishkin et al., 2024]. This interpretation naturally extends to non-Euclidean norms, whi
This paper offers a new theoretical interpretation of a widely observed phenomenon in deep learning, providing a deeper understanding of gradient descent behavior.
Improved theoretical understanding of deep learning optimization can lead to more stable, efficient, and performant AI models, impacting the development velocity and capabilities of AI.
The theoretical framework for optimizing deep learning models is broadened, potentially guiding more effective algorithm design and leading to more robust AI systems.
- · AI researchers
- · Deep learning practitioners
- · Companies developing foundation models
- · Developers relying solely on empirical tuning without theoretical grounding
Refined understanding of machine learning optimization techniques, particularly concerning non-Euclidean geometries.
Development of new optimization algorithms that leverage this understanding, potentially leading to faster and more stable training of complex AI models.
Accelerated progress in AI capabilities across various domains due to more efficient and predictable training processes.
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