Edge Flow: A Tractable and Predictive Continuous-Time Model for Gradient Descent at the Edge of Stability
arXiv:2606.18080v1 Announce Type: new Abstract: Gradient descent in deep learning may operate at the edge of stability (EoS), a regime in which the largest eigenvalue of the loss Hessian hovers near the stability threshold $2/\eta$, where $\eta$ is the learning rate. Classical analysis tools such as gradient flow and the descent lemma do not apply here, motivating the search for a continuous-time model valid at EoS. We propose Edge Flow, a system of three coupled ordinary differential equations that provides a tractable, faithful, and predictive model of gradient descent dynamics at EoS. Edge
This research addresses a long-standing challenge in understanding the dynamics of gradient descent in deep learning, particularly at the 'edge of stability' regime.
Improved theoretical understanding of deep learning optimization can lead to more stable, efficient, and performant AI models, impacting the pace of AI development.
The proposed 'Edge Flow' model offers a new analytical tool for predicting and potentially controlling gradient descent behavior, which was previously difficult to model accurately.
- · AI researchers
- · Deep learning practitioners
- · AI model developers
Researchers gain a new theoretical framework for analyzing and optimizing deep neural networks.
More robust and efficient training algorithms could emerge, accelerating the development cycles for complex AI models.
These advancements might contribute to scaling AI capabilities in ways that were previously limited by computational efficiency or training stability.
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Read at arXiv cs.LG