arXiv:2606.15551v1 Announce Type: new Abstract: The Edge of Stability (EoS) phenomenon, where gradient descent operates with sharpness exceeding the classical convergence threshold yet the loss decreases over long timescales, is ubiquitous in modern deep learning but remains poorly understood in realistic settings. Prior rigorous analyses have been largely confined to scalar or low-dimensional losses with specific structural forms. In this work, we develop a bifurcation theory framework for gradient descent on the edge of stability that applies directly to overparameterized neural networks. By
The continuous evolution of deep learning models and the increasing complexity of their training dynamics necessitate more robust theoretical frameworks to understand their behavior, particularly at the 'Edge of Stability'.
This research provides a more sophisticated theoretical lens for understanding gradient descent behavior in deep learning, potentially leading to more stable, efficient, and predictable training of large AI models.
The understanding of why deep learning models converge despite operating at the 'Edge of Stability' in realistic, overparameterized settings becomes more rigorous, moving beyond simpler theoretical abstractions.
- · AI researchers
- · Deep learning practitioners
- · Hardware manufacturers optimising for AI workloads
Improved theoretical understanding of deep learning optimization provides new avenues for algorithmic development.
More stable and efficient training processes could accelerate the development and deployment of complex AI systems.
This newfound efficiency could reduce the computational burden, impacting the `compute-supply-chain` and `energy-bottleneck` narratives by allowing more performance from existing resources.
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Read at arXiv cs.LG