arXiv:2607.04993v1 Announce Type: cross Abstract: Many phenomena of deep learning are dynamical: they concern not only which minima exist, but how gradient descent reaches, avoids, or selects among them. Edge-of-stability behavior, sharpness oscillations, catapult phases, balancing, and movement toward flatter representations are effects of the training map itself, and are poorly captured by the small-step gradient-flow limit. This paper studies fixed-step gradient descent as a discrete dynamical system in a hierarchy of exactly solvable models retaining basic structures of deep learning: dept
This paper offers a novel analytical framework for understanding the internal dynamics of gradient descent, a fundamental process in AI training, moving beyond simplified models.
Improved theoretical understanding of AI training dynamics can lead to more efficient, stable, and predictable deep learning models, impacting research and deployment.
The focus shifts from viewing gradient descent as a simple optimization to recognizing its complex dynamical system properties, offering new avenues for algorithmic design.
- · AI researchers
- · Deep learning practitioners
- · Makers of AI development platforms
- · AI models with unstable training characteristics
- · Trial-and-error optimization methods
Refined understanding of deep learning training leads to more robust and performant AI models.
New AI architectures and optimization techniques emerge that explicitly leverage these dynamical insights, reducing training instability and costs.
More predictable and efficient AI development pipelines accelerate the deployment of complex AI systems across various industries.
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Read at arXiv cs.AI