arXiv:2606.06722v1 Announce Type: new Abstract: The training of neural networks often entails objective functions that are not globally $L$-smooth. For these functions, it is both theoretically and practically difficult to reply to the question: what is the largest possible step size that ensures the convergence of gradient descent (GD)? We address this longstanding open question in deep learning by providing a unifying definition of "large" step sizes that requires only local Lipschitz (or even H\"older) continuity of the gradient. We design first-order adaptive methods that provably yield la
This academic paper, published in 2026, details a theoretical advancement in understanding gradient descent, a fundamental aspect of AI training algorithms.
While a theoretical improvement, better understanding and optimizing training algorithms can contribute to more efficient and reliable AI development in the long run.
It provides a more unified definition of 'large' step sizes for gradient descent convergence, allowing for the design of adaptive methods.
- · AI researchers
- · Deep learning practitioners
Improved theoretical understanding of neural network training dynamics.
Potentially more efficient and stable AI model development over time.
These foundational improvements could enable faster progress in complex AI applications.
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Read at arXiv cs.LG