arXiv:2510.02779v4 Announce Type: replace Abstract: Recent advances have significantly improved our understanding of the generalization performance of gradient descent (GD) methods in deep neural networks. A natural and fundamental question is whether GD can achieve generalization rates comparable to the minimax optimal rates established in the kernel setting. Existing results either yield suboptimal rates of $O(1/\sqrt{n})$, or focus on networks with smooth activation functions, incurring exponential dependence on network depth $L$. In this work, we establish optimal generalization rates for
This research addresses a fundamental theoretical question in deep learning at a time of rapid advancements in AI model generalization and deployment.
Improved theoretical understanding of deep neural network generalization can lead to more robust, efficient, and predictable AI systems, impacting their development and deployment.
This work establishes optimal generalization rates for ReLU networks, offering theoretical guarantees comparable to kernel methods, which was previously a gap in understanding for deep learning.
- · AI researchers
- · Deep learning practitioners
- · Companies betting on AI scalability
- · Developers of theoretically suboptimal AI models
It provides a stronger theoretical foundation for the reliability and performance claims of deep learning models.
This could accelerate the development of explainable and auditable AI systems by demystifying aspects of their generalization behavior.
The insights might inform the design of next-generation deep learning architectures that inherently achieve better and more predictable generalization.
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