Mitigating the Curse of Dimensionality in Uniform Convergence of Deep Neural Networks via Smooth Activations
arXiv:2606.05599v1 Announce Type: new Abstract: This paper establishes a theoretical framework for the uniform convergence of smoothly activated deep neural network (DNN) estimators. While standard ReLU networks achieve minimax-optimal rates in the $L^2(P)$ norm for various nonparametric regression tasks, we establish a theoretical lower bound demonstrating that least-squares ReLU estimators can suffer from the curse of dimensionality in their uniform convergence behavior. Motivated by the need for reliable uniform guarantees in downstream tasks requiring worst-case reliability, we address thi
The continuous drive for more performant and reliable AI systems fuels research into fundamental limitations like the curse of dimensionality, especially as deep learning methods mature.
This research provides a theoretical framework to overcome a significant hurdle in AI, enhancing the reliability and applicability of deep neural networks in real-world scenarios requiring worst-case guarantees.
The understanding of deep neural network uniform convergence is advanced, potentially leading to more robust and deployable AI models by mitigating a known deep learning limitation.
- · AI researchers and developers
- · Industries relying on critical AI applications
- · Providers of smooth activation functions
- · Academic institutions
- · Deep learning models with unmitigated curse of dimensionality issues
- · Developers neglecting theoretical guarantees
Improved theoretical understanding of DNN performance leads to more reliable model development practices.
This enhanced reliability could accelerate AI adoption in high-stakes fields like autonomous systems or medical diagnostics.
Increased trust in AI's worst-case performance properties could unlock new applications and regulatory frameworks.
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