arXiv:2606.16975v1 Announce Type: cross Abstract: In this work, we investigate new activation functions for achieving arbitrary-accuracy Sobolev approximation by fixed-size neural networks. We first show that any function in $W^{2,\infty}((a,b)^d)$ can be approximated with arbitrary accuracy, measured in the $W^{1,\infty}$-norm, by a fixed-size neural network using the Elementary Universal Activation Function ($\mathrm{EUAF}$). To extend this result to $W^{s,\infty}((a,b)^d)$ for $s\in\mathbb{N}$, we introduce a smooth activation $\mathrm{DUAF}_{\infty}$ from the family of Differentiable Unive
The paper demonstrates a significant theoretical advancement in neural network architecture for more accurate and efficient approximation, responding to ongoing demands for improved AI model capabilities.
This research provides a foundational step towards building more robust and resource-efficient AI models, enabling new applications and potentially reducing the computational cost of AI development.
Neural networks can now achieve arbitrary accuracy in Sobolev approximation with fixed-size architectures, which could lead to more stable and predictable AI system performance.
- · AI researchers
- · Machine learning developers
- · Hardware manufacturers (indirectly through efficiency demands)
- · Cloud computing providers (through optimization of AI workloads)
- · Developers of less efficient approximation methods
More complex AI models can be deployed with greater reliability and less computational overhead.
The reduced resource demands could accelerate AI innovation and lower the barrier to entry for certain AI development tasks.
This could contribute to the broader availability and integration of sophisticated AI capabilities across various industries, impacting white-collar workflows and specialized applications.
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Read at arXiv cs.LG