Universal Smoothness via Bernstein Polynomials: A Constructive Approximation Approach for Activation Functions
The efficacy of deep neural networks is heavily reliant on the design of non-linear activation functions, yet existing approaches often struggle to balance optimization stability with computational efficiency. While piecewise linear functions offer inference speed, they suffer from optimization instability due to non-differentiability at the origin, whereas smooth counterparts typically incur significant computational overhead through their reliance on transcendental operations. To address these limitations, this paper proposes a general smoothing framework based on constructive approximation theory and introduces the Bernstein Linear Unit (BerLU). This novel activation function utilizes ...
| Authors | Wentao Zhang, Yutong Zhang, Yifan Zhu et al. |
|---|---|
| Primary category | cs.AI |
| Published | 4 May 2026 |
| Last updated at source | 4 May 2026 |
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 17 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.