Geometric Monomial (GEM): a family of rational 2N-differentiable activation functions
The choice of activation function plays a crucial role in the optimization and performance of deep neural networks. While the Rectified Linear Unit (ReLU) remains the dominant choice due to its simplicity and effectiveness, its lack of smoothness may hinder gradient-based optimization in deep architectures. In this work we propose a family of $C^{2N}$-smooth activation functions whose gate follows a log-logistic CDF, achieving ReLU-like performance with purely rational arithmetic. We introduce three variants: GEM (the base family), E-GEM (an $ε$-parameterized generalization enabling arbitrary $L^p$-approximation of ReLU), and SE-GEM (a piecewise variant eliminating dead neurons with $C^{2...
| Authors | Eylon E. Krause |
|---|---|
| Primary category | cs.LG |
| Published | 23 April 2026 |
| Last updated at source | 23 April 2026 |
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