parametric activation functions

**Parametric Activation Functions** are **activation functions with learnable parameters that are optimized during training** — allowing the network to discover the optimal nonlinearity for each layer, rather than relying on a fixed, hand-designed function. **Key Parametric Activations** - **PReLU**: Learnable negative slope $a$ in $max(x, ax)$. - **Maxout**: Max of $k$ learnable linear functions. - **PAU** (Padé Activation Unit): Learnable rational function $P(x)/Q(x)$ with polynomial numerator and denominator. - **Adaptive Piecewise Linear**: Learnable breakpoints and slopes for piecewise linear functions. - **ACON**: Learnable smooth approximation that interpolates between linear and ReLU. **Why It Matters** - **Flexibility**: Each layer can learn its own optimal nonlinearity, potentially outperforming any fixed activation. - **Overhead**: Adds few extra parameters but can significantly impact performance. - **Research**: Shows that the choice of activation function matters more than commonly assumed. **Parametric Activations** are **the adaptive nonlinearities** — letting the network evolve its own activation functions during training.