PReLU

Parametric Rectified Linear Unit

a variant of the Rectified Linear Unit (ReLU) activation function used in artificial neural networks, particularly in deep learning models. PReLU was introduced to address the “dead neuron” issue that can occur with the standard ReLU activation function, where some neurons become inactive and do not contribute to learning due to consistently negative input values and zero gradients.

The PReLU function is defined as:

\(f(x) = \begin{cases}x, & \text{if } x > 0 \\alpha x, & \text{if } x \leq 0\end{cases}\)

In this definition, α is a learnable parameter, typically initialized to a small positive value (e.g., 0.01). The parameter α allows the function to have a small, non-zero gradient for negative input values, which can help prevent dead neurons and improve the learning capability of the network. During the training process, α is learned along with the other weights and biases of the network through backpropagation.

The main advantages of using PReLU over the standard ReLU activation function are:

• Reduced dead neuron issue: PReLU mitigates the dead neuron problem by allowing small, non-zero gradients for negative input values, which helps maintain the learning capability of the neurons.
• Adaptability: PReLU is more adaptable than ReLU because it has learnable parameters that can be fine-tuned during training, enabling the network to learn the best activation function for the specific problem at hand.

However, PReLU has some limitations:

• Increased complexity: PReLU introduces additional learnable parameters, which can increase the model’s complexity and the amount of memory required to store the parameters.
• Slower training: The learning of additional parameters can result in slower training times compared to the standard ReLU activation function.

Despite these limitations, PReLU can be a useful activation function in deep learning models, especially when the dead neuron issue is a significant concern or when the adaptability of the activation function is desired.

• Abbreviation: PReLU