Parametric Rectified Linear Unit, commonly known as PReLU, is an activation function that enhances the traditional rectified unit with a slope for negative values.
What is an Activation Function?
Activation functions play a crucial role in neural networks, as they provide the nonlinearity vital for the networks to solve complex problems. The activation function determines whether the neuron should be activated or not, based on the weighted sum of inputs received by it. This way, the activation function enables the neural network to learn and generalize from input data.
The Traditional ReLU
The traditional rectified linear unit, Â commonly known as ReLU is a commonly used activation function that is defined as:
$$f\left(y\_{i}\right) = y\_{i} \text{ if } y\_{i} \ge 0$$ $$f\left(y\_{i}\right) = 0 \text{ if } y\_{i} \leq 0$$
The ReLU is an activation function that is linear for all values greater than or equal to zero, which enables it to learn faster, thereby leading to time and cost-effective training. Although in practice, the ReLU has limitations. For instance, any input value that is below or equal to zero causes the ReLU to produce an output of zero, leading to zero gradients during backpropagation. This characteristic is commonly referred to as the dying ReLU problem.
The PReLU Activation Function
PReLU improves ReLU by adding a slope for negative values, given as:
$$f\left(y\_{i}\right) = y\_{i} \text{ if } y\_{i} \ge 0$$ $$f\left(y\_{i}\right) = a\_{i}y\_{i} \text{ if } y\_{i} \leq 0$$
The slope, a, is a learnable parametric value that allows the PReLU activation function to explore negative values without suffering from the dying ReLU problem. During the learning process, the algorithm can optimize these negative slope values as per the given training data.
The Benefits of PReLU
PReLU introduces a slope for negative values, which enables it to learn better than ReLU as the function can use information from negative regions. The algorithm can learn the slopes that are well suited to the data to facilitate better accuracy in predictions. It has been found that different layers within neural networks may require varying types of nonlinearities.
The authors of PReLU found, through experiments with convolutional neural networks, that initial layers require larger positive slopes, which allows the network to have better edge detection capabilities. In contrast, the smaller slope in deep layers allows the network to differentiate more between the features, leading to better accuracy.
The Key to Better Accuracy:
For neural networks solid accuracy is fundamental; for PReLUs to be put to good use, focusing on the inter-layers is vital. PReLUs in this aspect stand out as it can adjust various slopes of the activation function based on the input data, resulting in better accuracy.
PReLU is a reliable and powerful activation function that has been appealing to many machine learning and deep learning practitioners. Its ability to have better accuracy owing to the slopes for negative values is a vital feature that is crucial for different layers in deep learning neural networks.
