Parameterized Exponential Linear Units, also known as PELU, is an activation function that is commonly used in neural networks. It is a modified version of the Exponential Linear Unit (ELU), which aims to improve the accuracy of models by learning the appropriate activation shape at each layer of a Convolutional Neural Network (CNN).
What is PELU?
PELU is a type of activation function, which determines the output of a neuron based on the input it receives. In simple terms, it decides whether the neuron should "fire" or not. PELU has two additional parameters compared to the ELU, which are a, b, and c, where c is greater than zero:
$$ f\left(x\right) = cx \text{ if } x > 0 $$ $$ f\left(x\right) = \alpha\exp^{\frac{x}{b}} - 1 \text{ if } x \leq 0 $$
Here, c is responsible for changing the slope in the positive quadrant, and b controls the scale of the exponential decay. Alpha (α) controls the saturation in the negative quadrant. All these parameters adjust the shape of the activation function, making it more effective for learning complex patterns.
The Advantages of Using PELU
PELU has several advantages over other activation functions, such as:
- It can help improve the accuracy of models, as the learning rate can be adjusted according to the specific properties of each layer.
- It is easier to compute compared to other activation functions, such as ReLU, making it faster to train models.
- It has a smoother gradient, making it more stable for training deep neural networks (DNNs).
Overall, PELU's ability to learn the appropriate activation shape at each layer, combined with its computational simplicity and better stability in DNN training, makes it a popular choice for many researchers and practitioners in the field of deep learning.
How PELU Works
PELU works by allowing the activation function to adapt to the specific properties of each layer. This is accomplished by adjusting the parameters a, b, and c at each layer, making it possible for the function to accurately capture the patterns present in the data.
At each layer of the neural network, the input data is multiplied by a weight matrix and passed through the activation function. The output of this is then fed into the next layer, and the process is repeated until the final layer produces the model's output.
The choice of activation function for each layer can have a significant impact on the performance of the model. Using PELU allows the network to adapt to the particular properties of the data, allowing it to learn more complex patterns.
PELU vs. other Activation Functions
PELU has been shown to outperform other activation functions, such as ReLU and its variants. ReLU (Rectified Linear Units) has been a popular choice for many researchers due to its simplicity and computational efficiency. However, ReLU can result in the "dying ReLU" problem, where some neurons stop firing, leading to dead areas in the network.
PELU overcomes this issue by having a dynamic slope, ensuring that all neurons continue to fire even when the input to the neuron is negative, thereby avoiding the "dying ReLU" problem. This makes PELU a robust activation function for deep neural network architectures, where each layer can have thousands or millions of neurons.
Other activation functions, such as Sigmoid and Tanh, have also been shown to have limitations when used in deep neural network architectures. These functions can result in the "vanishing gradient" and "exploding gradient" problems, affecting the accuracy of the models. PELU overcomes these issues by having a smoother gradient, making it more stable for training deep neural networks.
PELU is a powerful activation function that can help improve the accuracy of deep neural network architectures. It allows the activation function to adapt to the specific properties of each layer, making it more effective at capturing complex patterns in the data. Compared to other activation functions, PELU has several advantages, such as faster training, better accuracy, and greater stability in DNN training. As a result, it has become a popular choice for researchers and practitioners in the field of deep learning.
