Key Activation Functions to Know for Deep Learning Systems

Activation functions are crucial in neural networks, determining how inputs are transformed into outputs. They introduce non-linearity, enabling models to learn complex patterns, which is essential in deep learning, machine learning engineering, and fuzzy systems. Understanding these functions enhances model performance.

1. Sigmoid Function

   • Maps input values to a range between 0 and 1, making it useful for binary classification.
   • Has a characteristic S-shaped curve, which can lead to vanishing gradients for extreme input values.
   • Output is not zero-centered, which can slow down convergence during training.

2. Hyperbolic Tangent (tanh) Function

   • Maps input values to a range between -1 and 1, providing a zero-centered output.
   • Generally performs better than the sigmoid function due to its steeper gradient.
   • Still suffers from vanishing gradient issues for large input values.

3. Rectified Linear Unit (ReLU)

   • Outputs the input directly if positive; otherwise, it outputs zero, introducing non-linearity.
   • Computationally efficient and helps mitigate the vanishing gradient problem.
   • Can suffer from "dying ReLU" problem where neurons become inactive and stop learning.

4. Leaky ReLU

   • Similar to ReLU but allows a small, non-zero gradient when the input is negative.
   • Helps prevent the dying ReLU problem by keeping some information flowing through the network.
   • Still retains the computational efficiency of the standard ReLU.

5. Exponential Linear Unit (ELU)

   • Outputs the input directly if positive; otherwise, it outputs an exponential decay, which helps maintain a mean output close to zero.
   • Addresses the dying ReLU problem and provides smoother gradients.
   • Can be computationally more expensive than ReLU due to the exponential calculation.

6. Softmax Function

   • Converts a vector of raw scores (logits) into probabilities that sum to one, making it ideal for multi-class classification.
   • Emphasizes the largest values while suppressing smaller ones, enhancing the model's confidence in its predictions.
   • Sensitive to outliers, which can lead to instability in training.

7. Linear Activation Function

   • Outputs the input directly, maintaining a linear relationship between input and output.
   • Useful in the output layer for regression tasks where the prediction can take any real value.
   • Not suitable for hidden layers as it does not introduce non-linearity.

8. Step Function

   • Outputs a binary value (0 or 1) based on whether the input exceeds a certain threshold.
   • Simple and intuitive, but lacks gradient information, making it unsuitable for gradient-based optimization.
   • Primarily used in binary classification tasks or as a basic activation function in simple models.

9. Parametric ReLU (PReLU)

   • An extension of Leaky ReLU where the slope for negative inputs is learned during training.
   • Provides flexibility and can adapt to the data, potentially improving model performance.
   • Retains the benefits of ReLU while addressing its limitations.

10. Swish Function

    • A smooth, non-monotonic function defined as ( x \cdot \text{sigmoid}(x) ), which can outperform ReLU in some cases.
    • Combines the benefits of both linear and non-linear activations, allowing for better gradient flow.
    • Computationally more intensive than ReLU but can lead to improved model accuracy.