Linear Activation Functions in Neural Networks: Benefits and Applications of Sigmoid and Tanh

Neural networks, as complex computational models, utilize different activation functions in various layers to enhance their performance. While Rectified Linear Units (ReLU) and its variants dominate as the most popular choices for hidden layers, linear activation functions like the sigmoid and hyperbolic tangent (tanh) still hold significant value in specific scenarios. This article explores the benefits and applications of sigmoid and tanh activation functions, providing a comprehensive overview for those who are interested in leveraging these functions effectively.

Output Layer for Binary Classification

The sigmoid activation function is particularly beneficial in the output layer of binary classification models. It maps the network's raw output to a range between 0 and 1, making it suitable for problems where the network needs to make a binary decision, such as determining whether an email is spam or not. This is because the output can be directly interpreted as a probability, indicating the likelihood of the input belonging to a specific class.

Output Layer for Multiclass Classification: Softmax

The softmax activation function, which is closely related to the sigmoid function, is commonly employed in the output layer of multiclass classification models. It assigns probabilities to multiple classes, ensuring the sum of these probabilities across all classes equals 1. This makes the softmax function ideal for tasks where the output needs to indicate the degree of confidence in multiple possible outcomes, such as classifying images into several categories.

Bounded Outputs: Sigmoid and Tanh

Both the sigmoid and tanh functions are designed to squash input values into predefined ranges. Sigmoid maps inputs to the range [0, 1], which is particularly useful when you need to constrain the output of a neural network within a specific range for certain types of regression tasks. On the other hand, tanh maps inputs to the range [-1, 1], providing a centered output that can be advantageous in scenarios where the data has a higher tendency to be symmetrically distributed around zero.

Smoothness and Continuity: Sigmoid and Tanh

One of the key advantages of sigmoid and tanh functions is their smoothness and continuity. These functions have well-defined derivatives throughout their input ranges, which makes them ideal for training neural networks using gradient-based methods like gradient descent. This smoothness ensures that the optimization process is more stable and less likely to encounter issues such as oscillations or divergence, leading to more effective learning and faster convergence.

Historical Usage and Reinforcement

Historically, sigmoid and tanh functions have been extensively used in neural networks and are well-understood. Many older neural network architectures and learning algorithms were designed with these activation functions in mind, providing a solid foundation and familiarity that can facilitate the implementation of these functions in modern neural networks.

While sigmoid and tanh functions offer several benefits, they also have limitations, most notably the vanishing gradient problem. This issue can occur, especially in deep neural networks, where the gradients of these activation functions become very small, slowing down training and limiting the network's ability to capture complex patterns in the data. This is why ReLU and its variants have become more popular in hidden layers, as they mitigate the vanishing gradient problem and often lead to faster convergence and improved performance.

Nonetheless, understanding the benefits and applications of sigmoid and tanh activation functions can provide valuable insights for developers and researchers who need to address specific problems or leverage the strengths of these functions in their neural network models.