Tanh Activation Function: Exploring the Non-linear Activation

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In the world of artificial neural networks, activation functions play a crucial role in introducing non-linearity to the model, enabling it to learn complex patterns and relationships in the data. Among the popular activation functions is the tanh activation function, short for hyperbolic tangent. It is widely used due to its symmetric nature, allowing it to produce both positive and negative outputs, making it ideal for certain applications.


In this article, we will explore the tanh activation function formula in detail, understanding its properties, use cases, and why it is preferred over other activation functions in specific scenarios.


Tanh Activation Function: Understanding the Basics

The tanh activation function, mathematically represented as f(x) = (e^x – e^(-x)) / (e^x + e^(-x)), takes any input value and squashes it between -1 and 1. It is a scaled version of the hyperbolic sine function and is often considered a scaled version of the sigmoid activation function.


Advantages of Tanh Activation Function

The tanh activation function offers several advantages that make it a popular choice for certain tasks:


Zero-Centered Output: Unlike the sigmoid function, which centers around 0.5, the tanh function produces outputs centered around 0, making it more suitable for optimizing models efficiently.

Non-Linearity: The tanh function introduces non-linearity, allowing the neural network to learn complex relationships between features in the data.

Gradient Preservation: The derivative of the tanh function is well-behaved, and it avoids the vanishing gradient problem, enabling the network to propagate gradients effectively during backpropagation.

Symmetry: The tanh function is symmetric around the origin, which can be advantageous in certain applications.

Properties of Tanh Activation Function

The tanh activation function exhibits several essential properties that contribute to its effectiveness:


Range: The output of the tanh function ranges from -1 to 1.

Monotonicity: The function is monotonic, meaning it preserves the order of values, ensuring smooth transitions.

Continuity: The tanh function is continuous and differentiable across its entire domain.

Sigmoid Relation: The tanh function can be expressed in terms of the sigmoid function as tanh(x) = 2 * sigmoid(2x) – 1.

Tanh Activation Function vs. Sigmoid Activation Function

Both the tanh and sigmoid activation functions have their applications, but there are specific scenarios where tanh outperforms sigmoid:

  • Zero-Centered Output: While the sigmoid function produces values between 0 and 1, the tanh function outputs values between -1 and 1, which are beneficial in certain optimization algorithms.
  • Gradient Saturation: The gradients of the sigmoid function are small for extreme values, leading to vanishing gradients during backpropagation. The tanh function mitigates this issue to some extent due to its zero-centered output.
  • Computation: Although the sigmoid function is computationally less expensive, the tanh function’s benefits often outweigh the slightly higher computation cost.

Use Cases of Tanh Activation Function

The tanh activation function finds applications in various domains, including:

  • Hidden Layers: The tanh function is commonly used in hidden layers of neural networks, where non-linearity is crucial for feature learning.
  • Recurrent Neural Networks (RNNs): RNNs benefit from the tanh function as it helps capture long-term dependencies in sequential data.
  • Image Processing: In image processing tasks, tanh activation is employed for enhancing features and reducing noise.
  • Natural Language Processing (NLP): Tanh is used in NLP tasks for sentiment analysis and language generation.

Implementing the Tanh Activation Function

To implement the tanh activation function in a neural network, follow these steps:

  • Normalize Inputs: Ensure your input data is scaled between -1 and 1 for optimal performance.
  • Activation Function: Apply the tanh function element-wise to the hidden layers’ outputs during the forward pass.
  • Backpropagation: During backpropagation, compute the gradients of the tanh function and update the network’s weights accordingly.

Best Practices for Using Tanh Activation Function

When using the tanh activation function, consider the following best practices:

  • Normalization: Normalize your input data to ensure it falls within the range of tanh’s domain.
  • Exploding Gradients: The tanh function can also cause exploding gradients. To counter this, you can implement gradient clipping to limit the gradients during training.
  • Learning Rate: Adjust the learning rate based on your network architecture and problem complexity.
  • Regularization: Implement regularization techniques such as L2 regularization to avoid overfitting.


What are the main advantages of the tanh activation function over the sigmoid? The tanh activation function’s main advantages over the sigmoid include zero-centered output, better gradient preservation, and a wider range of outputs (-1 to 1).

Can I use the tanh activation function in the output layer for regression tasks? Yes, the tanh activation function can be used in the output layer for regression tasks, especially when the target variable has a range from negative to positive values.

Does the tanh activation function prevent the vanishing gradient problem completely? While the tanh activation function mitigates the vanishing gradient problem to some extent, it doesn’t eliminate it entirely. Careful architecture design and hyperparameter tuning are still necessary.

How can I initialize the weights when using the tanh activation function? To initialize the weights of your neural network, it is recommended to use techniques like Xavier (Glorot) initialization or He initialization for better convergence.

Is the tanh activation function suitable for binary classification tasks? Yes, the tanh activation function can be used for binary classification tasks, but it is often replaced with the sigmoid function, which produces outputs between 0 and 1.

Can the tanh activation function lead to the problem of exploding gradients? Yes, the tanh activation function can lead to exploding gradients, especially when dealing with very high or low input values. Gradient clipping can help alleviate this issue.


In conclusion, the tanh activation function is a powerful tool in the arsenal of activation functions used in artificial neural networks. Its zero-centered output, non-linearity, and gradient-preservation properties make it a valuable choice in various applications, including hidden layers, RNNs, image processing, and NLP tasks. However, it is essential to be mindful of potential issues like vanishing or exploding gradients and adopt best practices to ensure smooth training and optimal performance.


By understanding the strengths and weaknesses of the tanh activation function, you can leverage its capabilities to build more robust and accurate neural network models.



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