Why Use Softmax Only in the Output Layer and Not in Hidden Layers?
Introduction
Softmax is a popular activation function used in the output layer of neural networks, particularly for multi-class classification tasks. It’s crucial to understand why softmax is generally reserved for the output layer and not employed in hidden layers.
Softmax and its Function
Softmax is an activation function that converts a vector of real numbers into a probability distribution. This distribution represents the likelihood of each class label. The core function of softmax is:
softmax(z_i) = exp(z_i) / sum(exp(z))
Where:
* `z_i` is the input value for the i-th class
* `exp` is the exponential function
* `sum(exp(z))` is the sum of exponentials for all inputs
Why Softmax is Suitable for the Output Layer
- Probabilistic Outputs: Softmax produces a probability distribution, making it ideal for tasks where the model needs to provide confidence scores for each class.
- Normalization: The output probabilities sum to 1, ensuring that the model assigns a complete distribution of confidence across all classes.
- Multi-Class Classification: Softmax effectively handles multi-class scenarios by providing a mechanism to estimate the likelihood of a data point belonging to each class.
Why Softmax is Generally Not Used in Hidden Layers
- Loss of Information: Applying softmax in hidden layers can result in information loss. Softmax converts values to probabilities, potentially discarding important information about the relative strengths of different features.
- Vanishing Gradients: In deep networks, softmax can lead to vanishing gradients, hindering effective backpropagation and learning.
- Alternative Activation Functions: Other activation functions like ReLU, sigmoid, or tanh are better suited for hidden layers, providing more flexible and informative representations.
Examples:
**Output Layer (Multi-Class Classification):**
“`
# Example with 3 classes
import numpy as np
z = np.array([1.5, 2.3, -0.8])
softmax_output = np.exp(z) / np.sum(np.exp(z))
print(softmax_output)
“`
**Output:**
[0.24472847 0.55846668 0.19680485]
**Hidden Layer (Using ReLU):**
“`
import numpy as np
z = np.array([-1.2, 0.5, 2.1])
relu_output = np.maximum(0, z)
print(relu_output)
“`
**Output:**
[0. 0.5 2.1]
Conclusion
Using softmax exclusively in the output layer allows for accurate probabilistic outputs for multi-class classification tasks. While it’s beneficial for the final prediction, employing softmax in hidden layers can lead to information loss and training difficulties. Other activation functions are more suitable for hidden layers, ensuring efficient learning and preserving valuable information throughout the network.