Softmax vs Sigmoid: Which is Better?
The choice between Softmax and Sigmoid depends on the specific problem you’re trying to solve. Both functions are activation functions, but they are used in different contexts, and one is not inherently “better” than the other; they serve different purposes.
Let’s break it down:
1️⃣ Sigmoid (Used in Binary Classification or Multi-label Problems)
- Purpose: Sigmoid is used to map a single input to a probability between 0 and 1, making it suitable for binary classification or multi-label classification.
- Output: Sigmoid outputs a single probability for each input.
- Use Case:
- Binary classification: In binary classification, you output a probability indicating the likelihood of a single class (usually “1” or “positive class”).
- Multi-label classification: In multi-label classification, each class can have its own sigmoid output (independent probabilities for each class).
Formula:
S(x)=11+e−xS(x) = \frac{1}{1 + e^{-x}}S(x)=1+e−x1
Example (Python)
pythonCopy codeimport numpy as np
def sigmoid(x):
return 1 / (1 + np.exp(-x))
logits = np.array([2.0, -1.0, 0.5])
print(sigmoid(logits)) # Output: [0.88, 0.27, 0.62]
Use Case:
- Binary classification (e.g., predicting if an email is spam or not).
- Multi-label classification (e.g., assigning multiple categories to a single image).
2️⃣ Softmax (Used in Multi-class Classification)
- Purpose: Softmax is used to convert raw scores (logits) into a probability distribution over multiple classes, with the sum of the probabilities equaling 1.
- Output: It produces a vector of probabilities for each class in a multi-class classification problem.
- Use Case:
- Multi-class classification: In a multi-class classification problem, you use softmax in the output layer to assign probabilities to each class, ensuring that one class has the highest probability.
Formula:
Si=exi∑jexjS_i = \frac{e^{x_i}}{\sum_{j} e^{x_j}}Si=∑jexjexi
Where:
- xix_ixi is the raw score (logit) for class iii,
- The denominator is the sum of exponentials of all logits, ensuring the output is a valid probability distribution.
Example (Python)
import numpy as np
def softmax(x):
exp_x = np.exp(x - np.max(x)) # To avoid overflow
return exp_x / np.sum(exp_x)
logits = np.array([2.0, 1.0, 0.1])
print(softmax(logits)) # Output: [0.659, 0.242, 0.099]
Use Case:
- Multi-class classification (e.g., classifying an image into one of several categories).
🔑 Key Differences
| Feature | Sigmoid | Softmax |
|---|---|---|
| Purpose | Binary classification or multi-label classification | Multi-class classification |
| Output | Single probability between 0 and 1 | Vector of probabilities that sum to 1 |
| Use Case | Binary classification, multi-label classification | Multi-class classification (exclusive classes) |
| Formula | 11+e−x\frac{1}{1 + e^{-x}}1+e−x1 | exi∑jexj\frac{e^{x_i}}{\sum_{j} e^{x_j}}∑jexjexi |
| Behavior | Produces independent probabilities for each class | Ensures the sum of probabilities is 1, with one class likely having the highest probability |
| Number of Outputs | One probability per class | One probability per class, for all classes |
🛠️ When to Use Each?
- Use Sigmoid:
- For binary classification: When you need to classify into two categories (e.g., yes/no, true/false).
- For multi-label classification: When each class is independent and can be activated separately (e.g., predicting multiple categories like “sports” and “entertainment” for the same image).
- Use Softmax:
- For multi-class classification: When each example belongs to exactly one of several classes (e.g., classifying an image into one of many possible categories).
Which is Better?
- Better for Binary Classification: Sigmoid, because it directly outputs a probability for the “positive” class in binary tasks.
- Better for Multi-class Classification: Softmax, because it outputs probabilities for each class in a way that ensures they sum to 1, making it suitable for selecting the most likely class.
In summary:
- Sigmoid is better for binary or multi-label classification problems.
- Softmax is better for multi-class classification problems.
Let me know if you need further clarification! 😊