Softmax Function: Turning Scores into Probabilities

Softmax is a function that converts raw scores (logits) into probabilities. It’s mainly used for multi-class classification.

How It Works

• Takes a list of numbers (logits).
• Exponentiates them (makes them positive & larger).
• Divides each by the sum of all exponentiated values.
• The result is a probability distribution (all values sum to 1).

1️⃣ Real-Life Example (Ice Cream Choice)

Imagine you walk into an ice cream shop and see three flavors with "popularity scores":

• 🍦 Vanilla: 8
• 🍫 Chocolate: 5
• 🍓 Strawberry: 2

Softmax converts these scores into probabilities:

• Vanilla: 70% chance you'll pick it
• Chocolate: 25% chance
• Strawberry: 5% chance

🔹 Higher scores get higher probabilities, but everything adds up to 100%.

2️⃣ PyTorch Example

import torch
import torch.nn.functional as F

scores = torch.tensor([8.0, 5.0, 2.0])  # Ice cream popularity
probabilities = F.softmax(scores, dim=0)  # Apply softmax
print(probabilities)

✅ Output:

tensor([0.8438, 0.1142, 0.0420])

👉 Vanilla is most likely (84%), while Strawberry is least likely (4%).

3️⃣ Softmax in a Simple Model

You have a model predicting dog, cat, or rabbit from an image.

logits = torch.tensor([3.0, 1.0, 0.5])  # Model's raw scores
probs = F.softmax(logits, dim=0)  # Convert to probabilities
print(probs)

🔹 The highest value gets the highest probability.
🔹 All values sum to 1 (like percentages).

Why Use Softmax?

• Converts raw scores into probabilities.
• Ensures that predictions sum to 1.
• Helps in training deep learning models by providing a clear probability distribution.

Where is Softmax Used?

• Output layer of classification networks (e.g., image classification, NLP).
• Neural network interpreters for probabilistic decision-making.
• Multi-class classification problems, paired with cross-entropy loss.

TL;DR

• Softmax = Converts scores into probabilities.
• Bigger score → Higher probability.
• Total probability = 1 (like percentages).
• Used in multi-class classification (dog, cat, rabbit, etc.).

Super simple, right? 😃