• March 20, 2025

Softmax vs Argmax: What is Difference?

Both Softmax and Argmax are commonly used functions in machine learning, particularly in classification tasks. However, they serve different purposes:


1️⃣ Softmax (Probability Distribution)

  • Purpose: Softmax converts raw scores (logits) into a probability distribution over multiple classes.
  • Output: Produces probabilities for each class, with values between 0 and 1. The sum of all probabilities equals 1.
  • Use Case: Often used in the output layer of multi-class classification models, where you want to interpret the raw logits as probabilities.
  • Behavior: Softmax applies the exponential function to each input to emphasize the largest values and then normalizes them so that they sum to 1.

Formula:

Si=exi∑jexjS_i = \frac{e^{x_i}}{\sum_{j} e^{x_j}}Si​=∑j​exj​exi​​

Where:

  • xix_ixi​ is the raw input (logit) for class iii,
  • The denominator sums the exponentials of all logits to normalize the probabilities.

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).


2️⃣ Argmax (Index of the Maximum Value)

  • Purpose: Argmax identifies the index of the maximum value in a given array or vector.
  • Output: It returns the index of the element with the highest value, not the value itself.
  • Use Case: Often used after Softmax to determine which class has the highest probability, i.e., to pick the predicted class.
  • Behavior: Argmax simply finds the position of the highest value in the input array.

Formula:

argmax(x)=index of the maximum value in x\text{argmax}(x) = \text{index of the maximum value in } xargmax(x)=index of the maximum value in x

Example (Python)

import numpy as np

def argmax(x):
return np.argmax(x)

probabilities = np.array([0.659, 0.242, 0.099])
print(argmax(probabilities)) # Output: 0 (index of the highest probability)

Use Case: After applying Softmax, Argmax is used to pick the class with the highest probability as the model’s final prediction.


🔑 Key Differences

FeatureSoftmaxArgmax
PurposeConverts logits into probability distributionFinds the index of the highest value in an array
OutputA probability distribution (values between 0 and 1)Index of the maximum value
Use CaseMulti-class classification (raw scores to probabilities)Choosing the class with the highest probability (post-Softmax)
Output RangeProbabilities sum to 1Integer index of the max value
ExampleUsed for producing class probabilities in classifiersUsed for selecting the predicted class from the probabilities

🛠️ When to Use?

  • Use Softmax when you need to convert raw logits into probabilities, typically in multi-class classification tasks.
  • Use Argmax after Softmax (or any probability output) to pick the class with the highest probability.

Let me know if you need more examples or explanations! 🚀

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