• March 20, 2025

Log Softmax vs Softmax Pytorch

Both LogSoftmax and Softmax are widely used in PyTorch for classification tasks, but they differ in their outputs and use cases. Let’s compare them in terms of functionality, output, and use cases.


1️⃣ Softmax in PyTorch

  • Purpose: Softmax converts logits (raw scores) into probabilities. It is typically used in the output layer of a classification model for multi-class problems.
  • Output: A probability distribution where each output is between 0 and 1, and the sum of the probabilities equals 1.
  • Use Case: Used when you need probabilities to interpret the model’s predictions or perform tasks like multi-class classification.
  • PyTorch Function: torch.nn.functional.softmax or torch.softmax

Example of Softmax in PyTorch:

import torch
import torch.nn.functional as F

logits = torch.tensor([2.0, 1.0, 0.1])
softmax_output = F.softmax(logits, dim=0)
print(softmax_output) # Output: tensor([0.659, 0.242, 0.099])

Formula:

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

Where:

  • xix_ixi​ is the logit for class iii,
  • The denominator is the sum of all exponentials of logits.

2️⃣ LogSoftmax in PyTorch

  • Purpose: LogSoftmax is a logarithmic version of the Softmax function. Instead of returning probabilities, it returns log-probabilities. It is often used for numerical stability, especially in combination with loss functions like cross-entropy loss, which requires log-probabilities.
  • Output: Logarithmic probabilities (log values), which are more numerically stable than direct softmax outputs, especially when computing cross-entropy loss.
  • Use Case: Used when you need log-probabilities or are calculating cross-entropy loss (since cross-entropy combines log-probabilities and softmax in a numerically stable way).
  • PyTorch Function: torch.nn.functional.log_softmax or torch.log_softmax

Example of LogSoftmax in PyTorch:

import torch
import torch.nn.functional as F

logits = torch.tensor([2.0, 1.0, 0.1])
log_softmax_output = F.log_softmax(logits, dim=0)
print(log_softmax_output) # Output: tensor([-0.417, -1.417, -2.417])

Formula:

LogSoftmax(xi)=xi−log⁡(∑jexj)\text{LogSoftmax}(x_i) = x_i – \log\left(\sum_{j} e^{x_j}\right)LogSoftmax(xi​)=xi​−log(j∑​exj​)

Where:

  • xix_ixi​ is the logit for class iii,
  • The log of the sum is computed for normalization.

🔑 Key Differences

FeatureSoftmaxLogSoftmax
OutputProbabilities (values between 0 and 1)Log-probabilities (logarithmic values)
PurposeConvert logits to probabilitiesConvert logits to log-probabilities
Numerical StabilityLess stable for cross-entropy calculationsMore stable for calculating cross-entropy loss
Use CaseMulti-class classification (when probabilities are needed)When working with cross-entropy loss or when log-probabilities are needed
PyTorch Functiontorch.nn.functional.softmaxtorch.nn.functional.log_softmax
Formulaexi∑jexj\frac{e^{x_i}}{\sum_{j} e^{x_j}}∑j​exj​exi​​xi−log⁡(∑jexj)x_i – \log\left(\sum_{j} e^{x_j}\right)xi​−log(∑j​exj​)

🛠️ When to Use Each?

  • Use Softmax:
    • When you need the model output as probabilities for tasks like multi-class classification or decision-making.
    • Softmax is helpful when you need the interpretation of the output as the likelihood of each class.
  • Use LogSoftmax:
    • When you need log-probabilities, particularly for more stable loss calculations (such as cross-entropy loss). LogSoftmax is often used in conjunction with negative log-likelihood loss (NLLLoss) for classification tasks.
    • It is numerically more stable than Softmax, especially when calculating loss functions with large logits.

Which One to Choose?

  • Softmax is better when you need probabilities or when you’re interpreting model outputs directly.
  • LogSoftmax is preferred when you’re working with log-probabilities, especially for tasks that require cross-entropy loss in PyTorch.

Let me know if you need further clarifications!

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