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What are Logits in Machine Learning?

In machine learning, logits refer to the raw, unscaled output values from the final layer of a neural network—before any activation function like softmax or sigmoid is applied. They are not probabilities yet, but they play a critical role in converting model predictions into understandable outputs.
Logits are:

  • Real numbers (positive or negative)
  • Representations of a model’s confidence in its predictions
  • Input for probability-generating functions like softmax (multi-class) or sigmoid (binary)

 Why Use Logits Instead of Probabilities Directly?

While it’s tempting to work directly with probabilities, training neural networks using logits offers numerical stability and avoids problems like:

  • Vanishing gradients from small probability values
  • Rounding errors in floating-point calculations
  • Computational inefficiency when calculating logarithms of probabilities in loss functions

For this reason, popular loss functions like CrossEntropyLoss (for multi-class classification) and BCEWithLogitsLoss (for binary classification) expect logits, not probabilities.

Benefits of Using Logits

  • Training Stability: Loss functions compute gradients more accurately with logits.
  • Efficiency: Avoids redundant calculations—most loss functions include softmax/sigmoid internally.
  • Flexibility: Allows developers to control when and how to convert to probabilities.

Where are Logits Commonly Used?

Use Case Details
Binary Classification Output one logit, then apply sigmoid for probability.
Multi-Class Classification Output multiple logits, then apply softmax to interpret class probs.
Loss Calculation Use logits directly with loss functions for better accuracy and speed.

Binary Classification Example (Logits + Sigmoid)

Let’s say you’re building a spam classifier:

Step 1: Model Outputs a Logit

python

logit = 1.2 # Raw output from final layer

Step 2: Convert Logit to Probability

python

from math import exp

prob = 1 / (1 + exp(-logit)) # ≈ 0.768
print(f"Spam probability: {prob:.2%}")

This output means the model is 76.8% confident the email is spam.

Step 3: Loss Function (In PyTorch)

python

import torch
import torch.nn as nn

loss_fn = nn.BCEWithLogitsLoss()
output = torch.tensor([logit])
target = torch.tensor([1.0]) # True label = spam

loss = loss_fn(output, target)
print(loss.item())

Multi-class Classification Example (Logits + Softmax)

Suppose your model predicts whether an image is a Cat, Dog, or Rabbit:

Step 1: Output Logits

python

import torch

logits = torch.tensor([2.5, 0.3, -1.2]) # Cat, Dog, Rabbit

Step 2: Convert to Probabilities Using Softmax

python

import torch.nn.functional as F

probs = F.softmax(logits, dim=0)
print(probs) # tensor([0.81, 0.13, 0.06])

Step 3: Apply Cross-Entropy Loss

python

loss_fn = torch.nn.CrossEntropyLoss()
labels = torch.tensor([0]) # True class is 'Cat'

loss = loss_fn(logits.unsqueeze(0), labels)
print(loss.item())

Final Tips for Working With Logits

  • Don’t apply softmax or sigmoid manually before passing to loss functions like CrossEntropyLoss or BCEWithLogitsLoss—they already do that internally.
  • Use logits for model evaluation (before applying thresholds or extracting labels).
  • Convert logits to class predictions by using argmax() for multi-class, or thresholding (e.g., > 0.5) for binary.

Boost Your ML Projects with Expert Logits Integration

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Recap: Why Logits are Essential

  • Logits are the bridge between raw model output and interpretable predictions.
  • They offer better training dynamics, especially in deep learning models.
  • Used in loss calculation, gradient flow, and classification decision-making.

Understanding and leveraging logits correctly can make or break your model’s training effectiveness and prediction accuracy.

About Author

Jayanti Katariya is the CEO of Moon Technolabs, a fast-growing IT solutions provider, with 18+ years of experience in the industry. Passionate about developing creative apps from a young age, he pursued an engineering degree to further this interest. Under his leadership, Moon Technolabs has helped numerous brands establish their online presence and he has also launched an invoicing software that assists businesses to streamline their financial operations.

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