Intuition behind cross entropy loss in Machine Learning

Have you heard of cross-entropy loss, but are not sure exactly and intuitively what it is?



Say you have an ML model for a classification task. How can you measure its performance?



Cross Entropy Loss is the go-to metric for this.



Imagine you are showing a stick figure to 3 individuals, asking them to classify it as a dog, cat, tiger, or lion. Each person provides probabilities for their guesses:



Person 1: 20% dog, 29% cat, 31% tiger, 20% lion (uncertain and wrong).

Person 2: 97% dog, very low for others (confident and wrong).

Person 3: 97% cat, very low for others (confident and correct).



If the stick figure is actually a cat, how do we penalize their mistakes?



Cross Entropy Loss provides a logical way to penalize errors, rewarding confidence when correct and imposing heavy penalties when confidently wrong.



Here is the basic idea behind cross-entropy loss:



It focuses only on the true class, amplifying confidently wrong predictions using logarithmic scaling.

It ensures underconfident yet correct guesses are penalized less than confident but wrong ones.

It helps measure model performance—low loss means better predictions



Consider these 3 cases:



1) Model "A" is performing a 4-class classification task, and the loss is 1.38. How good is the model?



2) Model "B" performing a 1000-class classification and has a loss of 1.38 (same as Model "A"). How good is model "B"?



3) Model "C": An MNIST classifier (10-class problem) has a classification accuracy of 0.1. What might be the loss of this model?



*****



Model "A": If the loss is 1.38 in a 4-class classification task, the model is as poor as random guessing. Each class is equally likely (with a probability of 0.25), and the cross-entropy loss is: −ln⁡(0.25)=1.386. A loss of 1.38 indicates that model "A" has learned nothing meaningful.



Model "B": For a 1000-class classification task, random guessing would have a loss of: −ln⁡(0.001)=6.907. If the loss is 1.38, which is significantly lower than 6.907, the model is performing much better than random guessing. This means it is making predictions closer to the true labels and has learned meaningful patterns in the data.



Model "C": A classification accuracy of 0.1 indicates the model is doing random guessing. For random predictions in a 10-class problem, the cross-entropy loss would be: −ln⁡(0.1)=2.30. Therefore, the loss is likely to be around 2.30. If the model is slightly more confident when making correct predictions, the loss could be lower than 2.30. Conversely, if the model is more confident when making incorrect predictions, the loss could exceed 2.30.



This is the intuition behind cross-entropy.



Cross Entropy Loss is not just a formula; it encapsulates how well a model aligns its predictions with reality. This nuanced understanding helps build robust AI systems that can make impactful decisions.



Here is a lecture I published on Vizuara's YouTube channel on cross-entropy. You will definitely enjoy this: