Information Sciences

Machine Learning

20th century

Intermediate

Cross-Entropy Loss

L = -\sum_{i} y_i \log(\hat{y}_i)

Measures difference between true labels and predicted probabilities in classification.

By Various

Information Sciences

Cross-Entropy Loss

20th century · Various

Human Reviewed

84%

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Why it matters: Default training objective powering image recognition, NLP, and modern AI.

Discoverers: Various (20th century)

What does it mean?

Measures difference between true labels and predicted probabilities in classification.

Why should I care?

Default training objective powering image recognition, NLP, and modern AI.

Equation Compass

North — Prerequisites

West — History

Various

East — Applications

South — Derivations

Derivation

Variables & Units

Symbol	Name	Unit	Meaning
$L$	Loss	—	Cross-entropy loss
$y_i$	True label	—	One-hot or soft label
$\hat{y}_i$	Prediction	—	Predicted probability

Worked Example

Confident wrong prediction → very high loss.

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Sources & further reading

Search Wikipedia Search Wolfram MathWorld Open in Wolfram|Alpha Watch explainers on YouTube

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