IOAI ML Notes Mathematics FundamentalsProbability

Entropy, Cross-Entropy, and KL Divergence

Math fundamentals note for IOAI ML preparation.

16 February 2026

Syllabus Map

Study map: Syllabus Study Map

Core Idea

Entropy measures uncertainty in a distribution.
Cross-entropy evaluates predictive coding loss.
KL divergence measures mismatch between distributions.

Key Formulas

H(P)=-\sum_x P(x)\log P(x)

D_{KL}(P\|Q)=\sum_x P(x)\log\frac{P(x)}{Q(x)}

Why This Matters for ML

Cross-entropy is the default objective for modern classification.
KL divergence measures distribution mismatch in variational, distillation, and representation settings.
Entropy regularization appears in uncertainty-aware and exploration-driven methods.
These information measures connect probabilistic predictions to optimization objectives.

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