# Entropy, Cross-Entropy, KL Divergence, and Mutual Information: Information Theory's Life in LLMs

> Source: https://sukruyusufkaya.com/en/learn/llm-muhendisligi/entropi-kl-divergence-mutual-information
> Updated: 2026-05-13T13:00:23.193Z
> Category: LLM Mühendisliği
> Module: Module 1: The AI Engineer's Mathematical Arsenal
**TLDR:** Shannon entropy, the true meaning of cross-entropy as LLM loss, KL divergence asymmetry and forward vs reverse KL (mode covering vs mode seeking), the role of KL constraint in RLHF/DPO, JS and Wasserstein, mutual information, knowledge distillation math.