# MLE, MAP, Posterior: The Grammar of Modeling — The Mathematical Root of Pretrain Loss

> Source: https://sukruyusufkaya.com/en/learn/llm-muhendisligi/mle-map-posterior-modelleme-grameri
> Updated: 2026-05-13T13:00:23.105Z
> Category: LLM Mühendisliği
> Module: Module 1: The AI Engineer's Mathematical Arsenal
**TLDR:** See that LLM pretrain loss is a Maximum Likelihood Estimation (MLE) objective, that fine-tuning is mathematically Bayesian updating, and that regularization corresponds to MAP. Cross-entropy = NLL relation, prior choice, conjugate priors.