Explain LLM training

Large Language Model Training Modern LLM training follows a systematic approach from data to deployment: Training Pipeline Overview Large Language Model training is a multi-stage process that transforms raw text data into sophisticated AI systems capable of understanding and generating human language. Core Training Stages - **Data Collection & Processing**: Curating massive text corpora from diverse sources - **Tokenization**: Converting text into numerical representations - **Pre-training**: Learning language patterns through next-token prediction - **Post-training**: Alignment with human preferences and safety constraints The Foundation: Pre-training Pre-training is the computationally intensive phase where models learn fundamental language understanding. Mathematical Foundation Next-Token Prediction Objective The core training objective is autoregressive language modeling: $$ \mathcal{L} = -\sum_{t=1}^{T} \log P(x_t | x_{