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Large Language Models (LLMs) Explained: From Math Intuition to Python (Hugging Face Transformers)

This article helps you move beyond the vague idea that “AI is a black box” by breaking down how a Large Language Model (LLM) actually generates an answer—in a way you can verify and reproduce. We’ll walk through the core inference pipeline step by step: Tokenizer → model outputs (logits) → softmax probabilities → sampling/decoding strategies → multi-turn context formatting → a simplified end-to-end Pipeline API. Along the way, we’ll translate abstract ideas like matrix operations and probability distributions into concrete, runnable examples using Hugging Face Transformers, so you can see exactly how “intelligence-like” behavior emerges from computation.