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**Title: How Language Models Generate Text: A Peek Under the Hood** Have you ever wondered how AI tools like ChatGPT or Gemini craft coherent sentences, answer questions, or even write code? The secret lies in a process called **autoregressive text generation**—a method that powers most modern neural language models (LMs). Let’s break down how it works! --- ### **Step 1: Start with a Prefix** Imagine you type the phrase *“The cat sat on the”* into an AI chatbot. This input is called the **prefix**, and the LM’s job is to predict what comes next. --- ### **Step 2: Predict the Next Token** Using its neural network (often a Transformer-based architecture), the LM analyzes the prefix and generates a **probability distribution** over its fixed vocabulary. For example, it might assign: - 60% probability to *“mat”* - 30% to *“rug”* - 10% to *“floor”* This distribution reflects the model’...