Simplest Codings

When a Large Language Model (LLM) like GPT generates text, it doesn't simply pick the single most probable next word at every step. Doing so — known as greedy decoding — often leads to repetitive, suboptimal, or even incoherent outputs. Instead, most production-grade language models use a smarter strategy called Beam Search . In this post, we'll break down: What Beam Search is and why it exists How it compares to Greedy and Exhaustive search The step-by-step algorithm with a visual walkthrough A full implementation in Java and C++ Its strengths, weaknesses, and modern variants The Problem: Decoding from a Language Model A language model assigns a probability to every possible next token given the preceding context: P(token | previous tokens) Generating a complete sequence means making a chain of these decisions . The goal is to find the sequence with the highest joint probability : P(w1, w2, ..., wN) = P(w1) × P(w2|w1) × P(w3|w1,w2) × ... Sea...