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Beam Search: A Detailed Explanation with Logic and Code Example

Beam search is a heuristic search algorithm that explores a graph by expanding the most promising nodes in a limited manner. It's primarily used for sequence prediction tasks like machine translation, speech recognition, and image captioning where the number of possible sequences is enormous. Unlike exhaustive search methods (like breadth-first search) that explore all possibilities, beam search maintains a "beam" of `k` best candidate sequences at each step. This `k` is called the "beam width."

Here's a comprehensive breakdown of beam search:

*1. The Problem: Sequence Prediction and the Exponential Search Space*

Imagine you're building a machine translation system that translates English to French. Given an English sentence, the system needs to generate the most probable French translation. Each word in the French sentence can be chosen from a vocabulary (potentially thousands of words).

The number of possible French sentences grows exponentially with the length of the sentence. For example, if the vocabulary has 10,000 words, and we want to generate a 10-word sentence, there are 10,000sup10/sup (10sup40/sup) possibilities. Exhaustively searching through all of these to find the best translation is computationally infeasible.

*2. The Idea Behind Beam Search*

Beam search provides a more practical approach. Instead of exploring every possible sequence, it keeps track of the `k` most promising partial sequences ("candidates") at each step. It then expands these `k` sequences by considering the next possible words and keeping only the top `k` sequences after this expansion. This process repeats until a stopping criterion (e.g., a maximum sentence length or an end-of-sentence token) is reached.

*3. How Beam Search Works: A Step-by-Step Explanation*

Let's break down the process with a concrete example:

*Task:* Translate "Hello world" from English to French (simplified for ...

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