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Maximum a Posteriori (MAP) decoding is a search objective in text generation that aims to identify the single output sequence `y` which has the highest conditional probability `Pr(y|x)` given an input `x`. This approach focuses on finding the single most likely hypothesis from the entire space of possible outputs.

Maximum a Posteriori (MAP) Decoding

An AI development team is creating two distinct text generation applications. For which of the two applications described below would the objective of finding the single, most probable output sequence be more suitable? Justify your reasoning by explaining the trade-offs of this objective in the context of both applications.

Selecting a Text Generation Objective

A text generation model builds its output by selecting the single most probable word at each step. Explain why this step-by-step approach is not guaranteed to find the single output sequence with the highest overall probability.

Local vs. Global Optimality in Text Generation

A language model is tasked with generating a 50-word summary. The stated goal is to find the single sequence of 50 words that has the highest overall probability given the input text. Why is it computationally infeasible to guarantee finding this exact sequence in practice?

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