Search Space in LLM Inference

An LLM is tasked with completing the input sequence x = 'The best way to learn a new skill is'. During the inference process, a search algorithm considers several potential continuations, such as y1 = 'to practice consistently', y2 = 'by reading a book', and y3 = 'through immersive experience'. How are these potential continuations best described within the context of the search problem?

Justification for Hypothesis Simplification

During language model inference, a 'hypothesis' refers exclusively to a potential output sequence, and the input sequence is not considered part of its formal definition.