A language model is tasked with completing the sentence: 'The old sea captain stared at the stormy sky and said, 'It's going to be a...'' The model's internal scores (logits) for the next token are highest for 'rough', followed by 'long', 'dark', and then 'whale'. The model generates two different completions using different settings:

• Completion A: '...rough night.'
• Completion B: '...whale of a tale.'

Based on the probability formula $Pr(y_i|...) = \frac{\exp(u_{y_i} / \beta)}{\sum_{y_j \in V} \exp(u_{y_j} / \beta)}$, which statement most accurately analyzes the relationship between the temperature parameter ($\beta$) and the generated completions?

Effect of Temperature on Token Generation

Analyzing Temperature's Impact on Token Probabilities