A language model's inference process aims to find an output sequence y that maximizes the conditional probability Pr(y|x) given an input x. Suppose the model has the input 'The sun is shining and the sky is' and calculates the probabilities for the next word as follows:

• Pr('blue' | 'The sun is shining and the sky is') = 0.65
• Pr('clear' | 'The sun is shining and the sky is') = 0.25
• Pr('vast' | 'The sun is shining and the sky is') = 0.09
• Pr('falling' | 'The sun is shining and the sky is') = 0.01

Based only on the objective of maximizing the conditional probability, which of the following statements correctly identifies the best next word and the reason for its selection?

A language model's objective is to find the output sequence with the highest overall conditional probability. Given the input 'The weather is', the model needs to generate a two-word sequence. It has calculated the following probabilities:

Probabilities for the first word:

• Pr('nice' | 'The weather is') = 0.6
• Pr('cold' | 'The weather is') = 0.4

Probabilities for the second word, depending on the first:

• Pr('today' | 'The weather is nice') = 0.5
• Pr('and' | 'The weather is cold') = 0.9

Based on the objective of maximizing the total sequence probability, which of the following sequences is the optimal choice and why?

Comparing Output Sequence Probabilities

Formula for Optimal Output Sequence in LLMs