Multiple Choice

A language model is being trained on a dataset of input-output pairs (x, y). Two different training objectives are proposed:

  • Objective A: Maximize the sum of log Pr(y|x) over all pairs in the dataset.
  • Objective B: Maximize the sum of log Pr(sequence) over all pairs, where sequence is the concatenation of x and y.

Under which of the following conditions will optimizing for Objective B be mathematically equivalent to optimizing for Objective A?

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Updated 2025-09-26

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