Short Answer

Deconstructing the Weak-to-Strong Fine-Tuning Objective

A common method for improving a powerful model involves training it on data labeled by a less powerful, 'weak' model. The optimization goal for this process is captured by the following mathematical expression:

θ~=argmaxθxXlogPrθs(y^x)\tilde{\theta} = \arg \max_{\theta} \sum_{\mathbf{x} \in X} \log \Pr_{\theta}^{s}(\hat{\mathbf{y}}|\mathbf{x})

Explain the specific role and significance of the following three components within this objective function:

  1. The term y^\hat{\mathbf{y}}
  2. The expression Prθs(x)\Pr_{\theta}^{s}(\cdot|\mathbf{x})
  3. The operator argmaxθ\arg \max_{\theta}

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Updated 2025-10-08

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