Notational Simplification in Fine-Tuning Formulas

A language model is being fine-tuned on a dataset of customer support chat logs to improve its ability to generate helpful responses. The training process is guided by the objective function: $\tilde{\theta} = \arg \max_{\hat{\theta}^{+}} \sum_{(\text{query},\text{response})\in\mathcal{D}} \log \mathrm{Pr}_{\hat{\theta}^{+}}(\text{response}|\text{query})$ During one step of this process, the model processes a single (query, response) pair from the dataset. What is the role of the specific component log Pr(response|query) for this single pair?

The following equation represents the primary goal of a common model training process. Match each mathematical symbol from the equation to its correct description.

$\tilde{\theta} = \arg \max_{\hat{\theta}^{+}} \sum_{(\mathbf{x},\mathbf{y})\in\mathcal{D}} \log \mathrm{Pr}_{\hat{\theta}^{+}}(\mathbf{y}|\mathbf{x})$

Evaluating an Alternative Fine-Tuning Objective

Token-Level Conditional Log-Probability in Supervised Fine-Tuning