Mathematical Formulation of the Supervised Fine-Tuning Objective

A machine learning engineer is performing supervised fine-tuning on a pre-trained language model. The process involves three distinct states for the model's parameters:

1. The initial parameters loaded from the pre-trained model before any new training begins.
2. The parameters as they are being iteratively updated by the optimization algorithm on the new dataset.
3. The final, converged parameters after the fine-tuning process is complete.

Which option correctly maps the standard notation to these three states?

Notation for Predicted Output During Fine-Tuning

In the mathematical description of a model fine-tuning process, different symbols are used to represent the model's parameters at various stages. Match each symbol with its correct description.

Correcting Fine-Tuning Parameter Notation

Optimal Parameters Formula in Fine-Tuning